x, y, a, and b are positive integers. When x is divided by y

Question

x, y, a, and b are positive integers. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9. Which of the following is NOT a possible value for y + b?

A. 24
B. 21 
C. 20 
D. 17
E. 15

My answer is A as I can get other values. But the OA is not given. What I am keen on asking is "I have solved this question by picking the values for x,y,a and b. Is there any shortcut and do you guys agree with my answer?

Bunuel · Accepted Answer

Important note: remainder is ALWAYS less than divisor, thus y>6 and b>9 --> y+b>15.

Answer: E.

KarishmaB · Answer

I would suggest you to analyze each statement as you read it. Often, you will find that you are very close to the answer by the time you read the last sentence of the question.

"When x is divided by y, the remainder is 6."
Here, I say to myself, "Ok, so y must be greater than 6 and x is either 6 or at least 6 greater than y."

If y is anything less than 6, you can make one more group!

When a is divided by b, the remainder is 9.
Now I say, "b must be greater than 9 and a is either 9 or at least 9 greater than y."

Which of the following is NOT a possible value for y + b
I already know that y must be greater than 6 and b must be greater than 9. So (y+b) must be greater than 15. Now I will just look for an option <= 15

enigma123 · Answer

Thanks for the tip.

MSoS · Answer

Sometimes the answers is so easy. U just need to figure it out.

Thanks Bunuel I picked "E" too, but tried to figure it out by picking numbers. Took me ages

erikvm · Answer

Question: If 15 is not in the answer choice, is the answer to this question "any number that is not a multiple of 10 + multiple of 7"?

So, 37 and 38 would be okay, but 39 no, correct?

KarishmaB · Answer

I am not sure what you mean by "37 and 38 would be okay, but 39 no"

y should be at least 7 and b should be at least 10. So their sum should be at least 17.
The sum could be 18 (y is 8 and b is 10 or y is 7 and b is 11) or it could be 19 or 20 or 37 or 38 or 39. 
If it is 39, y could be 9 and b could be 30. There are no constraints except that the sum should be at least 17 and y should be at least 7 and b should be at least 10.

So a case such as x = 15, y = 9 will give remainder 6 and a = 39 and b = 30 will give remainder 9.

erikvm · Answer

What I meant was that the result cannot be something that is a multiple of 10x + 7y. 37 is the same as 30(3) + 7(1). 38 = 7(4) + 10(1). But there is no way to arrive at 39 with a multiple of 10 + multiple of 7. In other words, my question is: Would the answer to this question be "anything that is not "10x + 7y" or is it simply "x + y must be more than 16?"

Doesnt this question have anything to do with multiples of x and y?

KarishmaB · Answer

Why not? Sum can be 17 or 37 or 38.

It is possible that y = 7 and b = 10.
x = 13, y = 7, remainder of x/y = 6
a = 19, b = 10, remainder of a/b = 9
y + b = 17

Sum 37 is also possible:
It is possible that y = 7 and b = 30.
x = 13, y = 7, remainder of x/y = 6
a = 39, b = 30, remainder of a/b = 9
y + b = 37

etc

erikvm · Answer

Well that kinda enforces my question. All of those options are actually a multiple of 10 + multiple of 7?

37 is the same as 10*3 + 7*1. 
17 is the same as 10*1 + 7*1
38 is the same as 10*1 + 7*4

My question remains; Is anything that is   not   a multiple of 10x + 7y the correct answer?

All the options except 15 is actually a multiple of 10x + 7y

a)24 - same as 7*2 + 10*1
b)21 - same as 7*3 + 10*0
c)20 - same as 7*0 + 10*2
d)17 - same as 10*1 + 7*1
e)15 - No combination of 10x + 7y can give us 15.

So: Is this just a coincidence here, or is the "pattern" to this question? i.e: Could the question stem just as well say "Which of the following answer choices is not a multiple of 10 + multiple of 7?

KarishmaB · Answer

I did show above that a sum of 18 is also possible. 39 is also possible. ANY sum is possible as long as it is more than 16.
So no, the question is not the same as "Which of the following answer choices is not a multiple of 10 + multiple of 7?"
It is the same as "Which of the following is less than 17?"
Every number which is 17 or more can be written as y + b where y is more than 6 and b is more than 9. That is the ONLY constraint.

saukrit · Answer

The remainder is always greater than the divisor. Why?

Let us take a case to understand it: 16/9 has a remainder 7....Can, in any case, be the remainder greater than 9. The answer is an obvious No. But then why does GMAT have to test a concept which is so obvious. The test presents information in such a way that you may never reach a thinking point which was so obvious unless you are already prepared to see it in ways similar to this question.

So here y>6 and b>9 for the above reason. hence y+b>15 .  Hence the answer is E

aanya2000 · Answer

However what if x= 1, y= 6, a= 1, b= 9. It’s now where mentioned that x and a cannot be equal.

Posted from my mobile device

bumpbot · Answer

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x, y, a, and b are positive integers. When x is divided by y

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