With # and & each representing different digits in the

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 am; Followed by:2 members

With # and & each representing different digits in the

by Gmat_mission » Mon Jun 10, 2019 5:37 am

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With # and & each representing different digits in the problem below, the difference between #&& and ## is 667. What is the value of &?

#&&
- ##
_____
667

(A) 3
(B) 4
(C) 5
(D) 8
(E) 9

[spoiler]OA=B[/spoiler]

Source: Veritas Prep

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Source: Beat The GMAT — Problem Solving | Mon Jun 10, 2019 5:37 am

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 am; Location: Montreal; Thanked: 1090 times; Followed by:355 members; GMAT Score:780

by Ian Stewart » Mon Jun 10, 2019 6:36 am

We're subtracting something between 10 and 99, and arriving at 667. So we must be subtracting from a number between 677 and 766, and the digit # could only be 6 or 7. But it can't be 6, because 6&& - 66 will never be equal to 667 (it could be at most 633), so # must be 7. So we have this problem:

7&& - 77 = 667
7&& = 667 + 77 = 744

and & = 4.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Fri Jun 14, 2019 2:43 pm

Gmat_mission wrote:With # and & each representing different digits in the problem below, the difference between #&& and ## is 667. What is the value of &?

#&&
- ##
_____
667

(A) 3
(B) 4
(C) 5
(D) 8
(E) 9

[

We see that # (in the hundreds digit) represents either 6 (if there is no borrowing from the tens digit) or 7 (if there is borrowing). However, no matter if it's 6 or 7, it's also the tens digit of the subtrahend, and since the tens digit of the difference is also 6, there must be borrowing. So # must be 7. In that case, & (in the tens digit) is either 3 or 4. It can be 3 and by borrowing from 7 (in the hundreds place) becomes 13 and 13 - 7 = 6 (if there is no borrow from the units digit). It can be 4 and by borrowing from 7 (in the hundreds place) and by lending 1 to the units digit becomes 13 and 13 - 7 = 6. We can see which one is correct by checking both cases:

733 - 77 = 656 (This is not correct.)

744 - 77 = 667 (This is correct.)

Answer: B

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