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Bunuel
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If x and y are positive integers and 2x 3 = 6 3y what is the least Feb 01, 2023 5:06 pm
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

25% (medium)

Question Stats:

77% (01:18) correct 23% (01:27) wrong based on 56 sessions

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If x and y are positive integers and 2x – 3 = 6 – 3y, what is the least possible value of x?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
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C
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If x and y are positive integers and 2x 3 = 6 3y what is the least Feb 01, 2023 5:12 pm
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We get simplifying
2x= 9-3y
RHS will be even always
So LHS has to be even as well possible when y is odd
So least value y =1 and x is then 3

Bunuel
If x and y are positive integers and 2x – 3 = 6 – 3y, what is the least possible value of x?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
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GMAT 1: 760 Q51 V40
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If x and y are positive integers and 2x 3 = 6 3y what is the least Feb 01, 2023 6:34 pm
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Bunuel
If x and y are positive integers and 2x – 3 = 6 – 3y, what is the least possible value of x?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
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Solution:

  • x and y are positive integers
  • We are given \(2x – 3 = 6 – 3y\)
    \(⇒2x=9-3y\)
    \(⇒x=\frac{9-3y}{2}\)
    \(⇒x=\frac{8+1-2y-y}{2}\)
    \(⇒x=4-y+\frac{1-y}{2}\)
  • Since x is a positive integer, \(1-y\) needs to be the multiple of 2 which is possible when \(y=1\)
    \(⇒x_{min}=4-1+\frac{1-1}{2}\)
    \(⇒x_{min}=3\)

Hence the right answer is Option C
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Bunuel
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