Ay + B = C

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rahulvsd: Master | Next Rank: 500 Posts; Posts: 184; Joined: Tue Sep 07, 2010 9:43 amFollowed by: 1 member; Thanked: 6 times

by rahulvsd » Fri Apr 20, 2012 7:42 am

How many different numbers y are there such that Ay + B = C (A, B, and C are known) ?

1. C > B
2. A >1

[spoiler]OA: B. I found this question weird. Please explain. [/spoiler]

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Source: Beat The GMAT — Data Sufficiency | Fri Apr 20, 2012 7:42 am

aneesh.kg: Master | Next Rank: 500 Posts; Posts: 385; Joined: Mon Apr 16, 2012 8:40 amFollowed by: 29 members; Location: Pune, India; Thanked: 186 times

by aneesh.kg » Fri Apr 20, 2012 11:03 am

Given:
y = (C - B)/A

Statement 1: C - B > 0
which only tells that the numerator of 'y' is positive. Depending on the value of A, y can hold many values.

Statement 2: A > 0
this talks about only the denominator. Based on the values of B and C, y can hold many values.
There is no way (B) could be the correct option.

Let's try to combine the two statements.
Now, y = (positive quantity)/(A quantity greater than 1)

Again, 'y' can hold many values. The question doesn't even say that 'y' has to be an integer.

No conclusive answer. (E) should be correct.

Aneesh Bangia
GMAT Math Coach
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neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

by neelgandham » Fri Apr 20, 2012 12:24 pm

How many different numbers y are there such that Ay + B = C (A, B, and C are known) ?

The question states that the value of y = (C-B)/A. So, if the value of A is not equal to zero, we can say that y =(C-B)/A, a single value. If the value of A is zero, the value of y is undefined and there are infinite/No numbers in the number system that satisfy the equation.

1. C > B

The statement doesn't speak of A or its value, hence the statement is insufficient to answer the question.

2. A > 1

If the value of A is greater than 1, then we know that A is definitely not equal to 0. So, The value of y = (C-B)/A and y has just one value. Therefore the statement is sufficient to answer the question.

IMO B

Anil Gandham
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aneesh.kg: Master | Next Rank: 500 Posts; Posts: 385; Joined: Mon Apr 16, 2012 8:40 amFollowed by: 29 members; Location: Pune, India; Thanked: 186 times

by aneesh.kg » Fri Apr 20, 2012 12:33 pm

I agree with the analysis above.
I didn't note that the values of A,B and C are known, and that's the catch.

Aneesh Bangia
GMAT Math Coach
[email protected]

GMATPad:
Facebook Page: https://www.facebook.com/GMATPad

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