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If y > x, is y > 64 (1) x has 7 factors (all even but one) and is div

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Bunuel
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If y > x, is y > 64 (1) x has 7 factors (all even but one) and is div [#permalink] New post   21 Jan 2020, 04:40
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34% (02:40) correct 66% (02:37) wrong based on 139 sessions
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If y > x, is y > 64

(1) x has 7 factors (all even but one) and is divisible by only one prime number.
(2) |y - 64| > |x - 64|


Are You Up For the Challenge: 700 Level Questions
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D
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Re: If y > x, is y > 64 (1) x has 7 factors (all even but one) and is div [#permalink] New post   21 Jan 2020, 04:50
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Bunuel wrote:
If y > x, is y > 64?

(1) x has 7 factors (all even but one) and is divisible by only one prime number.
(2) |y - 64| > |x - 64|


Are You Up For the Challenge: 700 Level Questions



Given: y > x

Question : is y > 64?

Statement 1: x has 7 factors (all even but one) and is divisible by only one prime number.

i.e. \(x = 2^6 = 64\) which is the only possible value of x

P.S. 2^6 has 7 factors {1, 2, 4, 8, 16, 32, 64} only one odd rest all even factors

and y > x therefore y > 64

SUFFICIENT

Statement 2: |y - 64| > |x - 64|

DIstance between y and 64 is Greater than distance between x and 64 and Y is to the right of x on number line because y > x therefore

y must be to the right of 64 and x must be somewhere between y and 64

SUFFICIENT

Answer: Option D
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If y > x, is y > 64 (1) x has 7 factors (all even but one) and is div [#permalink] New post   21 Jan 2020, 08:21
Bunuel wrote:
If y > x, is y > 64

(1) x has 7 factors (all even but one) and is divisible by only one prime number.
(2) |y - 64| > |x - 64|



(1) x has 7 factors (all even but one) and is divisible by only one prime number. sufic

num.f(x)=7 (all even except one); x=prime^6=2^6=64; y>64.

(2) |y - 64| > |x - 64| sufic

y-64≥0…y≥64; x-64≥0…x≥64
---(-)--(-)---64----+--+---
x,y<64: -(y-64)>-(x-64)…-y+x>0…x>y=false;
x,y≥64: (y-64)>(x-64)…y-x>0…y>x=true; y>64.

Ans (D)
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If y > x, is y > 64 (1) x has 7 factors (all even but one) and is div [#permalink] New post   21 Jan 2020, 12:57
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If y > x, is y > 64 ?

(Statement1): x has 7 factors (all even but one) and is divisible by only one prime number.

\(a^{6}\) —> (6+1)= 7 factors
—> a should be prime number and even number at the same time—> 2 could be prime and even
\(x= 2^{6} = 64\) —> y >64 (yes)
Sufficient

(Statement2): |y - 64| > |x - 64|
—> square both sides
\((y—64)^{2} > (x—64)^{2}\)

\(y^{2} —128y+ 64^{2} > x^{2} —128x+64^{2} \)
\(y^{2}—128y > x^{2} —128x\)
(y—x)( y+x) —128(y—x) > 0
(y—x)(y+x—128) >0

Given that y—x >0, then —> y+x—128 >0
—> y+x >128

Now, we have two inequalities:
y—x > 0
y+x >128
By adding together:
—> 2y > 128 —> y > 64 (Yes)
Sufficient

The answer is D

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Re: If y > x, is y > 64 (1) x has 7 factors (all even but one) and is div [#permalink] New post   21 Jan 2020, 20:59
Bunuel wrote:
If y > x, is y > 64

(1) x has 7 factors (all even but one) and is divisible by only one prime number.
(2) |y - 64| > |x - 64|


Are You Up For the Challenge: 700 Level Questions

From 1
X=2^6=total 7 factors ( 6+ 1)
X=64
since Y>X
Y>64
Sufficient
From 2
Y>X
so Y-64>X-64( we can add or subtract in inequality)
and lY-64l>lX-64l
for this to be true Y>64
Sufficient
D:)
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Re: If y > x, is y > 64 (1) x has 7 factors (all even but one) and is div [#permalink] New post   22 Jan 2020, 05:38
I didn't understand how Statement 2 is sufficient. Could someone post step by step answer
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If y > x, is y > 64 (1) x has 7 factors (all even but one) and is div [#permalink] New post   23 Jan 2020, 07:31
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ayushsaxena04 wrote:
I didn't understand how Statement 2 is sufficient. Could someone post step by step answer


if using step process , here how it works

consider what is given in the question , y > x

consider both mods give negative value ie , . suppose y < 64 and X < 64, you get

-(y-64)>-(x-64)
-y+64 > -x+ 64

ie X > Y , but this contradicts with condition given in the question iteself, so in statement 2 consider Y>64 and solve you again get Y > X . so you can say Y>64.
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Re: If y > x, is y > 64 (1) x has 7 factors (all even but one) and is div [#permalink] New post   05 Nov 2022, 08:41
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Re: If y > x, is y > 64 (1) x has 7 factors (all even but one) and is div [#permalink]
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