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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mikepamlyla
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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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich
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Does (a/100) * (b/100) * c = integer?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
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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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
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