Let S be the set of all 7-digit numbers N such that the sum of the dig

Question

Let S be the set of all 7-digit numbers N such that the sum of the digits of N is divisible by 7.

A and B are two 7-digit numbers:
 A = 4,893,P12

B = 5,857,0Q5 
Select a value for  P  so that A is an element of S. Select a value for  Q  so that B is an element of S. Make two selections, one in each column.

ID: 101101

chetan2u · Accepted Answer

Had calculator not been allowed, I would have thought of dividing numbers into multiples of 7. But as calulator is allowed, I would straight forward substitute the options and find the answer.

A = 4893P12: P as 8 makes the number divisible by 7.
B=58570Q5: Q as 7 makes the number divisible by 7.

Bunuel, please check the value of B. It may be different, otherwise the answer should be 7

The above in spoiler is a reminder not to be casual while reading the question.
 
A = 4,893,P12
Sum of digits = 4+8+9+3+P+1+2 = 27+P = 28-1+P........So P-1 should be 7 or a multiple of 7 .....P=8

B = 5,857,0Q5
Sum of digits = 5+8+5+7+0+Q+5 = 30+P = 28+2+P........So P+2 should be 7 or a multiple of 7..... P=5

GMAT695 · Answer

Bunuel  is the OA correct ?

Bunuel · Answer

That's the OA's given in the book.

Aryaa03 · Answer

chetan2u 
I am afraid this question actually talks about the sum of the digits and then the divisibility of that sum with 7.

A = 4,893,P12   ==> Sum = 27+P ; For this to be divisible by 7, P should be 8
B = 5,857,0Q5   ==>  Sum = 30 + Q ; For this to be divisible by 7, Q should be 5

Bunuel · Answer

I think, you are missing a point:

Let S be the set of all 7-digit numbers N such that  the sum of the digits of N  is divisible by 7.

So,  the sum of the digits of N  is divisible by 7, not N itself.

chetan2u · Answer

Thanks  Bunuel  and  Aryaa03 , how easy it is not to read the wordings carefully...

aliquidasperiores · Answer

Did anyone else find an error in this question in GMAT OG 25-26? The question says "sum of digits of N is divisible by 6" but the answer talks about divisibility by 7.
Of course none of the answers are correct for P if we need to check divisibility by 6

DashStar · Answer

Yes! They need to fix this.

Let S be the set of all 7-digit numbers N such that the sum of the dig

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