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If x is even and 90<= x <=100,what is the value of x?

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by uptowngirl92 » Fri Jul 17, 2009 3:43 am
If x is even and 90<= x <=100,what is the value of x?
1. x and [fraction]x/2[/fraction] have the same distinct prime factors.
2.[fraction]x/2 has two prime factors[/fraction]
[spoiler=]Ans:c[/spoiler]

Guys my process is very cumbersome and time consuming plus I got jumbled up inbetween?Anyone has a better way and solve my querie?

Given x=even so x can be,90,92,94,96,98,100
Therfore,x/2=45,46,47,48,49,50 respectivly.

From 1,90=2x3x3x5 and 45=3x3x5.ELIMINATE for absence of 2.
92=2x2x23 and 46=2x23.POSSIBLE.
94=2x47 and 47=1x47.ELIMINATE.
Similiarly, we find the pair of 100 and 50 is also possible.
Hence,BCE is left.

From2,92 and 46 and 50 and 100,two pairs satisfy.

Now when we take both the statements combined how do we get the answer?100=2x2x5x5 and 50=2x5x5
50 has two prime factors namely 2 and 5 and both of the nos have the same distinct factors.
Confused!!
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by sreak1089 » Fri Jul 17, 2009 5:06 am
Statement # 1: x and x/2 have distinct prime factors

I see that 92, 96 and 100 each of them have same distinct
prime factors as 46, 48 and 50.
Hence, statement # 1 is NOT sufficient.

Statement # 2: x/2 has two prime factors.

49 (7 x 7) and 46 (2 x 23) satisfy statement # 2.
Hence, statement # 2 is NOT sufficient.

Combining statement # 1 and # 2, we are left with 92 as answer.
Hence C.

PS: I hope I am right :)
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by sreak1089 » Fri Jul 17, 2009 7:13 am
Can anyone validate my reasoning here please?
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by PussInBoots » Sun Jul 19, 2009 10:00 pm
"x/2 has 2 prime factor"
46 has two prime factors: 2 and 23
48 has two prime factors: 2 and 3 (3*2^4)
50 has two prime factors: 2 and 5 (2 * 5^2)

Isn't wording in this problem wrong?
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by kaulnikhil » Sun Jul 19, 2009 10:36 pm
i guess the answer should be E. 92 and 96 satisfy both these condition ....
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by uptowngirl92 » Thu Aug 20, 2009 4:28 pm
The ans in the book is "c"
However,I think there is difference when we say "prime factors" and "distinct prime factors"..can anyone clarify this?
eg,for this problem,combining the two statements:
92=2 * 23>>Two DISTINCT prime factors
96=2*2*2*2*3>>Again 2 and 3 are two prime factors..but are they distinct??Confused:(
100=5*5*2>>same problem as above.
Somebody pls clarify.
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by PAB2706 » Fri Aug 21, 2009 6:45 am
i dnt like the wording of this questions...is this an official question? if yes... no comments.

i guess this is y the answer might be C

we get 3 numbers satifying condition 1

92 prime factors = 23x4 46 = 23x2 (distinct facors are 23 and 2 )

96 prime factors = 3x2^5 48 = 3x2^4 (distinct factors are 2 and 3 )

100 prime factors 5x5x2x2 50 = 5x5x2 ( distinct factors 5 and 2 )

thus insufficient

statement 2 gives us two numbers 49 = 7x7 and 46 = 23x2

now statement 2 tells us that x/2 has two prime factors and stat 1 tells us that two prime factors are distinct...

thus only 23x2 satisfies condition
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by navalpike » Fri Aug 21, 2009 7:13 am
Can you please name the "book" from which you got this question?
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