CAT 2021 Question Paper | Quant Slot 3

CAT 2021 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 13 : If \(3 x+2|y|+y=7\) and \(x+|x|+3 y=1\), then \(x+2 y\) is

Video Explanation

Explanatory Answer

We are given two equations: 3x + 2|y| + y = 7 and x + |x| + 3y = 1
|x| or the modulus of x, is a function of x, that gives the magnitude of x.
|x| = -(x); if x is negative, and
|x| = x; if x is non-negative.
Therefore, depending on whether ‘x’ and ‘y’ are positive or negative, we assume the following cases for the two equations given.
Case (i): ‘x’ and ‘y’ are both positive.
|x| = x and |y| = y
3x + 2|y| + y = 7
x + |x| + 3y = 1
3x + 2y + y = 7
x + x + 3y = 1
3x + 3y = 7
2x + 3y = 1
Solving the two equations, we get x = 6 and y = -11/3.
Since this is contradictory to the assumption that y is positive, we discard this case.
Case (ii): ‘x’ and ‘y’ are both negative.
|x| = -x and |y| = -y
3x + 2|y| + y = 7
x + |x| + 3y = 1
3x - 2y + y = 7
x - x + 3y = 1
3x - y = 7
3y = 1
Solving the two equations, we get x = 22/9 and y = 1/3.
Since this is contradictory to the assumption that both x and y are both negative, we discard this case.
Case (iii): ‘x’ is negative and ‘y’ is positive.
|x| = -x and |y| = y
3x + 2|y| + y = 7
x + |x| + 3y = 1
3x + 2y + y = 7
x - x + 3y = 1
3x + 3y = 7
3y = 1
Solving the two equations, we get x = 2 and y = 1/3.
Since this is contradictory to the assumption that both x is negative, we discard this case.
Case (iv): ‘x’ is positive and ‘y’ is negative.
|x| = x and |y| = -y
3x + 2|y| + y = 7
x + |x| + 3y = 1
3x - 2y + y = 7
x + x + 3y = 1
3x - y = 7
2x + 3y = 1
Solving the two equations, we get x = 2 and y = -1.
This satisfies the assumption that x is positive and y is negative.
Hence x = 2 and y = -1
Therefore, x + 2y = 2 + 2(-1) = 0
Hence, x + 2y = 0.

The question is " If \(3 x+2|y|+y=7\) and \(x+|x|+3 y=1\), then \(x+2 y\) is "

Hence, the answer is '0'

Choice A is the correct answer.

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