CAT 2022 Question Paper | Quant Slot 1

CAT Questions

CAT 2022 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 15 : Let \(a\) and \(b\) be natural numbers. If \(a^2+a b+a=14\) and \(b^2+a b+b=28\), then \((2 a+b)\) equals

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Video Explanation

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Explanatory Answer

\(a^2+a b+a=14---(1)\)
\( b ^ { 2 } + a b + b = 28 - - - ( 2 ) \)
(1) + (2)
\( a ^ { 2 } + b ^ { 2 } + a b + ( a + b ) = 42 \)
\( ( a + b ) ^ { 2 } + ( a + b ) = 42 \)
\( ( a + b ) ( a + b + 1 ) = 42 \)
Since a and b are a + b will also be a natural number, let’s call it k.
k * (k +1) = 42
The product of two consecutive natural numbers is 42.
k = 6.
a + b = 6
\( a ^ { 2 } + a b + a = 14 \)
\( a ( a + b + 1 ) = 14 \)
\( a ( 6 + 1 ) = 14 \)
a = 2
b = 4.
2a + b = 4 + 4 = 8
2a + b = 8

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The question is " Let \(a\) and \(b\) be natural numbers. If \(a^2+a b+a=14\) and \(b^2+a b+b=28\), then \((2 a+b)\) equals "

Hence, the answer is '8'

Choice D is the correct answer.