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Unique Value/Divisibility Question Type

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Unique Value/Divisibility Question Type

by mattnyc15 » Sat Oct 01, 2016 11:04 am
I've seen this question type over and over again throughout various materials.

Here's an example:

Image

My question is have you seen a question on the official GMAT or otherwise that has 2 prime numbers in this question type that is NOT sufficient with a total value? I ask because it takes me forever, up to 3:30 - 4:00 minutes, to solve -- and I'd like to know if and when a total value is introduced in conjunction with two prime values that statement would most always be sufficient?
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by GMATGuruNY » Sat Oct 01, 2016 2:20 pm
If a DS problem is constrained to POSITIVE INTEGERS, we should suspect that one equation with two variables might be sufficient to solve for both variables.

Statement 2:
29c + 17b = 179.
Options for 29c:
29, 58, 87, 116, 145, 174.
Options for 17b:
17, 34, 51, 68, 85, 102, 119, 136, 153, 170.
Only the combination in red will yield a sum of 179.
Thus, 29c = 145, implying that c=5.
SUFFICIENT.

Statement 1:
c ≥ 5.
Since c can be different values, INSUFFICIENT.

The correct answer is B.
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by ceilidh.erickson » Sat Oct 01, 2016 7:32 pm
mattnyc15 wrote: My question is have you seen a question on the official GMAT or otherwise that has 2 prime numbers in this question type that is NOT sufficient with a total value? I ask because it takes me forever, up to 3:30 - 4:00 minutes, to solve -- and I'd like to know if and when a total value is introduced in conjunction with two prime values that statement would most always be sufficient?
No, I have never seen a question like that. I won't swear that you'll never see such a question...

Consider:
I bought $2 apples and $3 oranges and spent a total of $20.
Well, I could have bought 4 apples and 4 oranges for $8 and $12 respectively, or I could have bought 1 apple and 6 oranges for $2 and $18 respectively.

But... it's highly unlikely that the GMAT would do this to you, especially with large numbers. What the GMAT is really testing is whether you'll fall for the assumption that "I always need 2 equations for 2 variables." They want to trick the student who blindly follows the rules and doesn't think. For that reason, it's highly unlikely that they'd ever make you do all of that work to get to the same answer that someone who blindly followed the rule would have gotten to.

So, save yourself the 4:00 min and just bet on a single equation being sufficient, as long as the coefficients don't share any factors.

For another example, see OG2015 DS #132:
Joanna bought only $0.15 and $0.29 stamps. How many $0.15 stamps did she buy?
(1) She bought $4.40 worth of stamps.
(2) She bought the same number of $0.15 and $0.29 stamps.
And for more, see here: https://www.manhattanprep.com/gmat/blog ... ons-rules/
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Harvard Graduate School of Education
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by GMATGuruNY » Sun Oct 02, 2016 3:40 am
An alternate line of reasoning:

Statement 1 indicates that c≥5, implying that the least amount spent on the ink cartridges = 5*29 = 145 and that the next greatest amount = 6*29 = 174.
Statement 2 indicates that the total amount spent = 179.

Clearly, the two statements combined are sufficient to determine that the amount spent on the color cartridges = 145, since 174 is too great.
Eliminate E.

But if the correct answer is C, then virtually every test-taker will answer the question correctly, rendering the question worthless.
Implication:
The correct answer CANNOT be C.

Statement 1 on its own indicates only that c≥5, with the result that c can be any integer value greater than or equal to 5.
Since Statement 1 on its own is clearly insufficient, eliminate A and D.

The correct answer is B.
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