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by phoenix9801 » Sun May 20, 2012 2:35 pm
2-
If 7(x + 1) = 8(y − 1), and x and y are both positive integers, what is the least possible value of x + y?
a) 1
b) 2
c) 7
d) 9
e) 15
Last edited by phoenix9801 on Sun May 20, 2012 6:05 pm, edited 1 time in total.
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Source: — Problem Solving |

by Anurag@Gurome » Sun May 20, 2012 5:56 pm
2-
If 7(x + 1) = 8(y - 1), and x and y are both positive integers, what is the least possible value of x + y?
a) 1
b) 2
c) 7
d) 9
e) 15
x + y cannot be 1 as x and y are both positive integers.
x + y cannot be 2, because then x = y = 1 but in that case 7(x + 1) is not equal to 8(y - 1)
Now x = 2, 3, 4, 5, 6 gives the value of 7(x + 1) as 21, 28, 35, 42, 49, which cannot be equal to 8(y - 1) for any integer value, as these values are not multiples of 8.

Next, if x = 7, y = 8, then 7(x + 1) = 7 * 8 = 56 and 8(y - 1) = 8 * 7 = 56
So, x + y = 15

The correct answer is E.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

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