DS: q 74 from 198 700 Level Question

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tallazndood: Junior | Next Rank: 30 Posts; Posts: 24; Joined: Tue Nov 17, 2009 12:53 pm; Location: California; GMAT Score:670

DS: q 74 from 198 700 Level Question

by tallazndood » Sun Jan 24, 2010 9:39 pm

Question:
74) Sum of positive integers x and y is 72. What is xy?
1. x = y + 1
2. x and y have same tens digit

OA: D

Comment: I just don't see how the OA can be correct based on the question. Can someone please help enlighten me? Thank you in advance!

Quote

Source: Beat The GMAT — Data Sufficiency | Sun Jan 24, 2010 9:39 pm

papgust: Community Manager; Posts: 1537; Joined: Mon Aug 10, 2009 6:10 pm; Thanked: 653 times; Followed by:252 members

by papgust » Sun Jan 24, 2010 10:17 pm

I believe that question is wrongly transcribed. It should be x + y = 77 in the question stem. I remember working out this problem few days back. As an aside, from statement I says x and y are consecutive integers. So, no consecutive integers will add upto 72. So, please check the question once again. However, i'll show the solution assuming that it is 77 and NOT 72.

I. x = y + 1

x and y are consecutive integers. Only possible combination of (x,y) adding to 77 is (38,39). Sufficient.

II. x and y are both double digits from statement II. It varies only with unit's digit.
Assume s as x's unit digit and t as y's unit digit.

Possible combinations of x and y are (1s,1t), (2s,2t), (3s, 3t) and (4s,4t).

(1s, 1t) can be ruled out since it does not add upto 77. Take the maximum value of s and t. (19, 19) ==> This will only add upto 38. So eliminate.

Same logic goes for (2s,2t).

(4s,4t) can also be ruled out. Take minimum possible values of s and t. (40, 40) ==> This goes beyond 77 i.e. 80. So, Eliminate.

Only pair left is (3s, 3t). Either it could be (38, 39) or (39, 38). But question asks only for value of xy. Both pairs provide same value of xy. So, statement II is sufficient.