If a^2b^2c^3 = 4500. Is b + c = 7?

hey... thanks
this is what i answered... but the correct answer is E...
i need an explanation.......
if it is E, then y so....

4500 = (2²)(3²)(5³) = (a²)(b²)(c³)
Comparing the terms we see that, c = 5
But a and b can have different sets of values.

1. a = ±2, b = ±3
2. a = ±3, b = ±2
3. a = ±1, b = ±6
4. a = ±6, b = ±1

Statement 1: a, b and c are positive integers
Hence, we should discard the negative values of a and b. Still we have four possible sets of values for a and b,

1. a = 2, b = 3
2. a = 3, b = 2
3. a = 1, b = 6
4. a = 6, b = 1

Thus (b + c) can have different possible values.

Not sufficient

Statement 1: a > b
Hence, we should discard the values of a and b such that a < b. Still we have different sets of values for a and b,

1. a = ±2, b = -3
2. a = 3, b = ±2
3. a = ±1, b = -6
4. a = 6, b = ±1

Thus (b + c) can have different possible values.

Not sufficient

1 & 2 Together : Still we can have two different sets of values for a and b,

1. a = 3, b = 2
2. a = 6, b = 1

Thus (b + c) can be equal to either 6 or 7.

Not sufficient

If a^2b^2c^3 = 4500. Is b+c = 7 ?
(1) a, b and c are positive integers
(2) a > b

2^23^25^3 = 4500 and from statement 1 and 2, it can be deduced that b=2, c=5 and b+c =7, why the answer is E, shouldn't it be C?

a,b and c don't have to be prime.
a=6 and b=1 will also satisfy the 2 statements alone and b+c=1+5 = 6. insuff together. hence E

Good question....But is GMAC really expecting us to figure that out in a span of 2 min???

yes...such questions may very well appear in the actual GMAT

Seriouslly very good question. Even after looking at the anwer I was not able to figure out how this can be possible.
I thought about this and realised how our mind works in one direction. As it has been so well trained to do the prime factors as soon as you see any problem like this. It can not think any other situation.

Thanks for posting such question which can break the mindset.

fantastic problem, but i got stumped.. i selected C as the answer and now i understand why the answer is E

Great question! Fell in to the trap and picked C. E makes perfect sense.

Hi All,

We're told that (A^2)(B^2)(C^3) = 4500. We're asked if B+C = 7. This is a YES/NO question. This question really tests the 'thoroughness' of your thinking - and it's likely that many Test Takers would get this question wrong because they wouldn't consider all of the possible options.

To start, it would help to 'break down' 4500 into pieces...
4500 = (9)(500) =
(3^2)(5)(100) =
(3^2)(5)(2^2)(5^2) =
(2^2)(3^2)(5^3)

Based on the starting equation, we know that C MUST be +5. However, there are more than just these two possible values for A and B. Since we're SQUARING terms, A and B could be (2 or -2) and (3 or -3). In addition, this question is NOT forcing us to deal with Prime Numbers, so there is another option besides "2 and 3" to consider.... "1 and 6" is another possible pairing of values for A and B....
(1^2)(6^2)(5^3)
...meaning that we would have to also consider that the values could be (1 or -1) and (6 or -6):

(1) A, B and C are POSITIVE integers

IF....
A=2, B=3, C=5 then the answer to the question is NO
A=3, B=2, C=5 then the answer to the question is YES
Fact 1 is INSUFFICIENT

2) A > B
A=3, B=2, C=5 then the answer to the question is YES
A=6, B=1, C=5 then the answer to the question is NO
Fact 2 is INSUFFICIENT

Combined, we already have two groups of values that fit both Facts and produce different answers to the given question:
A=3, B=2, C=5 then the answer to the question is YES
A=6, B=1, C=5 then the answer to the question is NO
Combined, INSUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,
Rich

Explanation:

Given a2 b2 c3 = 4500
⇒ a2 b2 c3 = 22 32 53
⇒ a = ±2, b = ±3 and c = 5
or a = ±3, b = ±2 and c = 5
or a = ±1, b = ±6 and c = 5
or a = ±6, b = ±1 and c = 5
or a, b and c can be decimal numbers.

Considering statement 1:
a, b and c are positive integers
⇒ a = 2, b = 3 and c = 5
or a = 3, b = 2 and c = 5
⇒ b + c = 8 or 7 (depending whether a = 2 or 3, respectively)
Since we are not getting a definite answer from above statement , statement 1 itself is not sufficient to provide the answer.

Considering statement 2:
a > b
Let us consider 4 possible values of a (2, −2, 3 and −3):
If we consider a = 2, then b has to be −3 (since statement 2 says a > b). Also, c = 5 ⇒ b + c = 2.
If we consider a = −2, then b has to be −3 (since statement 2 says a > b). Also, c = 5 ⇒ b + c = 2.
If we consider a = 3, then b may be 2 or −2 (in both cases, a > b). Also, c = 5 ⇒ b + c = 7 or 3.
And if we consider a = −3, then no possible value of b satisfies a > b.
Hence, b + c may be either 2 or 7 or 3. ⇒ b + c may or may not be 7.
Further, if a, b and c are decimals then there are infinite combinations of b and c.
Since we are not getting a definite answer from above statement , statement 2 also itself is not sufficient to provide the answer.

Considering statement 1 and 2 both:
Statement 1 gives: b = 1, 2, 3 or 6
Statement 2 gives: b = 1 or 2 or some decimal number.

Hence, the value of b + c can be 6 or 7.

Since we are not getting a definite answer from combination of statements 1 and 2.

Answer: E.

I think, I deserve a Kudus :D Lol

it's a hard question. easy to ommit the case of 1!
it didn't mention a,b,c are primes

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.