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Retired Moderator

Joined: **07 Jun 2014 **

Posts: **4805**

WE:**Business Development (Energy and Utilities)**

QOTD#25 Evangeline must spend of her weekly salary on rent a
[#permalink]
30 Apr 2017, 14:14

2

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5

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Question Stats:

Evangeline must spend \(\frac{3}{8}\) of her weekly salary on rent and \(\frac{1}{6}\) of her remaining salary on food. Which of the following could be percentages of her weekly salary that Evangeline devotes to entertainment, while still enabling her to place \(\frac{4}{9}\) of her salary into a savings account?

Indicate all such percentages.

A. 0.5%

B. 5.0%

C. 7.5%

D. 10.0%

E. 15.0%

F. 25.0%

G. 50.0%

_________________

Indicate all such percentages.

A. 0.5%

B. 5.0%

C. 7.5%

D. 10.0%

E. 15.0%

F. 25.0%

G. 50.0%

Drill 4

Question: 13

Page: 323

Question: 13

Page: 323

_________________

Sandy

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Retired Moderator

Joined: **07 Jun 2014 **

Posts: **4805**

WE:**Business Development (Energy and Utilities)**

Re: QOTD#25 Evangeline must spend of her weekly salary on rent a
[#permalink]
04 May 2017, 01:35

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Explanation

The problem has percents in the answers and no real values in the question, so it’s a Hidden Plug In; the hidden variable in this case is Evangeline’s weekly salary.

To find an easy number, try multiplying the denominators in the problem: \(8 \times 6 \times 9 = 432\), so Evangeline makes \($432\)per week. Now work the problems in bite-sized pieces.

She spends \(\frac{3}{8} \times $432 = $ 162\) on rent, leaving her with \($432 - $162 = $270\).

Of that, she spends , \(\frac{1}{6}\) or $45, on food, leaving her with \($270 - $45 = $225\).

If she wants to put \(\frac{4}{9}\) of her weekly salary, or $192, into a savings account, then she can only spend \($225 - $192 = $33\) on entertainment.

Finally, use your onscreen calculator to determine that 33 is just over 7.6% of 432, so choices (A), (B), and (C) will all work.

_________________

Sandy

If you found this post useful, please let me know by pressing the Kudos Button

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The problem has percents in the answers and no real values in the question, so it’s a Hidden Plug In; the hidden variable in this case is Evangeline’s weekly salary.

To find an easy number, try multiplying the denominators in the problem: \(8 \times 6 \times 9 = 432\), so Evangeline makes \($432\)per week. Now work the problems in bite-sized pieces.

She spends \(\frac{3}{8} \times $432 = $ 162\) on rent, leaving her with \($432 - $162 = $270\).

Of that, she spends , \(\frac{1}{6}\) or $45, on food, leaving her with \($270 - $45 = $225\).

If she wants to put \(\frac{4}{9}\) of her weekly salary, or $192, into a savings account, then she can only spend \($225 - $192 = $33\) on entertainment.

Finally, use your onscreen calculator to determine that 33 is just over 7.6% of 432, so choices (A), (B), and (C) will all work.

_________________

If you found this post useful, please let me know by pressing the Kudos Button

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Re: QOTD#25 Evangeline must spend of her weekly salary on rent a
[#permalink]
14 Dec 2018, 15:20

1

1

Bookmarks

Full disclosure: Sandy's way may be faster for you.

Let S = Weekly salary

Here is what we know

3/8(S) = rent

1/6 (5/8)S = food (because she spends 1/6 of what is remaining after rent, what is remaining after rent is 5/8 S)

4/9S = savings

And finally, the amount ratio/percentage of entertainment is unknown, we label it x.

x(s) = entertainment

Now note, if we add up all of these, we should get her total salary, no more (but possibly less)

3/8 S + 5/38 S + 4/9 S + x S <= S

3/8 + 5/38 + 4/9 S + x <= 1

x <= .076

Thus, A, B, and C are the answers.

Let S = Weekly salary

Here is what we know

3/8(S) = rent

1/6 (5/8)S = food (because she spends 1/6 of what is remaining after rent, what is remaining after rent is 5/8 S)

4/9S = savings

And finally, the amount ratio/percentage of entertainment is unknown, we label it x.

x(s) = entertainment

Now note, if we add up all of these, we should get her total salary, no more (but possibly less)

3/8 S + 5/38 S + 4/9 S + x S <= S

3/8 + 5/38 + 4/9 S + x <= 1

x <= .076

Thus, A, B, and C are the answers.

Re: QOTD#25 Evangeline must spend of her weekly salary on rent a
[#permalink]
26 Sep 2021, 09:37

QuantumWonder wrote:

Full disclosure: Sandy's way may be faster for you.

Let S = Weekly salary

Here is what we know

3/8(S) = rent

1/6 (5/8)S = food (because she spends 1/6 of what is remaining after rent, what is remaining after rent is 5/8 S)

4/9S = savings

And finally, the amount ratio/percentage of entertainment is unknown, we label it x.

x(s) = entertainment

Now note, if we add up all of these, we should get her total salary, no more (but possibly less)

3/8 S + 5/38 S + 4/9 S + x S <= S

3/8 + 5/38 + 4/9 S + x <= 1

x <= .076

Thus, A, B, and C are the answers.

Let S = Weekly salary

Here is what we know

3/8(S) = rent

1/6 (5/8)S = food (because she spends 1/6 of what is remaining after rent, what is remaining after rent is 5/8 S)

4/9S = savings

And finally, the amount ratio/percentage of entertainment is unknown, we label it x.

x(s) = entertainment

Now note, if we add up all of these, we should get her total salary, no more (but possibly less)

3/8 S + 5/38 S + 4/9 S + x S <= S

3/8 + 5/38 + 4/9 S + x <= 1

x <= .076

Thus, A, B, and C are the answers.

why less than or equal to? Why not = ?

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WE:**Analyst (Investment Banking)**

Re: QOTD#25 Evangeline must spend of her weekly salary on rent a
[#permalink]
01 Oct 2021, 05:15

1

computerbot wrote:

QuantumWonder wrote:

Full disclosure: Sandy's way may be faster for you.

Let S = Weekly salary

Here is what we know

3/8(S) = rent

1/6 (5/8)S = food (because she spends 1/6 of what is remaining after rent, what is remaining after rent is 5/8 S)

4/9S = savings

And finally, the amount ratio/percentage of entertainment is unknown, we label it x.

x(s) = entertainment

Now note, if we add up all of these, we should get her total salary, no more (but possibly less)

3/8 S + 5/38 S + 4/9 S + x S <= S

3/8 + 5/38 + 4/9 S + x <= 1

x <= .076

Thus, A, B, and C are the answers.

Let S = Weekly salary

Here is what we know

3/8(S) = rent

1/6 (5/8)S = food (because she spends 1/6 of what is remaining after rent, what is remaining after rent is 5/8 S)

4/9S = savings

And finally, the amount ratio/percentage of entertainment is unknown, we label it x.

x(s) = entertainment

Now note, if we add up all of these, we should get her total salary, no more (but possibly less)

3/8 S + 5/38 S + 4/9 S + x S <= S

3/8 + 5/38 + 4/9 S + x <= 1

x <= .076

Thus, A, B, and C are the answers.

why less than or equal to? Why not = ?

Hi There!

It is less than equal to because, it is possible that entertainment is the complete % left of it could be some % of the left %. Thus, less than equal to.

Regards

S

gmatclubot

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