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EXERCISES FROM GMAT PREP- NEED SOME HELP!!

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by bobdylan » Wed Apr 04, 2012 11:13 am
1) What is the greatest prime number of 4^17 - 2^28?
a) 2
b)3
c)5
d)7
e)11

2)If N denotes a number to the left of the number line such that the square of N is less than 1/100, then the reciprocal must be.....


Thanks!
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by Pharo » Wed Apr 04, 2012 12:13 pm
Q1:

Let's rewrite that equation.

q = 4^17 - 2^28
= (2^2)^17 - 2^28
= 2^34 - 2^28
= (2^28) * ((2^6) - 1)
= (2^28) * (64-1)
= (2^28) * (63)
= (2^28) * (7 * 3 * 3)

; hence the answer is D :)
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by Pharo » Wed Apr 04, 2012 12:34 pm
Q2:

What are you asking exactly? Or rather, what are the options? An answer to this question can be "negative" (i.e. "then the reciprocal must be negative") or "less then -10".
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by GMATGuruNY » Wed Apr 04, 2012 2:17 pm
If n denotes a number to the left of 0 on the number line such that the square of n is less than 1/100, then the reciprocal of n must be

A. less than -10
B. between -1 and -1/10
C. between -1/10 and 0
D. between 0 and -1/10
E. greater than 10
Let n = -1/20.
This works because (-1/20)² = 1/400, and 1/400 < 1/100.
The reciprocal of n = -20.

Only answer choice A works:
-20 is less than -10.

The correct answer is A.
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by Anurag@Gurome » Wed Apr 04, 2012 6:47 pm
bobdylan wrote:1) What is the greatest prime number of 4^17 - 2^28?
a) 2
b)3
c)5
d)7
e)11

Thanks!
4^17 - 2^28
= (2²)^17 - 2^28
= 2^34 - 2^28
= 2^28(2^6 - 1)
= 2^28(63)
= 2^28(7 * 3^2)

Therefore, the greatest prime factor of 4^17 - 2^28 is 7.

The correct answer is D.
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by Anurag@Gurome » Wed Apr 04, 2012 6:49 pm
bobdylan wrote: 2)If N denotes a number to the left of the number line such that the square of N is less than 1/100, then the reciprocal must be.....


Thanks!
n is to the left of 0 on the number line, i.e. n < 0
As n² < 1/100, n lies between -1/10 and 1/10

Hence, -1/10 < n < 0
--> 1/n < -10
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