GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 24 Feb 2020, 04:43

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 61440
If y > x, is y > 64 (1) x has 7 factors (all even but one) and is div  [#permalink]

### Show Tags

21 Jan 2020, 03:40
2
5
00:00

Difficulty:

95% (hard)

Question Stats:

37% (02:41) correct 63% (02:32) wrong based on 54 sessions

### HideShow timer Statistics

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

_________________
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 3186
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: If y > x, is y > 64 (1) x has 7 factors (all even but one) and is div  [#permalink]

### Show Tags

21 Jan 2020, 03:50
2
1
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

_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
VP
Joined: 24 Nov 2016
Posts: 1224
Location: United States
If y > x, is y > 64 (1) x has 7 factors (all even but one) and is div  [#permalink]

### Show Tags

21 Jan 2020, 07:21
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)
Director
Joined: 25 Jul 2018
Posts: 564
If y > x, is y > 64 (1) x has 7 factors (all even but one) and is div  [#permalink]

### Show Tags

21 Jan 2020, 11:57
2
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
—> 2y > 128 —> y > 64 (Yes)
Sufficient

Posted from my mobile device
Manager
Joined: 10 Dec 2017
Posts: 178
Location: India
Re: If y > x, is y > 64 (1) x has 7 factors (all even but one) and is div  [#permalink]

### Show Tags

21 Jan 2020, 19:59
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:)
Intern
Joined: 23 Dec 2019
Posts: 4
Re: If y > x, is y > 64 (1) x has 7 factors (all even but one) and is div  [#permalink]

### Show Tags

22 Jan 2020, 04:38
I didn't understand how Statement 2 is sufficient. Could someone post step by step answer
Manager
Joined: 22 Sep 2018
Posts: 67
If y > x, is y > 64 (1) x has 7 factors (all even but one) and is div  [#permalink]

### Show Tags

23 Jan 2020, 06:31
1
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.
If y > x, is y > 64 (1) x has 7 factors (all even but one) and is div   [#permalink] 23 Jan 2020, 06:31
Display posts from previous: Sort by