Better Solution than what GMAT Provides? (2 questions)

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Hello, I am doing the MGMAT study guide and the way the official guide describes how these 2 questions below are done are not consistent with methods taught by MGMAT. I was wondering if there was an easier way?

D13. If s and t are positive integers such that s/t = 64.12, which of the following could be a remainder when s is divided by t?

a. 2
b. 4
c. 8
d. 20
e. 45

D15. THe product of all the prime numbers less than 20 is closest to which of the following powers of 10?

a. 10^9
b. 10^8
c. 10^7
d. 10^6
e. 10^5

the official guide for this 2nd problem says to multiply 2,3,5,7,11,13,17 and 19. Surely we do not have that much time on the actual exam. Is there another way?
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by Anurag@Gurome » Mon Jan 30, 2012 10:40 pm
fangtray wrote:Hello, I am doing the MGMAT study guide and the way the official guide describes how these 2 questions below are done are not consistent with methods taught by MGMAT. I was wondering if there was an easier way?

D13. If s and t are positive integers such that s/t = 64.12, which of the following could be a remainder when s is divided by t?

a. 2
b. 4
c. 8
d. 20
e. 45
We know that dividend = quotient * divisor + remainder
Here, let us assume that quotient = q and remainder = r. Given, dividend = s and divisor = t
So, s = q * t + r or s/t = q + r/t, where 0 ≤ r/t < 1
So, 64.12 = 64 + 12/100
or 64.12 = 64 + 3/25
This implies r/t = 3/25 or 25r = 3t, where r should be a multiple of 3 so that the remainder evenly divides 3t. From the given answer choices, 45 is the only integer that is a multiple of 3.

The correct answer is E.
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by Anurag@Gurome » Mon Jan 30, 2012 10:57 pm
fangtray wrote:Hello, I am doing the MGMAT study guide and the way the official guide describes how these 2 questions below are done are not consistent with methods taught by MGMAT. I was wondering if there was an easier way?
D15. THe product of all the prime numbers less than 20 is closest to which of the following powers of 10?

a. 10^9
b. 10^8
c. 10^7
d. 10^6
e. 10^5

the official guide for this 2nd problem says to multiply 2,3,5,7,11,13,17 and 19. Surely we do not have that much time on the actual exam. Is there another way?
We can regroup the numbers, 2, 3, 5, 7, 11, 13, 17, and 19, to multiply them.
2 * 3 * 5 * 7 * 11 * 13 * 17 * 19
= (2 * 5) * (3 * 7) * 11 * 13 * 17 * 19
= 10 * 21 * 11 * 13 * 17 * 19

Now approximating, we get 10 * 20 * 10 * 10 * 20 * 20 = 8 * 10^6, which is 10^7 appr.

The correct answer is C.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
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by GMATGuruNY » Tue Jan 31, 2012 7:47 am
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