A magazine stand owner sells cups of coffee

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

A magazine stand owner sells cups of coffee

by BTGmoderatorDC » Wed Jan 17, 2018 8:44 pm

A magazine stand owner sells cups of coffee, newspapers, and packs ofgum. Compared to the number of cups of coffee he sells, he sells twice as many packs of gum, and three times as many newspapers. If he charges $1.25 for a cup of coffee, $.50 for a newspaper, and $.35 for a pack of gum, and sells no other items, which of the following could be the amount of his total gross sales on a given day?

I.$345.00
II.$58.65
III.$22.15

A. I only
B. I + II only
C. I + III only
D. II and III only
E. I, II and III only

Which of the choices is the best answer? Can some experts show me the correct solution?

OA B

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Source: Beat The GMAT — Problem Solving | Wed Jan 17, 2018 8:44 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 am; Location: Grand Central / New York; Thanked: 470 times; Followed by:34 members

by Jay@ManhattanReview » Wed Jan 17, 2018 9:55 pm

lheiannie07 wrote:A magazine stand owner sells cups of coffee, newspapers, and packs of gum. Compared to the number of cups of coffee he sells, he sells twice as many packs of gum, and three times as many newspapers. If he charges $1.25 for a cup of coffee, $.50 for a newspaper, and $.35 for a pack of gum, and sells no other items, which of the following could be the amount of his total gross sales on a given day?

I.$345.00
II.$58.65
III.$22.15

A. I only
B. I + II only
C. I + III only
D. II and III only
E. I, II and III only

Which of the choices is the best answer? Can some experts show me the correct solution?

OA B

On a ratio scale, the number of coffee, gums, and newspapers are 1, 2, and 3, respectively.

Gross sales on ratio scale = 1.25*1 + 0.35*2 + 0.50*3 = 1.25 + 0.70 + 1.50 = $3.45.

The gross sales would a multiple of $3.45. For example, 3.45; 2*3.45 = 6.90; 3*3.45 = 10.35 etc...

We need to see which of the given three figures I. $345.00; II. $58.65; and III. $22.15 is/are multiple of $3.45. This calls for a hit and trial. We see that I. #345 is 100*3.45, so this is correct. Similarly, $58.65/$3.45 = 17, an integer, so II is also correct. But $22.15/$3.45 = between 6 and 7, not an integer. So, only $345 and $58.65 can be possible gross sales.

The correct answer: B

Hope this helps!

-Jay
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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Sat Jan 20, 2018 6:22 am

lheiannie07 wrote:A magazine stand owner sells cups of coffee, newspapers, and packs ofgum. Compared to the number of cups of coffee he sells, he sells twice as many packs of gum, and three times as many newspapers. If he charges $1.25 for a cup of coffee, $.50 for a newspaper, and $.35 for a pack of gum, and sells no other items, which of the following could be the amount of his total gross sales on a given day?

I.$345.00
II.$58.65
III.$22.15

A. I only
B. I + II only
C. I + III only
D. II and III only
E. I, II and III only

We can let the number of packs of gum = g, the number of newspapers = n, and the number of cups of coffee = c, and create the equations:

2c = g

and

3c = n

We need to determine the value of:

1.25c + 0.5n + 0.35g

Substituting, we have:

1.25c + 0.5(3c) + 0.35(2c)
1.25c + 1.5c + 0.7c
3.45c = ?

Now let's check which Roman numerals is an integer multiple of 3.45.

I.$345.00
Since 345/3.45 = 100, we see that I could be the total gross sales.

II.$58.65
Since 58.65/3.45 = 17, we see that II could be the total gross sales.

III.$22.15
Since 22.15/3.45 = 6.42, we see that III could NOT be the total gross sales.

Answer: B

Scott Woodbury-Stewart
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