GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Dec 2018, 20:24

### 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 December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### FREE Quant Workshop by e-GMAT!

December 16, 2018

December 16, 2018

07:00 AM PST

09:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.

# Alice has x stamps and Thomas has y stamps, where x and y ar

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 06 Aug 2011
Posts: 339
Alice has x stamps and Thomas has y stamps, where x and y ar  [#permalink]

### Show Tags

Updated on: 07 Jan 2014, 04:35
1
8
00:00

Difficulty:

45% (medium)

Question Stats:

75% (02:41) correct 25% (03:22) wrong based on 149 sessions

### HideShow timer Statistics

Alice has x stamps and Thomas has y stamps, where x and y are positive integers. The ratio of x to y is 7 to 3. If Alice gives Thomas z stamps, where z is a positive integer and z < x, and no other changes take place in the numbers of stamps that Alice and Thomas have, then the ratio of the number of stamps that Alice has to the number of stamps that Thomas has will become 7 to 8. Which of the following equations correctly describes z in terms of x?

A. z = x/3
B. z = x/2
C. z = 2x/3
D. z = 3x/2
E. z = 3x

_________________

Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !

Originally posted by sanjoo on 07 Jan 2014, 04:23.
Last edited by Bunuel on 07 Jan 2014, 04:35, edited 2 times in total.
Edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 51218
Re: Alice has x stamps and Thomas has y stamps, where x and y ar  [#permalink]

### Show Tags

07 Jan 2014, 04:35
2
2
sanjoo wrote:
Alice has x stamps and Thomas has y stamps, where x and y are positive integers. The ratio of x to y is 7 to 3. If Alice gives Thomas z stamps, where z is a positive integer and z < x, and no other changes take place in the numbers of stamps that Alice and Thomas have, then the ratio of the number of stamps that Alice has to the number of stamps that Thomas has will become 7 to 8. Which of the following equations correctly describes z in terms of x?

A. z = x/3
B. z = x/2
C. z = 2x/3
D. z = 3x/2
E. z = 3x

The ratio of x to y is 7 to 3 --> $$\frac{x}{y}= \frac{7}{3}$$ --> $$3x=7y$$;

If Alice gives Thomas z stamps, then the ratio of the number of stamps that Alice has to the number of stamps that Thomas has will become 7 to 8 --> $$\frac{x-z}{y+z} = \frac{7}{8}$$ --> $$8x-8z=7y+7z$$ --> $$8x=7y+15z$$.

Subtract the first equation from the second: $$8x-3x=(7y+15z)-7y$$ --> $$5x=15z$$ --> $$z=\frac{x}{3}$$.

_________________
Senior Manager
Joined: 20 Aug 2015
Posts: 390
Location: India
GMAT 1: 760 Q50 V44
Re: Alice has x stamps and Thomas has y stamps, where x and y ar  [#permalink]

### Show Tags

06 Oct 2015, 02:49
1
Ratio of x:y = 7 : 3
$$x/y=7/3$$ or $$3x=7y$$ (i)

After Alice gives Thomas z stamps, ratio of the number of stamps = 7 : 8
$$x−z/y+z=7/8$$
Or $$8x−8z=7y+7z$$
$$8x=7y+15z.$$ (ii)

On performing (ii) - (i), $$5x=15z$$
Or $$z=x/3$$

Option A
Intern
Joined: 20 Apr 2017
Posts: 13
GPA: 3.74
Re: Alice has x stamps and Thomas has y stamps, where x and y ar  [#permalink]

### Show Tags

14 Jun 2017, 20:45
sanjoo wrote:
Alice has x stamps and Thomas has y stamps, where x and y are positive integers. The ratio of x to y is 7 to 3. If Alice gives Thomas z stamps, where z is a positive integer and z < x, and no other changes take place in the numbers of stamps that Alice and Thomas have, then the ratio of the number of stamps that Alice has to the number of stamps that Thomas has will become 7 to 8. Which of the following equations correctly describes z in terms of x?

A. z = x/3
B. z = x/2
C. z = 2x/3
D. z = 3x/2
E. z = 3x

Given that
X/Y = 7/3 --------- ( 1 )

( X - Z ) / ( Y + Z ) = 7/8
=> ( X - Z ) ( 3X/7 + Z ) = 7/8 ( from equation 1 )
=> 8X - 8Z = 3X + 7Z
=> 5X = 15Z
=> Z = X/3

Manager
Joined: 08 Sep 2017
Posts: 77
GMAT 1: 710 Q49 V39
Alice has x stamps and Thomas has y stamps, where x and y are...  [#permalink]

### Show Tags

25 Jun 2018, 16:31
Alice has x stamps and Thomas has y stamps, where x and y are positive integers. The ratio of x to y is 7 to 3. If Alice gives Thomas z stamps, where z is a positive integer and z < x, and no other changes take place in the numbers of stamps that Alice and Thomas have, then the ratio of the number of stamps that Alice has to the number of stamps that Thomas has will become 7 to 8. Which of the following equations correctly describes z in terms of x?

A) z = x/3
B) z = x/2
C) z = 2x/3
D) z = 3x/2
E) z = 3x
_________________

Kudos please if you liked my post

Thanks!

Math Expert
Joined: 02 Aug 2009
Posts: 7108
Re: Alice has x stamps and Thomas has y stamps, where x and y are...  [#permalink]

### Show Tags

25 Jun 2018, 18:12
Carlgrc wrote:
Alice has x stamps and Thomas has y stamps, where x and y are positive integers. The ratio of x to y is 7 to 3. If Alice gives Thomas z stamps, where z is a positive integer and z < x, and no other changes take place in the numbers of stamps that Alice and Thomas have, then the ratio of the number of stamps that Alice has to the number of stamps that Thomas has will become 7 to 8. Which of the following equations correctly describes z in terms of x?

A) z = x/3
B) z = x/2
C) z = 2x/3
D) z = 3x/2
E) z = 3x

X/y=7/3....y=3x/7
Also (x-z)/(y+z)=7/8
8x-8z=7y+7z......8x-7y=15z
Substitute y = 3x/7
So 8x-7*3x/7=15z......8x-3x=15z.....5x=15z
Z=X/3

A
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Manager
Joined: 09 Jun 2018
Posts: 185
Location: United States
GPA: 3.95
WE: Manufacturing and Production (Energy and Utilities)
Re: Alice has x stamps and Thomas has y stamps, where x and y are...  [#permalink]

### Show Tags

25 Jun 2018, 18:41
x/y = 7/3 hence, 7y = 3x

(x-z)/(y+z) = 7/8
8x - 8z = 7y + 7z = 3x + 7z
5x = 15z
z = x/3
so A
_________________

If you found this relevant and useful, please Smash that Kudos button!

Math Expert
Joined: 02 Sep 2009
Posts: 51218
Re: Alice has x stamps and Thomas has y stamps, where x and y ar  [#permalink]

### Show Tags

25 Jun 2018, 18:44
Carlgrc wrote:
Alice has x stamps and Thomas has y stamps, where x and y are positive integers. The ratio of x to y is 7 to 3. If Alice gives Thomas z stamps, where z is a positive integer and z < x, and no other changes take place in the numbers of stamps that Alice and Thomas have, then the ratio of the number of stamps that Alice has to the number of stamps that Thomas has will become 7 to 8. Which of the following equations correctly describes z in terms of x?

A) z = x/3
B) z = x/2
C) z = 2x/3
D) z = 3x/2
E) z = 3x

Merging topics. Please search before posting a question.
_________________
Re: Alice has x stamps and Thomas has y stamps, where x and y ar &nbs [#permalink] 25 Jun 2018, 18:44
Display posts from previous: Sort by