DS - Topic Factors ; Help needed GMAT around the corner

[soni_pallavi]

Q1)

What is the value of a/b,given that a&b are positive integers

1)a^2 - b^2 = 169

2) a-b = 1

Thanks

[Mike@Magoosh]

Q1) What is the value of a/b,given that a&b are positive integers

1)a^2 - b^2 = 169
2) a-b = 1

I'm happy to help.

With the individual statement, neither can be solved so that you can isolate a value of a/b, so both are insufficient on their own.

When we have both equations, we can solve for the values of a & b, which means we could find a/b if we wanted, so combined, the statements are sufficient.

We know we can solve when we have both equations because we can use the Difference of Squares formula, arguably the GMAT's favorite algebra pattern:

a^2 - b^2 = (a+b)*(a-b)

See https://magoosh.com/gmat/2012/gmat-quant ... o-squares/

Does that make sense?

Mike

[eaakbari]

[eaakbari]

Mike,

Since a^2 - b^2 = 169
implying (a-b)*(a+b) = 169
(a-b)*(a+b) = 13*13

since a & b are integers this leaves only one case of a = 13 and b = 0

Am I right or wrong?


As a general question, when x & y are positive integers, does that imply they are non-zero?

[Mike@Magoosh]

Mike,
Since a^2 - b^2 = 169
implying (a-b)*(a+b) = 169
(a-b)*(a+b) = 13*13

since a & b are integers this leaves only one case of a = 13 and b = 0
Am I right or wrong?

Unfortunately, wrong. You see, if all we have is (a-b)*(a+b) = 169, we can't solve for a & b at all. The fact that we also have a-b=1 means that a+b = 169, and we can solve ---- as it happens, the values are a = 85 and b = 84.

Does that make sense?

As a general question, when x & y are positive integers, does that imply they are non-zero?

Zero is neither positive nor negative. Positive integers are {1, 2, 3, 4, ....} but not zero.

Mike

[Anindya Madhudor]

(a-b)*(a+b)=169 means, either of the following could be true
i. (a-b) * (a+b) = 13 * 13
ii. (a-b) * (a+b) = 1 * 169
So, statement 2 alone is not sufficient

[soni_pallavi]

I would have thought that the answer is C as well ; but the answer given is A, hence the confusion.

[[email protected]]

Took me sometime, but this is what I think -

Keeping in mind that a and b are positive integers.

Option 1) a^2 - b^2 = 169

There can be 3 cases here -
Case I :: (a-b).(a+b) = 1.169
(a-b) = 1 and (a+b) = 169, solving the equation gives a = 85, b = 84. This sounds good as a
and b are also positive integers
Case II :: (a-b).(a+b) = 169.1
(a-b) = 169 and (a+b) = 1, solving the equation gives a = 85, b = -84. This doesn't sound
good as a and b should be positive integers
Case III :: (a-b).(a+b) = 13.13
(a-b) = 13 and (a+b) = 13, solving the equation gives, a = 13, b = 0. This doesn't sound
good as a and b should be positive integers.
So this leaves us with one possibility i.e. Case I which is definite enough to give us a unique ratio of a/b. SUFFICIENT.

Option 2) a-b = 1. Gives us numerous possibilities, hence INSUFFICIENT.

May be thats why I believe, OA is A. Feedback most welcome.

[GMAT Kolaveri]

OA cannot be A. What is the source of this question?

With statement 1 we can get different values for a and b. Hence ST 1 alone is not sufficient.
Combing both we can get a unique values for a and b. So we can get unique value for a/b.

[soni_pallavi]

I agree...the answer should infact be C...

This was on a mock test i took at a GMAT Coaching institute...i'll have to get it checked.