Quantitative Aptitude – Modern Maths – Progressions – If a1 = 1/(2*5), a2 = 1/(5*8)

Quantitative Aptitude – Modern Maths – Progressions

Question

CAT 2017 - Afternoon slot - Quantitative Aptitude - Modern Maths - Progressions - If a1 = 1(25), a2 = 1(58)
If a1 = 1/(2*5), a2 = 1/(5*8), a3 = 1/(8*11),……, then a1 + a2 +……..+ a100 is

A) 25/151
B) 1/2
C) 1/4
D) 111/55

Answer

Option (A)

Solution

From CAT 2017 – Quantitative Aptitude – Modern Maths – Progressions, we can see that,
The 100th term will be 1/299*302
The series is:
1/(2*5) + 1/(5*8) + 1/(8*11) + ……………+ 1/(299*302)
It can also be written as
3[1/2 – 1/5 + 1/5 – 1/8 + ………………………+ 1/299 – 1/302]
3(1/2 – 1/302) = 300/(3*2*302)
25/151
Option (A)

Download CAT 2017 Question Paper with answers and detailed solutions in PDF

CAT 2017 Questions from Quantitative Aptitude – Modern Maths

Quantitative Aptitude – Modern Maths – Progressions – Q1: An infinite geometric progression a1, a2, a3,… has the property that an = 3(a(n+ l) + a(n+2) +….) for every n ≥ 1. If the sum a1 + a2 + a3 +……. = 32, then a5 is
Quantitative Aptitude – Modern Maths – Progressions – Q2: Let a1, a2, a3, a4, a5 be a sequence of five consecutive odd numbers. Consider a new sequence of five consecutive even numbers ending with 2a3.
Quantitative Aptitude – Modern Maths – Progressions – Q3: Let a1, a2,……..a3n be an arithmetic progression with a1 = 3 and a2 = 7. If a1 + a2 + ….+a3n = 1830, then what is the smallest positive integer m such that m (a1 + a2 + …. + an ) > 1830?
Quantitative Aptitude – Modern Maths – Progressions – Q4: If the square of the 7th term of an arithmetic progression with positive common difference equals the product of the 3rd and 17th terms, then the ratio of the first term to the common difference is
Quantitative Aptitude – Modern Maths – P&C – Q1: How many four digit numbers, which are divisible by 6, can be formed using the digits 0, 2, 3, 4, 6, such that no digit is used more than once and 0 does not occur in the left-most position?
Quantitative Aptitude – Modern Maths – P&C – Q2: In how many ways can 8 identical pens be distributed among Amal, Bimal, and Kamal so that Amal gets at least 1 pen, Bimal gets at least 2 pens, and Kamal gets at least 3 pens?
Quantitative Aptitude – Modern Maths – P&C – Q3: In how many ways can 7 identical erasers be distributed among 4 kids in such a way that each kid gets at least one eraser but nobody gets more than 3 erasers?
Quantitative Aptitude – Modern Maths – P&C – Q4: Let AB, CD, EF, GH, and JK be five diameters of a circle with center at O. In how many ways can three points be chosen out of A, B, C, D, E, F, G, H, J, K, and O so as to form a triangle?

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Quantitative Aptitude – Modern Maths – Progressions – If a1 = 1/(2*5), a2 = 1/(5*8)
5 (100%) 51 votes

Quantitative Aptitude – Modern Maths – Progressions – An infinite GP a1, a2, a3,….

Quantitative Aptitude – Modern Maths – Progressions

Question

CAT 2017 - Afternoon slot - Quantitative Aptitude - Modern Maths - Progressions - An infinite GP a1, a2, a3,....
An infinite geometric progression a1, a2, a3,… has the property that an = 3(a(n+ l) + a(n+2) +….) for every n ≥ 1. If the sum a1 + a2 + a3 +……. = 32, then a5 is

A) 1/32
B) 2/32
C) 3/32
D) 4/32

Answer

Option (C)

Solution

From CAT 2017 – Quantitative Aptitude – Modern Maths – Progressions, we can see that,
For any n ≥ 1, an = 3 (a(n+1) + a(n+2) + ……..)
So, a1 = 3 (a2 + a3 + ……) or r = 1/4 and
a1 + a2 + a3 +………… = 4a1/3 = 32
So, a1 = 24
GP = 24, 6, 1.5,…….
a5 = 1.5/16 = 3/32
Option (C)

Download CAT 2017 Question Paper with answers and detailed solutions in PDF

CAT 2017 Questions from Quantitative Aptitude – Modern Maths

Quantitative Aptitude – Modern Maths – Progressions – Q1: If a1 = 1/(2*5), a2 = 1/(5*8), a3 = 1/(8*11),……, then a1 + a2 +……..+ a100 is
Quantitative Aptitude – Modern Maths – Progressions – Q2: Let a1, a2, a3, a4, a5 be a sequence of five consecutive odd numbers. Consider a new sequence of five consecutive even numbers ending with 2a3.
Quantitative Aptitude – Modern Maths – Progressions – Q3: Let a1, a2,……..a3n be an arithmetic progression with a1 = 3 and a2 = 7. If a1 + a2 + ….+a3n = 1830, then what is the smallest positive integer m such that m (a1 + a2 + …. + an ) > 1830?
Quantitative Aptitude – Modern Maths – Progressions – Q4: If the square of the 7th term of an arithmetic progression with positive common difference equals the product of the 3rd and 17th terms, then the ratio of the first term to the common difference is
Quantitative Aptitude – Modern Maths – P&C – Q1: How many four digit numbers, which are divisible by 6, can be formed using the digits 0, 2, 3, 4, 6, such that no digit is used more than once and 0 does not occur in the left-most position?
Quantitative Aptitude – Modern Maths – P&C – Q2: In how many ways can 8 identical pens be distributed among Amal, Bimal, and Kamal so that Amal gets at least 1 pen, Bimal gets at least 2 pens, and Kamal gets at least 3 pens?
Quantitative Aptitude – Modern Maths – P&C – Q3: In how many ways can 7 identical erasers be distributed among 4 kids in such a way that each kid gets at least one eraser but nobody gets more than 3 erasers?
Quantitative Aptitude – Modern Maths – P&C – Q4: Let AB, CD, EF, GH, and JK be five diameters of a circle with center at O. In how many ways can three points be chosen out of A, B, C, D, E, F, G, H, J, K, and O so as to form a triangle?

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Quantitative Aptitude – Modern Maths – Progressions – An infinite GP a1, a2, a3,….
5 (100%) 52 votes

Quantitative Aptitude – Modern Maths – P&C – How many four digit numbers

Quantitative Aptitude – Modern Maths – Permutation and Combination

Question

CAT 2017 - Afternoon slot - Quantitative Aptitude - Modern Maths - P&C - How many four digit numbers
How many four digit numbers, which are divisible by 6, can be formed using the digits 0, 2, 3, 4, 6, such that no digit is used more than once and 0 does not occur in the left-most position?

Answer

50

Solution

From CAT 2017 – Quantitative Aptitude – Modern Maths – Permutation and Combination, we can see that,
For a number to be divisible by 6, it should have both 2 and 3 as factors.
For 3: The sum of digits should be divisible by 3
For 2: The last digit of the number should be even
There can be three such cases, (0,2,3,4), (0,2,4,6) and (2,3,4,6)

1st case: (0,2,3,4)
When the last digit is ‘0’
The number of combinations can be 3! = 6
When the last digit is 2/4
The number of combinations will be 2*2*1*2 = 8
Total = 14

2nd case: (0,2,4,6)
When the last digit is ‘0’
The number of combinations = 3! = 6
When the last digit is 2/4/6
The number of combinations = 2*2*1*3 = 12
Total = 18

3rd case: (2,3,4,6)
Last digit has to be 2/4/6
So, the number of combinations = 3*2*1*3 = 18
Total number of combinations = 14+18+18 = 50
Answer: 50

Download CAT 2017 Question Paper with answers and detailed solutions in PDF

CAT 2017 Questions from Quantitative Aptitude – Modern Maths

Quantitative Aptitude – Modern Maths – P&C – Q1: In how many ways can 8 identical pens be distributed among Amal, Bimal, and Kamal so that Amal gets at least 1 pen, Bimal gets at least 2 pens, and Kamal gets at least 3 pens?
Quantitative Aptitude – Modern Maths – P&C – Q2: In how many ways can 7 identical erasers be distributed among 4 kids in such a way that each kid gets at least one eraser but nobody gets more than 3 erasers?
Quantitative Aptitude – Modern Maths – P&C – Q3: Let AB, CD, EF, GH, and JK be five diameters of a circle with center at O. In how many ways can three points be chosen out of A, B, C, D, E, F, G, H, J, K, and O so as to form a triangle?
Quantitative Aptitude – Modern Maths – Progressions – Q1: If a1 = 1/(2*5), a2 = 1/(5*8), a3 = 1/(8*11),……, then a1 + a2 +……..+ a100 is
Quantitative Aptitude – Modern Maths – Progressions – Q2: Let a1, a2, a3, a4, a5 be a sequence of five consecutive odd numbers. Consider a new sequence of five consecutive even numbers ending with 2a3.
Quantitative Aptitude – Modern Maths – Progressions – Q3: Let a1, a2,……..a3n be an arithmetic progression with a1 = 3 and a2 = 7. If a1 + a2 + ….+a3n = 1830, then what is the smallest positive integer m such that m (a1 + a2 + …. + an ) > 1830?
Quantitative Aptitude – Modern Maths – Progressions – Q4: If the square of the 7th term of an arithmetic progression with positive common difference equals the product of the 3rd and 17th terms, then the ratio of the first term to the common difference is
Quantitative Aptitude – Modern Maths – Progressions – Q5: An infinite geometric progression a1, a2, a3,… has the property that an = 3(a(n+ l) + a(n+2) +….) for every n ≥ 1. If the sum a1 + a2 + a3 +……. = 32, then a5 is

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Quantitative Aptitude – Modern Maths – P&C – How many four digit numbers
5 (100%) 51 votes

Quantitative Aptitude – Modern Maths – P&C – In how many ways can 8 identical

Quantitative Aptitude – Modern Maths – Permutation and Combination

Question

CAT 2017 - Afternoon slot - Quantitative Aptitude - Modern Maths - P&C - In how many ways can 8 identical
In how many ways can 8 identical pens be distributed among Amal, Bimal, and Kamal so that Amal gets at least 1 pen, Bimal gets at least 2 pens, and Kamal gets at least 3 pens?

Answer

6

Solution

From CAT 2017 – Quantitative Aptitude – Modern Maths – Permutation and Combination, we can see that,
Number of pens that Amal gets = a+1
Number of pens that Bimal gets = b+2
Number of pens that Kamal gets = k+3
So, (a+1) + (b+2) + (k+3) = 8
a + b + k = 2
So, we get (2 + 3 – 1)C(3-1) = 6 [Based on the formula, (n+r-1)C(r-1)]
Answer: 6

Download CAT 2017 Question Paper with answers and detailed solutions in PDF

CAT 2017 Questions from Quantitative Aptitude – Modern Maths

Quantitative Aptitude – Modern Maths – P&C – Q1: How many four digit numbers, which are divisible by 6, can be formed using the digits 0, 2, 3, 4, 6, such that no digit is used more than once and 0 does not occur in the left-most position?
Quantitative Aptitude – Modern Maths – P&C – Q2: In how many ways can 7 identical erasers be distributed among 4 kids in such a way that each kid gets at least one eraser but nobody gets more than 3 erasers?
Quantitative Aptitude – Modern Maths – P&C – Q3: Let AB, CD, EF, GH, and JK be five diameters of a circle with center at O. In how many ways can three points be chosen out of A, B, C, D, E, F, G, H, J, K, and O so as to form a triangle?
Quantitative Aptitude – Modern Maths – Progressions – Q1: If a1 = 1/(2*5), a2 = 1/(5*8), a3 = 1/(8*11),……, then a1 + a2 +……..+ a100 is
Quantitative Aptitude – Modern Maths – Progressions – Q2: Let a1, a2, a3, a4, a5 be a sequence of five consecutive odd numbers. Consider a new sequence of five consecutive even numbers ending with 2a3.
Quantitative Aptitude – Modern Maths – Progressions – Q3: Let a1, a2,……..a3n be an arithmetic progression with a1 = 3 and a2 = 7. If a1 + a2 + ….+a3n = 1830, then what is the smallest positive integer m such that m (a1 + a2 + …. + an ) > 1830?
Quantitative Aptitude – Modern Maths – Progressions – Q4: If the square of the 7th term of an arithmetic progression with positive common difference equals the product of the 3rd and 17th terms, then the ratio of the first term to the common difference is
Quantitative Aptitude – Modern Maths – Progressions – Q5: An infinite geometric progression a1, a2, a3,… has the property that an = 3(a(n+ l) + a(n+2) +….) for every n ≥ 1. If the sum a1 + a2 + a3 +……. = 32, then a5 is

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Quantitative Aptitude – Modern Maths – P&C – In how many ways can 8 identical
5 (100%) 53 votes

Quantitative Aptitude – Modern Maths – Progressions – Let a1, a2, a3, a4, a5

Quantitative Aptitude – Modern Maths – Progressions

Question

CAT 2017 - Afternoon slot - Quantitative Aptitude - Modern Maths - Progressions - Let a1, a2, a3, a4, a5
Let a1, a2, a3, a4, a5 be a sequence of five consecutive odd numbers. Consider a new sequence of five consecutive even numbers ending with 2a3.

If the sum of the numbers in the new sequence is 450, then a5 is

Answer

51

Solution

From CAT 2017 – Quantitative Aptitude – Modern Maths – Progressions, we can see that,
5 consecutive odd numbers are a1 , a2 , a3 , a4 , a5.
5 consecutive even numbers are 2a3 – 8, 2a3 – 6, 2a3 – 4, 2a3 – 2, 2a3
Sum of these 5 numbers = 10a3 – 20 = 450
a3 = 47 and a5 = 51.

Download CAT 2017 Question Paper with answers and detailed solutions in PDF

CAT 2017 Questions from Quantitative Aptitude – Modern Maths

Quantitative Aptitude – Modern Maths – Progressions – Q1: If a1 = 1/(2*5), a2 = 1/(5*8), a3 = 1/(8*11),……, then a1 + a2 +……..+ a100 is
Quantitative Aptitude – Modern Maths – Progressions – Q2: An infinite geometric progression a1, a2, a3,… has the property that an = 3(a(n+ l) + a(n+2) +….) for every n ≥ 1. If the sum a1 + a2 + a3 +……. = 32, then a5 is
Quantitative Aptitude – Modern Maths – Progressions – Q3: Let a1, a2,……..a3n be an arithmetic progression with a1 = 3 and a2 = 7. If a1 + a2 + ….+a3n = 1830, then what is the smallest positive integer m such that m (a1 + a2 + …. + an ) > 1830?
Quantitative Aptitude – Modern Maths – Progressions – Q4: If the square of the 7th term of an arithmetic progression with positive common difference equals the product of the 3rd and 17th terms, then the ratio of the first term to the common difference is
Quantitative Aptitude – Modern Maths – P&C – Q1: How many four digit numbers, which are divisible by 6, can be formed using the digits 0, 2, 3, 4, 6, such that no digit is used more than once and 0 does not occur in the left-most position?
Quantitative Aptitude – Modern Maths – P&C – Q2: In how many ways can 8 identical pens be distributed among Amal, Bimal, and Kamal so that Amal gets at least 1 pen, Bimal gets at least 2 pens, and Kamal gets at least 3 pens?
Quantitative Aptitude – Modern Maths – P&C – Q3: In how many ways can 7 identical erasers be distributed among 4 kids in such a way that each kid gets at least one eraser but nobody gets more than 3 erasers?
Quantitative Aptitude – Modern Maths – P&C – Q4: Let AB, CD, EF, GH, and JK be five diameters of a circle with center at O. In how many ways can three points be chosen out of A, B, C, D, E, F, G, H, J, K, and O so as to form a triangle?

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b) 2 Live Classes (online) every week for doubt clarification
c) Study Material & PDFs for practice and understanding
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Quantitative Aptitude – Modern Maths – Progressions – Let a1, a2, a3, a4, a5
4.9 (98.71%) 62 votes

Quantitative Aptitude – Modern Maths – Progressions – Let a1, a2,……..a3n be an arithmetic progression

Quantitative Aptitude – Modern Maths – Progressions

Question

CAT 2017 - Forenoon slot - Quantitative Aptitude - Modern Maths - Progressions - Let a1, a2,……..a3n be an arithmetic progression
Let a1, a2,……..a3n be an arithmetic progression with a1 = 3 and a2 = 7. If a1 + a2 + ….+a3n = 1830, then what is the smallest positive integer m such that m (a1 + a2 + …. + an ) > 1830?

A) 8
B) 9
C) 10
D) 11

Answer

Option (B)

Solution

From CAT 2017 – Quantitative Aptitude – Modern Maths – Progressions, we can see that,
a = 3
a + d = 7 => d=4
Applying formula of sum for AP
(3n/2) [6 + (3n-1)4] = 1830
On solving, we get n = 10
m>61/7
Max positive integer value of m = 9
Option (B)

Download CAT 2017 Question Paper with answers and detailed solutions in PDF

CAT 2017 Questions from Quantitative Aptitude – Modern Maths

Quantitative Aptitude – Modern Maths – Progressions – Q1: If a1 = 1/(2*5), a2 = 1/(5*8), a3 = 1/(8*11),……, then a1 + a2 +……..+ a100 is
Quantitative Aptitude – Modern Maths – Progressions – Q2: An infinite geometric progression a1, a2, a3,… has the property that an = 3(a(n+ l) + a(n+2) +….) for every n ≥ 1. If the sum a1 + a2 + a3 +……. = 32, then a5 is
Quantitative Aptitude – Modern Maths – Progressions – Q3: Let a1, a2, a3, a4, a5 be a sequence of five consecutive odd numbers. Consider a new sequence of five consecutive even numbers ending with 2a3. If the sum of the numbers in the new sequence is 450, then a5 is
Quantitative Aptitude – Modern Maths – Progressions – Q4: If the square of the 7th term of an arithmetic progression with positive common difference equals the product of the 3rd and 17th terms, then the ratio of the first term to the common difference is
Quantitative Aptitude – Modern Maths – P&C – Q1: How many four digit numbers, which are divisible by 6, can be formed using the digits 0, 2, 3, 4, 6, such that no digit is used more than once and 0 does not occur in the left-most position?
Quantitative Aptitude – Modern Maths – P&C – Q2: In how many ways can 8 identical pens be distributed among Amal, Bimal, and Kamal so that Amal gets at least 1 pen, Bimal gets at least 2 pens, and Kamal gets at least 3 pens?
Quantitative Aptitude – Modern Maths – P&C – Q3: In how many ways can 7 identical erasers be distributed among 4 kids in such a way that each kid gets at least one eraser but nobody gets more than 3 erasers?
Quantitative Aptitude – Modern Maths – P&C – Q4: Let AB, CD, EF, GH, and JK be five diameters of a circle with center at O. In how many ways can three points be chosen out of A, B, C, D, E, F, G, H, J, K, and O so as to form a triangle?

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Quantitative Aptitude – Modern Maths – Progressions – Let a1, a2,……..a3n be an arithmetic progression
5 (100%) 53 votes

Quantitative Aptitude – Modern Maths – Permutation and Combination – In how many ways can 7 identical erasers

Quantitative Aptitude – Modern Maths – Permutation and Combination

Question

In how many ways can 7 identical erasers be distributed among 4 kids in such a way that each kid gets at least one eraser but nobody gets more than 3 erasers?

A) 16
B) 20
C) 14
D) 15

Answer

Option (A)

Solution

From CAT 2017 – Quantitative Aptitude – Modern Maths – Permutation and Combination, we can see that,
a + b + c + d = 7
Since, each kid gets 1 eraser, so a + b + c + d = 3
Now, no child can get more than 3 erasers.
There can be two cases. 2, 1, 0, 0 which can be represented in 4!/2! Ways = 12 ways
And 1,1,1,0 which can be represented in 4!/3! Ways = 4 ways
Answer: 16
Option (A)

Download CAT 2017 Question Paper with answers and detailed solutions in PDF

CAT 2017 Questions from Quantitative Aptitude – Modern Maths

Quantitative Aptitude – Modern Maths – P&C – Q1: How many four digit numbers, which are divisible by 6, can be formed using the digits 0, 2, 3, 4, 6, such that no digit is used more than once and 0 does not occur in the left-most position?
Quantitative Aptitude – Modern Maths – P&C – Q2: In how many ways can 8 identical pens be distributed among Amal, Bimal, and Kamal so that Amal gets at least 1 pen, Bimal gets at least 2 pens, and Kamal gets at least 3 pens?
Quantitative Aptitude – Modern Maths – P&C – Q3: Let AB, CD, EF, GH, and JK be five diameters of a circle with center at O. In how many ways can three points be chosen out of A, B, C, D, E, F, G, H, J, K, and O so as to form a triangle?
Quantitative Aptitude – Modern Maths – Progressions – Q1: If a1 = 1/(2*5), a2 = 1/(5*8), a3 = 1/(8*11),……, then a1 + a2 +……..+ a100 is
Quantitative Aptitude – Modern Maths – Progressions – Q2: Let a1, a2, a3, a4, a5 be a sequence of five consecutive odd numbers. Consider a new sequence of five consecutive even numbers ending with 2a3.
Quantitative Aptitude – Modern Maths – Progressions – Q3: Let a1, a2,……..a3n be an arithmetic progression with a1 = 3 and a2 = 7. If a1 + a2 + ….+a3n = 1830, then what is the smallest positive integer m such that m (a1 + a2 + …. + an ) > 1830?
Quantitative Aptitude – Modern Maths – Progressions – Q4: If the square of the 7th term of an arithmetic progression with positive common difference equals the product of the 3rd and 17th terms, then the ratio of the first term to the common difference is
Quantitative Aptitude – Modern Maths – Progressions – Q5: An infinite geometric progression a1, a2, a3,… has the property that an = 3(a(n+ l) + a(n+2) +….) for every n ≥ 1. If the sum a1 + a2 + a3 +……. = 32, then a5 is

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Know More about Online CAT Course

Quantitative Aptitude – Modern Maths – Permutation and Combination – In how many ways can 7 identical erasers
5 (100%) 54 votes

Quantitative Aptitude – Modern Maths – Progressions – If the square of the 7th term

Quantitative Aptitude – Modern Maths – Progressions

Question

CAT 2017 - Forenoon slot - Quantitative Aptitude - Modern Maths - Progressions - If the square of the 7th term
If the square of the 7th term of an arithmetic progression with positive common difference equals the product of the 3rd and 17th terms, then the ratio of the first term to the common difference is

A) 2 : 3
B) 3 : 2
C) 3 : 4
D) 4 : 3

Answer

Option (A)

Solution

From CAT 2017 – Quantitative Aptitude – Modern Maths – Progressions, we can see that,
(a+6d)^2 = (a+2d)(a+16d)
a^2 + 12 ad + 36d^2 = a^2 + 18 ad + 32d^2
Since, d is positive,
We get the ratio of a:d = 2:3
Option (A)

Download CAT 2017 Question Paper with answers and detailed solutions in PDF

CAT 2017 Questions from Quantitative Aptitude – Modern Maths

Quantitative Aptitude – Modern Maths – Progressions – Q1: If a1 = 1/(2*5), a2 = 1/(5*8), a3 = 1/(8*11),……, then a1 + a2 +……..+ a100 is
Quantitative Aptitude – Modern Maths – Progressions – Q2: An infinite geometric progression a1, a2, a3,… has the property that an = 3(a(n+ l) + a(n+2) +….) for every n ≥ 1. If the sum a1 + a2 + a3 +……. = 32, then a5 is
Quantitative Aptitude – Modern Maths – Progressions – Q3: Let a1, a2, a3, a4, a5 be a sequence of five consecutive odd numbers. Consider a new sequence of five consecutive even numbers ending with 2a3. If the sum of the numbers in the new sequence is 450, then a5 is
Quantitative Aptitude – Modern Maths – Progressions – Q4: Let a1, a2,……..a3n be an arithmetic progression with a1 = 3 and a2 = 7. If a1 + a2 + ….+a3n = 1830, then what is the smallest positive integer m such that m (a1 + a2 + …. + an ) > 1830?
Quantitative Aptitude – Modern Maths – P&C – Q1: How many four digit numbers, which are divisible by 6, can be formed using the digits 0, 2, 3, 4, 6, such that no digit is used more than once and 0 does not occur in the left-most position?
Quantitative Aptitude – Modern Maths – P&C – Q2: In how many ways can 8 identical pens be distributed among Amal, Bimal, and Kamal so that Amal gets at least 1 pen, Bimal gets at least 2 pens, and Kamal gets at least 3 pens?
Quantitative Aptitude – Modern Maths – P&C – Q3: In how many ways can 7 identical erasers be distributed among 4 kids in such a way that each kid gets at least one eraser but nobody gets more than 3 erasers?
Quantitative Aptitude – Modern Maths – P&C – Q4: Let AB, CD, EF, GH, and JK be five diameters of a circle with center at O. In how many ways can three points be chosen out of A, B, C, D, E, F, G, H, J, K, and O so as to form a triangle?

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Quantitative Aptitude – Modern Maths – Progressions – If the square of the 7th term
5 (100%) 52 votes

Quantitative Aptitude – Modern Maths – Permutation and Combination – Let AB, CD

Quantitative Aptitude – Modern Maths – Permutation and Combination

Question

CAT 2017 - Forenoon slot - Quantitative Aptitude - Modern Maths - Permutation and Combination - Let AB, CD
Let AB, CD, EF, GH, and JK be five diameters of a circle with center at O. In how many ways can three points be chosen out of A, B, C, D, E, F, G, H, J, K, and O so as to form a triangle?

Answer

160

Solution

From CAT 2017 – Quantitative Aptitude – Modern Maths – Permutation and Combination, we can see that,
There are 11 points from which a triangle can be formed. But there are 5 lines which have 3 points linearly.
Number of triangles formed = 11C3 – 5 (because of the lines)
165 – 5 = 160 triangles
Answer: 160

Download CAT 2017 Question Paper with answers and detailed solutions in PDF

CAT 2017 Questions from Quantitative Aptitude – Modern Maths

Quantitative Aptitude – Modern Maths – P&C – Q1: How many four digit numbers, which are divisible by 6, can be formed using the digits 0, 2, 3, 4, 6, such that no digit is used more than once and 0 does not occur in the left-most position?
Quantitative Aptitude – Modern Maths – P&C – Q2: In how many ways can 8 identical pens be distributed among Amal, Bimal, and Kamal so that Amal gets at least 1 pen, Bimal gets at least 2 pens, and Kamal gets at least 3 pens?
Quantitative Aptitude – Modern Maths – P&C – Q3: In how many ways can 7 identical erasers be distributed among 4 kids in such a way that each kid gets at least one eraser but nobody gets more than 3 erasers?
Quantitative Aptitude – Modern Maths – Progressions – Q1: If a1 = 1/(2*5), a2 = 1/(5*8), a3 = 1/(8*11),……, then a1 + a2 +……..+ a100 is
Quantitative Aptitude – Modern Maths – Progressions – Q2: Let a1, a2, a3, a4, a5 be a sequence of five consecutive odd numbers. Consider a new sequence of five consecutive even numbers ending with 2a3.
Quantitative Aptitude – Modern Maths – Progressions – Q3: Let a1, a2,……..a3n be an arithmetic progression with a1 = 3 and a2 = 7. If a1 + a2 + ….+a3n = 1830, then what is the smallest positive integer m such that m (a1 + a2 + …. + an ) > 1830?
Quantitative Aptitude – Modern Maths – Progressions – Q4: If the square of the 7th term of an arithmetic progression with positive common difference equals the product of the 3rd and 17th terms, then the ratio of the first term to the common difference is
Quantitative Aptitude – Modern Maths – Progressions – Q5: An infinite geometric progression a1, a2, a3,… has the property that an = 3(a(n+ l) + a(n+2) +….) for every n ≥ 1. If the sum a1 + a2 + a3 +……. = 32, then a5 is

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Quantitative Aptitude – Modern Maths – Permutation and Combination – Let AB, CD
5 (100%) 57 votes