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 – Algebra – Functions – If f(x) = (5x+2)/(3x-5)

Quantitative Aptitude – Algebra – Functions

Question

CAT 2017 - Forenoon slot - Quantitative Aptitude - Algebra - Functions - If f(x) = (5x+2)(3x-5)
If f(x) = (5x+2)/(3x-5) and g(x) = x^2 – 2x – 1, then the value of g(f(f(3))) is

A) 2
B) 1/3
C) 6
D) 2/3

Answer

Option (A)

Solution

From CAT 2017 – Quantitative Aptitude – Algebra – Functions, we can see that,
f(3) = 17/4
f(17/4) = 3
g(3) = 2
Option (A)

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

CAT 2017 Questions from Quantitative Aptitude – Algebra – Functions

Quantitative Aptitude – Algebra – Functions – Q1: Let f(x) = 2x-5 and g(x) = 7-2x. Then |f(x) + g(x)| = |f(x)| + |g(x)| if and only if
Quantitative Aptitude – Algebra – Functions – Q2: If f(ab) = f(a)f(b) for all positive integers a and b, then the largest possible value of f(1) is
Quantitative Aptitude – Algebra – Functions – Q3: Let f(x) = x^2 and g(x) = 2^x, for all real x. Then the value of f(f(g(x)) + g(f(x))) at x = 1 is
Quantitative Aptitude – Algebra – Functions – Q4: If f1(x) = x^2 + 11x + n and f2(x) = x, then the largest positive integer n for which the equation f1(x) = f2(x) has two distinct real roots, is
Quantitative Aptitude – Algebra – Functions – Q5: The area of the closed region bounded by the equation | x | + | y | = 2 in the two-dimensional plane is
Quantitative Aptitude – Algebra – Logarithms
Quantitative Aptitude – Algebra – Quadratic Equations
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Quantitative Aptitude – Algebra – Functions – If f(x) = (5x+2)/(3x-5)
5 (100%) 57 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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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 – Geometry – Coordinate – The shortest distance

Quantitative Aptitude – Geometry – Coordinate

Question

CAT 2017 - Forenoon slot - Quantitative Aptitude - Geometry - Coordinate - The shortest distance
The shortest distance of the point (½, 1) from the curve y = |x -1| + |x + 1| is

A) 1
B) 0
C) √2
D) √3/2

Answer

Option (A)

Solution

From CAT 2017 – Quantitative Aptitude – Geometry – Coordinate, we can see that,
Quantitative Aptitude - Geometry - Coordinate - The shortest distance
The graph of y = |x – 1| + |x + 1| is shown above.
The shortest distance of (1/2, 1) from the graph is 1.
Option (A)

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

CAT 2017 Questions from Quantitative Aptitude – Geometry

Quantitative Aptitude – Geometry – Coordinate – Ques: The points (2, 5) and (6, 3) are two end points of a diagonal of a rectangle. If the other diagonal has the equation y = 3x + c, then c is
Quantitative Aptitude – Geometry – Circles – Q1: ABCD is a quadrilateral inscribed in a circle with centre O. If ∠COD = 120 degrees and ∠BAC = 30 degrees, then the value of ∠BCD (in degrees) is
Quantitative Aptitude – Geometry – Circles – Q2: Let ABC be a right-angled isosceles triangle with hypotenuse BC. Let BQC be a semi-circle, away from A, with diameter BC.
Quantitative Aptitude – Geometry – Triangles – Q1: Let P be an interior point of a right-angled isosceles triangle ABC with hypotenuse AB.
Quantitative Aptitude – Geometry – Triangles – Q2: Let ABC be a right-angled triangle with BC as the hypotenuse. Lengths of AB and AC are 15 km and 20 km, respectively.
Quantitative Aptitude – Geometry – Triangles – Q3: From a triangle ABC with sides of lengths 40 ft, 25 ft and 35 ft, a triangular portion GBC is cut off where G is the centroid of ABC. The area, in sq ft, of the remaining portion of triangle ABC is
Quantitative Aptitude – Geometry – Mensuration
Quantitative Aptitude – Geometry – Polygons – Ques: Let ABCDEF be a regular hexagon with each side of length 1 cm. The area (in sq cm) of a square with AC as one side is

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Quantitative Aptitude – Geometry – Coordinate – The shortest distance
5 (100%) 53 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
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Quantitative Aptitude – Algebra – Maxima Minima – If a, b, c, and d are integers

Quantitative Aptitude – Algebra – Maxima Minima

Question

CAT 2017 - Forenoon slot - Quantitative Aptitude - Algebra - Maxima Minima - If a, b, c, and d are integers
If a, b, c, and d are integers such that a + b + c + d = 30, then the minimum possible value of (a – b)^2 + (a – c)^2 + (a – d)^2 is

Answer

2

Solution

From CAT 2017 – Quantitative Aptitude – Algebra – Maxima Minima, we can see that,
a + b + c + d = 30
a, b, c, d are integers. (a – b)^2 + (a – c)^2 + (a – d)^2 would have its minimum value when each bracket has the least possible value. Let (a, b, c, d) = (8, 8, 7, 7) The given expression would be 2. It cannot have a smaller value.
Answer: 2

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

CAT 2017 Questions from Quantitative Aptitude – Algebra

Quantitative Aptitude – Algebra – Maxima Minima – Q1: If three sides of a rectangular park have a total length 400 ft, then the area of the park is maximum when the length (in ft) of its longer side is
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Quantitative Aptitude – Algebra – Maxima Minima – If a, b, c, and d are integers
5 (100%) 59 votes

Quantitative Aptitude – Algebra – Functions – If f1(x) = x^2 + 11x + n

Quantitative Aptitude – Algebra – Functions

Question

CAT 2017 - Forenoon slot - Quantitative Aptitude - Algebra - Functions - If f1(x) = x^2 + 11x + n
If f1(x) = x^2 + 11x + n and f2(x) = x, then the largest positive integer n for which the equation f1(x) = f2(x) has two distinct real roots, is

Answer

24

Solution

From CAT 2017 – Quantitative Aptitude – Algebra – Functions, we can see that,
f1(x) = f2(x)
x^2 + 11x +n = x
x^2 + 10x + n =0
To have distinct and real roots, D>0
D = b^2-4ac = 100 – 4n > 0
On solving the inequality, we get, n<25 So, max positive integer value of n = 24. Answer: 24

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

CAT 2017 Questions from Quantitative Aptitude – Algebra – Functions

Quantitative Aptitude – Algebra – Functions – Q1: Let f(x) = 2x-5 and g(x) = 7-2x. Then |f(x) + g(x)| = |f(x)| + |g(x)| if and only if
Quantitative Aptitude – Algebra – Functions – Q2: If f(ab) = f(a)f(b) for all positive integers a and b, then the largest possible value of f(1) is
Quantitative Aptitude – Algebra – Functions – Q3: Let f(x) = x^2 and g(x) = 2^x, for all real x. Then the value of f(f(g(x)) + g(f(x))) at x = 1 is
Quantitative Aptitude – Algebra – Functions – Q4: If f(x) = (5x+2)/(3x-5) and g(x) = x^2 – 2x – 1, then the value of g(f(f(3))) is
Quantitative Aptitude – Algebra – Functions – Q5: The area of the closed region bounded by the equation | x | + | y | = 2 in the two-dimensional plane is
Quantitative Aptitude – Algebra – Logarithms
Quantitative Aptitude – Algebra – Quadratic Equations
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Quantitative Aptitude – Algebra – Inequalities
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Quantitative Aptitude – Algebra – Functions – If f1(x) = x^2 + 11x + n
4.9 (98.79%) 66 votes

Quantitative Aptitude – Algebra – Inequalities – For how many integers n

Quantitative Aptitude – Algebra – Inequalities

Question

CAT 2017 - Forenoon slot - Quantitative Aptitude - Algebra - Inequalities - For how many integers n
For how many integers n, will the inequality (n – 5) (n – 10) – 3(n – 2) ≤ 0 be satisfied?

Answer

11

Solution

From CAT 2017 – Quantitative Aptitude – Algebra – Inequalities, we can see that,
On solving the equation, we get n^2 – 18n + 56 ≤ 0
Factorize and we get, (n-4)(n-14) ≤ 0
4 ≤ n ≤ 14
No of values of n =11
Answer: 11

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

CAT 2017 Questions from Quantitative Aptitude – Algebra

Quantitative Aptitude – Algebra – Inequalities – Ques: The number of solutions (x, y, z) to the equation x – y – z = 25, where x, y, and z are positive integers such that x ≤ 40, y ≤ 12, and z ≤ 12 is
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Quantitative Aptitude – Algebra – Inequalities – For how many integers n
5 (100%) 54 votes

Quantitative Aptitude – Algebra – Inequalities – The number of solutions (x, y, z)

Quantitative Aptitude – Algebra – Inequalities

Question

CAT 2017 - Forenoon slot - Quantitative Aptitude - Algebra - Inequalities - The number of solutions (x, y, z)
The number of solutions (x, y, z) to the equation x – y – z = 25, where x, y, and z are positive integers such that x ≤ 40, y ≤ 12, and z ≤ 12 is

A) 101
B) 99
C) 87
D) 105

Answer

Option (B)

Solution

From CAT 2017 – Quantitative Aptitude – Algebra – Inequalities, we can see that,
x = 25 + y + z. The possible values of x, y, z and the corresponding number of values of y, z are tabulated below (x, y, z are positive integers).
We see that 27 ≤ x ≤ 40
Quantitative Aptitude - Algebra - Inequalities - The number of solutions (x, y, z)
The number of solutions is 1 + 2 + …… + 12 + 11 + 10 = 78 + 21 = 99
Option (B)

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Quantitative Aptitude – Algebra – Inequalities – The number of solutions (x, y, z)
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