**Economist GMAT**

If \(a, b\), and \(c\) are integers, what is the value of \(a\)?

1) \(2^a+2^b=33\)

2) \(a\cdot c = 5\)

OA C

- ceilidh.erickson
- GMAT Instructor
**Posts:**2094**Joined:**04 Dec 2012**Thanked**: 1443 times**Followed by:**242 members

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**A**

**B**

**C**

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**E**

If \(a, b\), and \(c\) are integers, what is the value of \(a\)?

We're given no information in the question stem except that these variables are integers. So, we have to dive into the statements:

(1) \(2^a+2^b=33\)

Think of combinations of powers of 2 that would add to 33. Since 33 is odd, it must be (odd + even) or (even + odd). The only power of 2 that's odd is \(2^0=1\) .

\(2^0+2^5=1+32=33\)

We know that one of these values must be 0 and the other 5, but we don't know which is which. Insufficient.

(2) \(a\cdot c = 5\)

If both of these are integers, it must be 1*5 or 5*1. Since we don't know which is which, though, this is insufficient.

(1) and (2) together:

(1) tells us that \(a=0\) or \(a=5\), and (2) tells us that \(a=1\) or \(a=5\). Using the statements together, it must be the case that \(a=5\). Sufficient.

The answer is C.

We're given no information in the question stem except that these variables are integers. So, we have to dive into the statements:

(1) \(2^a+2^b=33\)

Think of combinations of powers of 2 that would add to 33. Since 33 is odd, it must be (odd + even) or (even + odd). The only power of 2 that's odd is \(2^0=1\) .

\(2^0+2^5=1+32=33\)

We know that one of these values must be 0 and the other 5, but we don't know which is which. Insufficient.

(2) \(a\cdot c = 5\)

If both of these are integers, it must be 1*5 or 5*1. Since we don't know which is which, though, this is insufficient.

(1) and (2) together:

(1) tells us that \(a=0\) or \(a=5\), and (2) tells us that \(a=1\) or \(a=5\). Using the statements together, it must be the case that \(a=5\). Sufficient.

The answer is C.

Ceilidh Erickson

Manhattan Prep GMAT & GRE instructor

EdM in Mind, Brain, and Education

Harvard Graduate School of Education

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- Ian Stewart
- GMAT Instructor
**Posts:**2583**Joined:**02 Jun 2008**Location:**Toronto**Thanked**: 1090 times**Followed by:**354 members**GMAT Score:**780

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Just because this is so important in so many questions: if ac = 5, and a and c are integers, there are four possibilities, not two: a and c can be 5 and 1, in either order, or they can be -5 and -1, in either order.ceilidh.erickson wrote: (2) \(a\cdot c = 5\)

If both of these are integers, it must be 1*5 or 5*1. Since we don't know which is which, though, this is insufficient.

Of course, when we combine the two statements, we can discard the negative solutions, but from Statement 2 alone, we have four possible values of a.

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

- ceilidh.erickson
- GMAT Instructor
**Posts:**2094**Joined:**04 Dec 2012**Thanked**: 1443 times**Followed by:**242 members

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Ian has an excellent point here! The question doesn't specify non-negative. I think this shows how we all really synthesize before we extrapolate - after reading statement 1, when I read statement 2 I immediately thought "well a=5, but I don't know that from this one alone" and didn't further pick apart what I already knew to be insufficient. But Ian's point is important - we can't assume a non-negative constraint where none is specified.Ian Stewart wrote:Just because this is so important in so many questions: if ac = 5, and a and c are integers, there are four possibilities, not two: a and c can be 5 and 1, in either order, or they can be -5 and -1, in either order.ceilidh.erickson wrote: (2) \(a\cdot c = 5\)

If both of these are integers, it must be 1*5 or 5*1. Since we don't know which is which, though, this is insufficient.

Of course, when we combine the two statements, we can discard the negative solutions, but from Statement 2 alone, we have four possible values of a.

Ceilidh Erickson

Manhattan Prep GMAT & GRE instructor

EdM in Mind, Brain, and Education

Harvard Graduate School of Education

Manhattan Prep instructors all have 99th+ percentile scores and expert teaching experience.

Sign up for a FREE TRIAL, and learn why we have the highest ratings in the GMAT industry!