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TOUGH DS

by mikepamlyla » Mon Jun 02, 2014 9:52 am
If a, b, and c are positive integers such that a < b < c, is a% of b% of c an integer?

(1) b = (a/100)^(-1)

(2) c = 100^b

I rephrased the original statement to read is abc/10000 an integer?

From statement 1 - ab=100 but don't know c insuff

Statement 2 is insuff, as we don't know a.

1&2 - since ab = 100 for abc/10000 to be an integer, could have to be at least 100. 10000/10000 = 1 an integer.

Ans c. Is this correct ??
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Source: — Data Sufficiency |

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by [email protected] » Mon Jun 02, 2014 10:56 am
Hi mikepamlyla,

You've correctly rephrased the original question, which is good. However, you've missed an important detail while working through this question...

We're told that A, B and C are POSITIVE INTEGERS and A < B < C. We're asked if ABC/10,000 is an integer? This is a YES/NO question.

**Before solving, it's worth noting the type of information that would PROVE that ABC/10,000 was an integer. Knowing all 3 values would be enough to answer the question OR knowing that 1 number was a multiple of 10,000 OR knowing that the product of 2 of the numbers was a multiple of 10,000.

Fact 1: B = (A/100)^-1

This means that B = 100/A

Let's TEST VALUES:
If...
A = 1
B = 100
C = 101
ABC = 10,100 and the answer to the question is NO.

A = 1
B = 100
C = 200
ABC = 20,000 and the answer to the question is YES.
Fact 1 is INSUFFICIENT

Fact 2: C = 100^B

Since A < B < C AND they're all POSITIVE INTEGERS, this means that B >= 2.

If...
B = 2
C = 10,000
A = 1
ABC = 20,000 and the answer to the question is YES. (notice that since C = 10.,000 so it doesn't really matter what A and B are)

B = 3
C = 1,000,000
A = 1 or 2
ABC is a multiple of 10,000 and the answer to the question is YES.

Under this Fact, C will ALWAYS be a multiple of 10,000, so the answer to the question will ALWAYS be YES.
Fact 2 is SUFFICIENT.

Final Answer: B

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by GMATGuruNY » Mon Jun 02, 2014 11:15 am
mikepamlyla wrote:If a, b, and c are positive integers such that a < b < c, is a% of b% of c an integer?

(1) b = (a/100)^(-1)

(2) c = 100^b
Does (a/100) * (b/100) * c = integer?

Test integer values such that a < b < c.

Statement 1: b = (a/100)¯¹
Thus, b = 100/a.

Test the smallest possible value for a.
Case 1: a=1
Here, b =100/1 = 100.
In this case, (a/100) * (b/100) * c = 1/100 * 100/100 * c = c/100.

If c = 200, then c/100 = 2, which is an integer.
If c = 201, then c/100 = 201/100, which is not an integer.
INSUFFICIENT.

Statement 2: c = 100^b
Test the smallest possible value for b.
Case 2: b=2
Here, a=1 and c = 100² = 10000.
In this case, (a/100) * (b/100) * c = 1/100 * 2/100 * 10000 = 2, which is an integer.

Test an extreme value for b.
Case 3: b=100
Here, c = 100¹��.
In this case, (a/100) * (b/100) * c = a/100 * 10/100 * 100¹�� = 10a * 100��, which is an integer.

Cases 2 and 3 illustrate that -- given that c = 100^b -- (a/100) * (b/100) * c will always be equal to an integer value.
SUFFICIENT.

The correct answer is B.
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