January 1st, 2020 by Ravi Handa

Quantitative Aptitude - Algebra - Functions - If f(ab) = f(a)f(b) for all positive
Quantitative Aptitude - Algebra - Functions
Question
If f(ab) = f(a)f(b) for all positive integers a and b, then the largest possible value of f(1) is
Answer
1
Solution
From CAT 2017 - Quantitative Aptitude - Algebra - Functions, we can see that,
Let us take the case when a=b=1
So, f(1) = f(1) f(1)
f(1) = [f(1)]^2
f(1)[f(1)-1] = 0
f(1) = 1
So, the maximum value of f(1) = 1
Answer: 1
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January 1st, 2020 by Ravi Handa

Quantitative Aptitude - Algebra - Number of integer solutions - 1/a + 1/b = 1/9
Quantitative Aptitude - Algebra - Number of integer solutions
Question
How many different pairs (a, b) of positive integers are there such that a â‰¤ b and
1/a + 1/b = 1/9
Answer
3
Solution
From CAT 2017 - Quantitative Aptitude - Algebra - Number of integer solutions, we can see that,
9(a + b) = ab
ab â€“ 9a â€“ 9b + 81 = 81
(a â€“ 9) (b â€“ 9) = 81 = 34
As a, b > 0 and a â‰¤ b, there are only 3 ordered pairs, given by a â€“ 9 = 1, 3 or 9 and corr

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January 1st, 2020 by Ravi Handa

Quantitative Aptitude - Algebra - Logarithms - If log (2^a Ã— 3^b Ã— 5^c)
Quantitative Aptitude - Algebra - Logarithms
Question
If log (2^a Ã— 3^b Ã— 5^c) is the arithmetic mean of log (2^2 Ã— 3^3 Ã— 5), log (2^6 Ã— 3 Ã— 5^7), and log(2 Ã— 3^2 Ã— 5^4), then a equals
Answer
3
Solution
From CAT 2017 - Quantitative Aptitude - Algebra - Logarithms, we can see that,
log (2^a. 3^b. 5^c) = [log (2^2.3^3.5) + log (2^6.3.5^7) + log (2.3^2.5^4)]/3
3 * log (2^a. 3^b. 5^c) = log (2^9.3^6.5^12)
log (2^a. 3^b. 5^c)^3 = log (2^9.3^6.5^12)
log (2^3a.

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January 1st, 2020 by Ravi Handa

Quantitative Aptitude - Algebra - If 9^(x-1/2) â€“ 2^(2x-2) = 4^x
Quantitative Aptitude - Algebra
Question
If 9^(x-1/2) â€“ 2^(2x-2) = 4^x â€“ 3^(2x-3) , then x is
A) 3/2
B) 2/5
C) 3/4
D) 4/9
Answer
Option (A)
Solution
From CAT 2017 - Quantitative Aptitude - Algebra, we can see that,
You can solve the question easily by putting in values from the options given.
When we put the value of x as 3/2, it satisfies the equation. So, 3/2 is the correct answer.
Option (A)
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January 1st, 2020 by Ravi Handa

Quantitative Aptitude - Algebra - Quadratic Equations - The minimum possible value
Quantitative Aptitude - Algebra - Quadratic Equations
Question
The minimum possible value of the sum of the squares of the roots of the equation x^2 + (a + 3)x - (a + 5) = 0 is
A) 1
B) 2
C) 3
D) 4
Answer
Option (C)
Solution
From CAT 2017 - Quantitative Aptitude - Algebra - Quadratic Equations, we can see that,
b and c can be the roots of the given equation.
We have to find, b^2 + c^2 = (b+c)^2 â€“ 2bc
b+c = -(a+3) and bc = -(a+5)
b^2 +

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January 1st, 2020 by Ravi Handa

Quantitative Aptitude - Algebra - Functions - Let f(x) = x^2 and g(x) = 2^x
Quantitative Aptitude - Algebra - Functions
Question
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
A) 16
B) 18
C) 36
D) 40
Answer
Option (C)
Solution
From CAT 2017 - Quantitative Aptitude - Algebra - Functions, we can see that,
f(g(x)) = 2^(2x)
g(f(x)) = 2^((x)^2)
f(f(g(x)) + g(f(x)) = (2^(2x) + 2^(x^2))^2
at x = 1, we get 36
Option (C)
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January 1st, 2020 by Ravi Handa

Quantitative Aptitude - Algebra - Logarithms - If x is a real number
Quantitative Aptitude - Algebra - Logarithms
Question
If x is a real number such that log(base 3)5 = log(base 5)(2 + x), then which of the following is true?
A) 0 < x < 3
B) 23 < x < 30
C) x > 30
D) 3 < x < 23
Answer
Option (D)
Solution
From CAT 2017 - Quantitative Aptitude - Algebra - Logarithms, we can see that,
Log(base 3)5 lies between 1 and 2 because Log(base 3)3 = 1 and Log(base 3)9 = 2
1 < Log(base 3)5 < 2
So, log(base 5)(2+x

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January 1st, 2020 by Ravi Handa

Quantitative Aptitude - Algebra - Maxima Minima - If three sides of a rectangular
Quantitative Aptitude - Algebra - Maxima Minima
Question
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
Answer
200
Solution
From CAT 2017 - Quantitative Aptitude - Algebra - Maxima Minima, we can see that,
Let a and b be the two sides of a rectangle.
a + 2b = 400
Area of rectangle = ab (We have to maximize it)
b = (400-a)/2
Put the value of b in ar

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December 30th, 2019 by Ravi Handa

Quantitative Aptitude - Algebra - Functions - If f(x) = (5x+2)/(3x-5)
Quantitative Aptitude - Algebra - Functions
Question
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 - Fun

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December 30th, 2019 by Ravi Handa

Quantitative Aptitude - Algebra - Maxima Minima - If a, b, c, and d are integers
Quantitative Aptitude - Algebra - Maxima Minima
Question
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 â€“ b)^2 + (a â€“ c)^2 + (a â€“ d)^2 would have its minimum value when each bracket has the least possible value. Let

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