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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## When a is divided by b the remainder... tagged by: BTGmoderatorLU ##### This topic has 2 expert replies and 0 member replies ### Top Member ## When a is divided by b the remainder... When a is divided by b the remainder is 13. When c is divided by d the remainder is 12. If a,b,c,d are all positive integers then which of these may be the value of b*d? 1)100 2)121 3)144 4)169 5)196 The OA is E. Can any expert help me with this PS question please? I don't have it clear. Thanks. ### GMAT/MBA Expert Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 122 members Upvotes: 1153 GMAT Score: 770 LUANDATO wrote: When a is divided by b the remainder is 13. When c is divided by d the remainder is 12. If a,b,c,d are all positive integers then which of these may be the value of b*d? 1)100 2)121 3)144 4)169 5)196 The OA is E. Can any expert help me with this PS question please? I don't have it clear. Thanks. Rule: The remainder must be less than the divisor. If a/b yields a remainder of 13, then b, the divisor, must be greater than 13. So the smallest possible value of b is 14. If c/d yields a remainder of 12, then d, the divisor, must be great than 12. So the smallest possible value of d is 13. Smallest possible value of b * d = 14 * 13. Answer choice D is 169 = 13 * 13, so the correct answer must be greater than this value. That leaves us with E _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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BTGmoderatorLU wrote:
When a is divided by b the remainder is 13. When c is divided by d the remainder is 12.
If a,b,c,d are all positive integers then which of these may be the value of b*d?

1)100
2)121
3)144
4)169
5)196
Recall that the remainder from any division of positive integers must be less than the divisor.

Since, when a is divided by b, the remainder is 13, then b must be at least 14.

Since, when c is divided by d, the remainder is 12, then d must be at least 13.

Thus, b*d is least 14*13 = 182. We see that only 196 could be the value of b*d.

_________________

Jeffrey Miller
jeff@targettestprep.com

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