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Princeton Review Practice Test

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Princeton Review Practice Test

by wlvoh » Wed Feb 28, 2007 5:10 pm
Q: In a sequence of 13 consecutive integers, all of which are less than 100, there are exactly 3 multiples of 6. How many integers in the sequence are prime?

1.) Both of the multiples of 5 in the sequence are also multiples of either 2 or 3.

2.) Only one of the two multiples of 7 in the sequence is not also a multiple of 2 or 3.

I believe the answer should be E, however the OA given is C.

Can anybody explain this one to me? Thanks.

wlvoh
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by Argen » Thu Mar 01, 2007 3:03 pm
I agree that the answer should be E. Two sequences that apply to both conditions are 6-18 and 42-54, in which the former has 5 primes and the latter 4. So that would negate the OA answer C.
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by rajesh_ctm » Wed Mar 14, 2007 6:43 pm
Even I think it is E!
6-18 has 4 prime numbers - 7,11,13,17
42-54 has 3 prime numbers - 43,47,53
66-78 has 3 prime numbers - 67,71,73
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by krishnamurthyu » Tue Sep 16, 2008 12:29 pm
Given:
S = ( X1,X2,X3..........X13) All < 100.
There are 3 Multiples of 6. there are 13 Numbers so
X1.......X7......X13 has to be multiples of 6 to accomodate at least 3 multiples out of 13 numbers.
Hence S6 = { (6a),......6(a+1)....6(a+2) } , where a=Positive Integer

How many Prime no.in the S6 set ?

1.Both the munltips of 5 are either multiples of 2 or 3
S6-1={6,7,8,9,10,11,12,13,14,15,16,17,18}
Here 10,15 divisible 2,3 respectively
Next if you start from 12.
S6-2=(12,13,14,15,16,17,18,19,20,21,22,23,24)
Next: (25,30), (30,35) : 25/35 Not divisible by either 2 or 3
like this : Only divisible sets are with
36,.. 40,45...48
66,...70,75...78
So we have 4 sets satisfying this condition.

2.Only one of the 2 multiples of 7 is not multipls of 2 or 3
In S6: multiple of 7 are : 7 and 14, 7 is not multiple of 2 or 3
like this 14,21 : hence not valid multiple of 2 or 3

3) 1 and 2
From 1)
S6-1=6...18
S6-2=12...24
S6-3=36...48
S6-4=66....78
From 2)
S6-2 : 14,21 divisble by 2,3 respectively,Hence is not valid
S6-3 : 42 : is only 1 Number as per condition 2) there are 2 numbers of 7 hence not valid.
S6-4:70,77
70 is Multiple of 2, but not 3
77 is not multiple of both 2 and 3
As per condition only one Num is not multiple of 2 or 3 here 70,77 i,e 2 numbers are not multiple of 3. Hence S6-4 is invalid.
S6-1 is the Only set ,No of Prime in this is (7,11,13,17) = 4. Ans

C


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by Ian Stewart » Tue Sep 16, 2008 12:58 pm
This question came up recently, and I posted a solution near the end of this thread:

www.beatthegmat.com/please-help-me-t17777.html
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