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

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Alice has x stamps and Thomas has y stamps, where x and y ar  [#permalink]

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New post Updated on: 07 Jan 2014, 04:35
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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

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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.
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Re: Alice has x stamps and Thomas has y stamps, where x and y ar  [#permalink]

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New post 07 Jan 2014, 04:35
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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: \(8x-3x=(7y+15z)-7y\) --> \(5x=15z\) --> \(z=\frac{x}{3}\).

Answer: A.
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Re: Alice has x stamps and Thomas has y stamps, where x and y ar  [#permalink]

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New post 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
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Re: Alice has x stamps and Thomas has y stamps, where x and y ar  [#permalink]

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New post 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

Answer : A
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Alice has x stamps and Thomas has y stamps, where x and y are...  [#permalink]

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New post 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
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Re: Alice has x stamps and Thomas has y stamps, where x and y are...  [#permalink]

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New post 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
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Re: Alice has x stamps and Thomas has y stamps, where x and y are...  [#permalink]

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New post 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
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Re: Alice has x stamps and Thomas has y stamps, where x and y ar  [#permalink]

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New post 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


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New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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