CAT 2017 – Slot 1 – Quantitative Ability – Suppose, log(base3)x = log(base12)y = a
Q. 1: Suppose, log(base3)x = log(base12)y = a, where x, y are positive numbers. If G is the geometric mean of x and y, and log(base6)G is equal to
A) √a
B) 2a
C) a/2
D) a
x=3^a and y=12^a
G = √(3^a * 12^a) = 6^a
Log (base 6) 6^a = a
Option (D)
Q. 2: If x + 1 = x^2 and x > 0, then 2x^4 is
A) 6 + 4√5
B) 3 + 5√5
C) 5 + 3√5
D) 7 + 3√5
x+1=x^2
Find out the roots of x = [1+/- root(5)]/2
X2 = [3 +/- √5]/2
X4 = [7 +/-3√5]/2
2×4 = 7 +/- 3√5
As the only option is 7 + 3√5 So, we go with that.
Option (D)
Q. 3: 
A) 1/3
B) 2/3
C) 5/6
D) 7/6
Correct Answer:- C
Explanation: 
Q. 4: If 9^(2x – 1) – 81^(x-1) = 1944, then x is
A) 3
B) 9/4
C) 4/9
D) 1/3
9^(2x-1) – 9^(2x-2) = 1944
It can be written as 3^(4x)/9 – 3^(4x)/81 = 1944
8(3^(4x)/81) = 1944
x =9/4
Option (B)
Q. 5: 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
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
The number of solutions is 1 + 2 + …… + 12 + 11 + 10 = 78 + 21 = 99
Option (B)
Checkout Other Questions of CAT 2017 Slot 1 Paper:
Verbal Ability : | Q.01- Q.06 | Q.07- Q.12 | Q.13- Q.18 | Q.19- Q.21 | Q.22- Q.24 | Q.25- Q.29 | Q.30 – Q.34 |
Logical Reasoning : | Q.01- Q.04 | Q.05- Q.08 | Q.09- Q.12 | Q.13- Q.16 | Q.17- Q.20 | Q.21- Q.24 | Q.25 – Q.28 | Q.29 – Q.32 |
Quantitative Aptitude: | Q.01- Q.05 | Q.06- Q.10 | Q.11- Q.15 | Q.16- Q.20 | Q.21- Q.25 | Q.26- Q.30 | Q.31 – Q.34 |
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