Is GMATPrep wrong or am I wrong?

[WilliamGCash]

I just took the GMATPrep CAT 2 yesterday and in reviewing my answers today I came across 2 questions on the Quant that I don't get how I'm wrong.

I'll try to post screen shots of the actual questions, but I'll type them out too...

Here's the first one:
It is a data suff question regarding "a certain list of integers". The question is "Is the product of all of the integers positive?"

(1) The product of the greatest and smallest integer is positive.
(2) There is an even number of integers in the list.



Now, my thought process is/was for (1) that if the product of greatest and smallest integer in the list is positive, then both the greatest and smallest integer must have the same sign.... and if the greatest and smallest integer have the same sign, then all the numbers between them have the same sign. If all of the numbers have the same sign, then the product of all of the numbers would be positive.... therefore, this is Sufficient.

(2) Insufficient, whether there is an even even number of integers or an odd number doesn't matter if we know nothing about the signs of the numbers involved.

So... how did I get this wrong? Why does the GMATPrep CAT believe that the answer is BOTH are necessary?

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Here's the other question:

This one is a problem solving question asking for the greatest prime factor of (4^17)-(2^28)



Again, my logic: (4^17)=(2^34)....
(2^34)-(2^28) = (2^6)
(2^6) = 2 x 2 x 2 x 2 x 2 x 2 = 64, so the greatest prime factor is 2. Simple, right?

GMATPrep says its 7? WTF?!?


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Somebody let me know if I'm missing something here.....

[pellucide]

Let me take a stab at it.

I just took the GMATPrep CAT 2 yesterday and in reviewing my answers today I came across 2 questions on the Quant that I don't get how I'm wrong.

I'll try to post screen shots of the actual questions, but I'll type them out too...

Here's the first one:
It is a data suff question regarding "a certain list of integers". The question is "Is the product of all of the integers positive?"

(1) The product of the greatest and smallest integer is positive.
(2) There is an even number of integers in the list.



Now, my thought process is/was for (1) that if the product of greatest and smallest integer in the list is positive, then both the greatest and smallest integer must have the same sign.... and if the greatest and smallest integer have the same sign, then all the numbers between them have the same sign. If all of the numbers have the same sign, then the product of all of the numbers would be positive.... therefore, this is Sufficient.

(2) Insufficient, whether there is an even even number of integers or an odd number doesn't matter if we know nothing about the signs of the numbers involved.

So... how did I get this wrong? Why does the GMATPrep CAT believe that the answer is BOTH are necessary?

1) You are right. Both the greatest and smallest integer must have the same sign. Which means all the integers in that set have same sign. Therefore, if all the intergers are all positive, then their product will be positive. However, if they are all negative, then we have to know the number of integers in the set to see if their product is positive or negative. If the number of intergers is Odd, their product will be negative. If the number of intergers is Even, then their product will be positive.
Examples:
i. Consider the set { 1, 3, 6,9}. The product of the greatest and smallest integer is 1 * 9 = 9 --> Positive. The product of all the integers in this set is 1 * 3 * 6 * 9 = 162 --> also positive.
ii. Consider the set {-9, -8, -6, -3} consisting of even number of negative integers. The product of the greatest and smallest integer is -3 * -9 = 27 --> Positive. The product of all the integers in this set is -9 * -8 * -6 * -3 = 1296 --> also positive.
iii. Consider the set {-9, -8, -6, -5, -3} consisting of odd number of negative integers. The product of the greatest and smallest integer is -3 * -9 = 27 --> Positive. However, The product of all the integers in this set is -9 * -8 * -6 * -5 * -3 = -6480, --> negative
So INSUFFICIENT.

(2) whether there is an even even number of integers or an odd number doesn't matter if we know nothing about the signs of the numbers involved. INSUFFICIENT

1) + 2) From the above discussion, we can see this belongs to the example type iii) So the prduct will always be positive. SUFFICIENT

-----------------------------------
Here's the other question:

This one is a problem solving question asking for the greatest prime factor of (4^17)-(2^28)



Again, my logic: (4^17)=(2^34)....
(2^34)-(2^28) = (2^6)
(2^6) = 2 x 2 x 2 x 2 x 2 x 2 = 64, so the greatest prime factor is 2. Simple, right?

GMATPrep says its 7? WTF?!?
----------------------------------------------------

Somebody let me know if I'm missing something here.....

(2^34)-(2^28) = 2^28(2^6 -1) = 2^28 * 63 = 2^28 * 9 * 7 = 2^28 * 3^2 * 7.
So the greatest prime factor is 7

[WilliamGCash]

Oh. Wow.

I see them both now.

Definitely need to work on exponents.

Sheesh. I take the GMAT in 2 days too. I guess its hard/impossible to have everything mastered.

[Brian@VeritasPrep]

Hey William,

That second question is pretty popular around here - I wrote on it just the other day so let me attach that here, too:


https://www.beatthegmat.com/greatest-pri ... tml#318444


You mention that you need to work on exponents - I'd highly recommend checking out our 5-day Exponent Challenge series that Veritas Prep did with BTG about a month ago. You'll see that really all exponent problems can be solved with 3 guiding principles:


1. Exponent rules are almost all related to multiplication and division with virtually no rules that directly apply to addition and subtraction. When facing exponent problems, look for opportunities to factor and multiply to put yourself in a position to use your multiplication-heavy exponent expertise.

2. Most exponent rules require you to have common bases in order to apply them, so look to break down bases into prime factors so that you have common bases with which to work.

3. Exponents are very pattern-driven, so when large numbers are present you can often establish a rule using small numbers and then extrapolate it to the larger ones.


https://www.beatthegmat.com/mba/2010/10/ ... nal-answer