It is currently 18 Nov 2017, 14:59

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If 20x = 49y, which of the following must be true?

Author Message
TAGS:

### Hide Tags

Board of Directors
Joined: 01 Sep 2010
Posts: 3372

Kudos [?]: 9279 [0], given: 1168

If 20x = 49y, which of the following must be true? [#permalink]

### Show Tags

01 Jan 2013, 14:59
4
This post was
BOOKMARKED
00:00

Difficulty:

85% (hard)

Question Stats:

29% (00:29) correct 71% (00:59) wrong based on 80 sessions

### HideShow timer Statistics

If 20x = 49y, which of the following must be true?

I. x > y

II. x^2 > y^2

III. x/7 is an integer

A) I only
B) II only
C) III only
D) I and III
E) I, II, and III
[Reveal] Spoiler: OA

_________________

Last edited by Bunuel on 02 Jan 2013, 04:31, edited 2 times in total.
Edited the question, the tags and moved to PS forum.

Kudos [?]: 9279 [0], given: 1168

Senior Manager
Joined: 31 Oct 2011
Posts: 484

Kudos [?]: 223 [0], given: 57

Schools: Johnson '16 (M)
GMAT 1: 690 Q45 V40
WE: Asset Management (Mutual Funds and Brokerage)
Re: If 20x = 49y, which of the following must be true? [#permalink]

### Show Tags

01 Jan 2013, 15:10
I'd plug in numbers here. Try the weird ones i.e. 0, -1, 1/2, etc. as it does not note that x or y are integers.

Plugging in 0, We find that statement 1 and 2 are false. Looking at what is left, the solution must be C, Statement III is correct since there is no answer for "None of the above".

Good question, what is the source?
_________________

My Applicant Blog: http://hamm0.wordpress.com/

Kudos [?]: 223 [0], given: 57

Board of Directors
Joined: 01 Sep 2010
Posts: 3372

Kudos [?]: 9279 [1], given: 1168

Re: If 20x = 49y, which of the following must be true? [#permalink]

### Show Tags

01 Jan 2013, 16:05
1
KUDOS
hi Hamm0

As you can see is Veritas prep.

I attacked the question in that way tell me if is correct

$$20x = 49y$$

$$20$$ $$=$$ $$2^2$$ $$*5$$

$$49$$ $$=$$ $$7^2$$

so basically we would have the second one in the LHS and viceversa to balance the equation $$BUT$$ we should consider also 0 because 0=0 so is equal ( but of course)

1)$$x > y$$true not always $$7^2$$$$>$$ $$2^2$$ $$*5$$ but we have also zero so x > y is not true

2) $$x^2$$ $$>$$ $$y^2$$ we know that x and y are always positive so basically we can reduce the second statement to $$x > y$$ and we know already insuff

3)$$\frac{x}{7}$$ $$= integer$$ yes $$\frac{7^2}{7}$$= $$integer$$always

C is correct
_________________

Kudos [?]: 9279 [1], given: 1168

Senior Manager
Joined: 31 Oct 2011
Posts: 484

Kudos [?]: 223 [1], given: 57

Schools: Johnson '16 (M)
GMAT 1: 690 Q45 V40
WE: Asset Management (Mutual Funds and Brokerage)
Re: If 20x = 49y, which of the following must be true? [#permalink]

### Show Tags

01 Jan 2013, 16:21
1
KUDOS
carcass wrote:
hi Hamm0

As you can see is Veritas prep.

I attacked the question in that way tell me is correct

$$20x = 49y$$

$$20$$ $$=$$ $$2^2$$ $$*5$$

$$49$$ $$=$$ $$7^2$$

so basically we would have the second one in the LHS and viceversa to balance the equation $$BUT$$ we should consider also 0 because 0=0 so is equal ( but of course)

1)$$x > y$$true not always $$7^2$$$$>$$ $$2^2$$ $$*5$$ but we have also zero so x > y is not true

2) $$x^2$$ $$>$$ $$y^2$$ we know that x and y are always positive so basically we can reduce the second statement to $$x > y$$ and we know already insuff

3)$$\frac{x}{7}$$ $$= integer$$ yes $$\frac{7^2}{7}$$= $$integer$$always

C is correct

A quick glance over says that is correct. Just a different approach. Often the GMAT will do this - offer several ways to solve a problem. No brownie points for doing the more difficult, so if you recognize it, go with whichever you're faster/more comfortable.
_________________

My Applicant Blog: http://hamm0.wordpress.com/

Kudos [?]: 223 [1], given: 57

Board of Directors
Joined: 01 Sep 2010
Posts: 3372

Kudos [?]: 9279 [0], given: 1168

Re: If 20x = 49y, which of the following must be true? [#permalink]

### Show Tags

01 Jan 2013, 16:26
hamm0 wrote:
carcass wrote:
hi Hamm0

As you can see is Veritas prep.

I attacked the question in that way tell me is correct

$$20x = 49y$$

$$20$$ $$=$$ $$2^2$$ $$*5$$

$$49$$ $$=$$ $$7^2$$

so basically we would have the second one in the LHS and viceversa to balance the equation $$BUT$$ we should consider also 0 because 0=0 so is equal ( but of course)

1)$$x > y$$true not always $$7^2$$$$>$$ $$2^2$$ $$*5$$ but we have also zero so x > y is not true

2) $$x^2$$ $$>$$ $$y^2$$ we know that x and y are always positive so basically we can reduce the second statement to $$x > y$$ and we know already insuff

3)$$\frac{x}{7}$$ $$= integer$$ yes $$\frac{7^2}{7}$$= $$integer$$always

C is correct

A quick glance over says that is correct. Just a different approach. Often the GMAT will do this - offer several ways to solve a problem. No brownie points for doing the more difficult, so if you recognize it, go with whichever you're faster/more comfortable.

I asked here because I was not sure (better i'm sure at 99% ) in particular on statement 2.

But if you said ok ...many Thanks
_________________

Kudos [?]: 9279 [0], given: 1168

Director
Joined: 17 Dec 2012
Posts: 623

Kudos [?]: 534 [0], given: 16

Location: India
Re: If 20x = 49y, which of the following must be true? [#permalink]

### Show Tags

01 Jan 2013, 16:42
carcass wrote:
If 20x = 49y, which of the following must be true?

I. $$x > y$$

II. $$x^2 > y^2$$

III. $$x/7$$ is an integer

A) I only
B) II only
C) III only
D) I and III
E) I, II, and III

We have 20x=49y
or x = 49y/20

I need not be true because x is greater than y only when y is positive.

II need not be true because both x and y can be zero. This applies to I also.

III also need not be true because x/7 =49y/140 = 7y/20.
We can see that x/7 need not be an integer as for example in the case of y=1.
_________________

Srinivasan Vaidyaraman
Sravna
http://www.sravnatestprep.com/regularcourse.php

Standardized Approaches

Kudos [?]: 534 [0], given: 16

Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132612 [6], given: 12326

Re: If 20x = 49y, which of the following must be true? [#permalink]

### Show Tags

02 Jan 2013, 04:49
6
KUDOS
Expert's post
carcass wrote:
If 20x = 49y, which of the following must be true?

I. x > y

II. x^2 > y^2

III. x/7 is an integer

A) I only
B) II only
C) III only
D) I and III
E) I, II, and III

This is a flawed question. None of the options must be true.

Notice that 20x = 49y holds true if x=y=0, thus I and II are not always true.

As for III: if x=1 and y=20/49, then x/7 won't be an integer.

If the question were:
If x and y are integers and 20x = 49y, which of the following must be true?

Then in this case III would be always true: RHS is a multiple of 7, thus LHS must also be a multiple of 7 and since 20 is not a multiple of 7, then x must be.

Hope it's clear.
_________________

Kudos [?]: 132612 [6], given: 12326

Board of Directors
Joined: 01 Sep 2010
Posts: 3372

Kudos [?]: 9279 [0], given: 1168

Re: If 20x = 49y, which of the following must be true? [#permalink]

### Show Tags

02 Jan 2013, 05:31
Bunuel wrote:
carcass wrote:
If 20x = 49y, which of the following must be true?

I. x > y

II. x^2 > y^2

III. x/7 is an integer

A) I only
B) II only
C) III only
D) I and III
E) I, II, and III

This is a flawed question. None of the options must be true.

Notice that 20x = 49y holds true if x=y=0, thus I and II are not always true.

As for III: if x=1 and y=20/49, then x/7 won't be an integer.

If the question were:
If x and y are integers and 20x = 49y, which of the following must be true?

Then in this case III would be always true: RHS is a multiple of 7, thus LHS must also be a multiple of 7 and since 20 is not a multiple of 7, then x must be.

Hope it's clear.

I perfectly understand what you say. Something it was not unclear to me either.

Though, my primary question was is me approach was correct generally speaking.

Thanks,

Regards
_________________

Kudos [?]: 9279 [0], given: 1168

Manager
Joined: 02 Sep 2012
Posts: 244

Kudos [?]: 226 [0], given: 99

Location: United States
Concentration: Entrepreneurship, Finance
GMAT Date: 07-25-2013
GPA: 3.83
WE: Architecture (Computer Hardware)
f 20x = 49y, which of the following must be true? [#permalink]

### Show Tags

04 May 2013, 20:22
If 20x = 49y, which of the following must be true?

I. x > y
II. x^2 > y^2
III. x/7 is an integer

A)I only
B)II only
C) III only
D)I and III
E)I, II, and III

OA after some discussion
_________________

"Giving kudos" is a decent way to say "Thanks" and motivate contributors. Please use them, it won't cost you anything

Kudos [?]: 226 [0], given: 99

Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 627

Kudos [?]: 1386 [0], given: 136

Re: f 20x = 49y, which of the following must be true? [#permalink]

### Show Tags

04 May 2013, 22:49
skamal7 wrote:
If 20x = 49y, which of the following must be true?

I. x > y
II. x^2 > y^2
III. x/7 is an integer

OA after some discussion

For x = 1,y = 20/49 and x>y. However, for x=-49,y = -20 and y>x. I is clearly not the right answer.
For y=0, x=0. Thus, even II doesn't hold good.
x/7 = 7y/20. For y=0, x/7 is an integer, however for y=1, it is not.
None of the options are (must be)true
_________________

Kudos [?]: 1386 [0], given: 136

VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1120

Kudos [?]: 2365 [0], given: 219

Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Re: f 20x = 49y, which of the following must be true? [#permalink]

### Show Tags

05 May 2013, 00:05
If 20x = 49y, which of the following must be true?

I. x > y
II. x^2 > y^2
III. x/7 is an integer

Just pick $$x=0$$ and $$y=0$$

Options I and II are false (0 is not $$> 0$$), only III is true. And holds true for each value of x because $$4*5*x=7*7*y$$ so or x=0 or x is a multiple of 7, in both cases $$\frac{x}{7}$$ is an integer.
C

PS: given that x, y are integers. Otherwise none must be true

Edit post:
A)I only
B)II only
C) III only
D)I and III
E)I, II, and III

These are Veritas possible answers. The "none" option is not available, as you see. So we must assume that are integers and that the question is not complete (it must specify that x,y are integers). However the question itself , because x and y could be fractions (no integers) has an hypothetical "F)none of the above" as correct answer. No doubt.

The question is incomplete
_________________

It is beyond a doubt that all our knowledge that begins with experience.

Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]

Kudos [?]: 2365 [0], given: 219

Manager
Joined: 02 Sep 2012
Posts: 244

Kudos [?]: 226 [0], given: 99

Location: United States
Concentration: Entrepreneurship, Finance
GMAT Date: 07-25-2013
GPA: 3.83
WE: Architecture (Computer Hardware)
Re: f 20x = 49y, which of the following must be true? [#permalink]

### Show Tags

05 May 2013, 00:16
if x =1/20 and y=1/49 still the equation holds right?

SO at this point of time option 3 also goes wrong...Any opinion on this?
_________________

"Giving kudos" is a decent way to say "Thanks" and motivate contributors. Please use them, it won't cost you anything

Kudos [?]: 226 [0], given: 99

Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 627

Kudos [?]: 1386 [1], given: 136

Re: f 20x = 49y, which of the following must be true? [#permalink]

### Show Tags

05 May 2013, 00:16
1
KUDOS
Zarrolou wrote:
If 20x = 49y, which of the following must be true?

I. x > y
II. x^2 > y^2
III. x/7 is an integer

Just pick $$x=0$$ and $$y=0$$

Options I and II are false (0 is not $$> 0$$), only III is true. And holds true for each value of x because $$4*5*x=7*7*y$$ so or x=0 or x is a multiple of 7, in both cases $$\frac{x}{7}$$ is an integer.
C

That is not true. It has not been mentioned that x and y are integers.
_________________

Kudos [?]: 1386 [1], given: 136

Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132612 [0], given: 12326

Re: f 20x = 49y, which of the following must be true? [#permalink]

### Show Tags

05 May 2013, 04:13
skamal7 wrote:
If 20x = 49y, which of the following must be true?

I. x > y
II. x^2 > y^2
III. x/7 is an integer

A)I only
B)II only
C) III only
D)I and III
E)I, II, and III

OA after some discussion

Merging similar topics.
_________________

Kudos [?]: 132612 [0], given: 12326

Re: f 20x = 49y, which of the following must be true?   [#permalink] 05 May 2013, 04:13
Display posts from previous: Sort by