The sum of positive integers x and y is 77, what is the

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Sun Aug 26, 2018 12:56 am

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The sum of positive integers x and y is 77, what is the value of xy?

(1) x=y+1
(2) x and y have the same tens digit.

OA D

Source: GMAT Prep

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Source: Beat The GMAT — Data Sufficiency | Sun Aug 26, 2018 12:56 am

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by GMATGuruNY » Sun Aug 26, 2018 2:38 am

BTGmoderatorDC wrote:The sum of positive integers x and y is 77, what is the value of xy?

(1) x=y+1
(2) x and y have the same tens digit.

Statement 1:
Substituting x=y+1 into x+y = 77, we get:
(y+1) + y = 77
2y = 76
y = 38, implying that x = 38+1 = 39.
Thus, xy = 39*38.
SUFFICIENT.

Statement 2:
For x and y to have the same tens digit and a sum of 77, they must be equal to the pair of values yielded by Statement 1:
38 and 39.
No other pair of integers has the same tens digit and a sum of 77.
Thus, xy = 38*39.
SUFFICIENT.

The correct answer is D.

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by fskilnik@GMATH » Sun Aug 26, 2018 1:42 pm

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masoom j negi: Senior | Next Rank: 100 Posts; Posts: 33; Joined: Thu Dec 20, 2018 2:09 am

by masoom j negi » Fri Dec 21, 2018 8:55 pm

x + y = 77 eq(1)
Statement 1. x = y + 1 eq(2)
Using eq(1) and eq(2), we get,
X = 39 and y = 38. So, xy = 1482. Hence, Sufficient.
Statement 2. X = 10a + b
Y = 10a + c
10a + b + 10a + c = 77
20a + b + c= 77( where a, b ,c are single digits)
This is possible only if (a, b, c) = (3, 8, 9) or (3, 9, 8)
So, the two no would be 36 and 37 in both the case.
Hence, xy = 38 x 39 = 1482. Hence, Sufficient.

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