Quantitative Aptitude - Number Systems - If a, b, c are three positive integers
Quantitative Aptitude - Number Systems
Question
If a, b, c are three positive integers such that a and b are in the ratio 3 : 4 while b and c are in the ratio 2:1, then which one of the following is a possible value of (a + b + c)?
A) 201
B) 205
C) 207
D) 210
Answer
Option (C)
Solution
From CAT 2017 - Quantitative Aptitude - Number Systems, we can see that,
Let us take a = 3x and b = 4x
Also, b = 2y and c = y
4x = 2y => y = 2x
Now, c =

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Quantitative Aptitude - Number Systems - The numbers 1, 2,...,9 are arranged
Quantitative Aptitude - Number Systems
Question
The numbers 1, 2,...,9 are arranged in a 3 X 3 square grid in such a way that each number occurs once and the entries along each column, each row, and each of the two diagonals add up to the same value.
If the top left and the top right entries of the grid are 6 and 2, respectively, then the bottom middle entry is
Answer
3
Solution
From CAT 2017 - Quantitative Aptitude - Number Systems, we can see that

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Quantitative Aptitude â€“ Number System â€“ If the sum of squares of two numbers
Slot -2 â€“Â Quantitative Aptitude â€“ Number System â€“ If the sum of squares of two numbers is 97
If the sum of squares of two numbers is 97, then which one of the following cannot be their product?
a) âˆ’32
b) 16
c) 48
d) 64
Answer: d) 64
Solution: let numbers are a and b.
Given, a^2+b^2=97
Using A.M.â‰¥G.M
(a^2+b^2)/2 â‰¥ (a^2 b^2 )^(1/2)=ab
ab â‰¤ 97/2 = 48.5
Thus product of numbers can not be greater than 48.5
Option d) 6

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Quantitative Aptitude â€“ Number System â€“ The smallest integer n for which
Slot -2 â€“Â Quantitative Aptitude â€“ Number System â€“ The smallest integer n for which
The smallest integer n for which 4^n > 17^19 holds, is closest to?
a) 33
b) 35
c) 37
d) 39
Answer: d) 39
Solution:
Given , 4^n > 17^19
OrÂ 16^(n/2) > 17^19
Now from the given options, the only possible value of n is 39 as for other
values n/2 will be less than 19 and 16 < 17.
Correct answer d) 39
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Quantitative Aptitude â€“ Arithmetic - Number System â€“ While multiplying three real numbers
Slot -1 â€“Â Quantitative Aptitude â€“ Arithmetic - Number System â€“ While multiplying three real numbers
While multiplying three real numbers, Ashok took one of the numbers as 73 instead of 37. As a result, the product went up by 720. Then the minimum possible value of the sum of squares of the other two numbers is?
Answer: 40
Solution: Let the other two numbers are a & b so
73ab - 37ab = 720
Or 36ab = 720
ab = 20
using

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Quantitative Aptitude â€“ Number System â€“ The number of integers x such
Slot -1 -Â Quantitative Aptitude â€“ Number System â€“ The number of integers x such that 0.25
The number of integers x such that 0.25Â <2xÂ <Â 200, and 2xÂ +2 is perfectly divisible by either 3 or 4, is?
Answer: 5
Solution: as given 0.25Â <Â 2xÂ <Â 200
Or Â¼ <Â 2xÂ <Â 200
So x = { -2, -1, 0,1,2,3,4,5,6,7}
Now 2xÂ +2 will be perfectly divisible by 3 if x is even non-negative integer and will be divisible by 4 if x = 1
So numb

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