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S99-19

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New post 16 Sep 2014, 00:53
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The Farmer in the Deli sandwich shop sells two kinds of sandwich: tuna melts and veggie melts. Each customer buys exactly one sandwich. If there were 300 customers yesterday, what fraction of veggie melts sold yesterday were bought by female customers?


(1) \(\frac{1}{2}\) of all sandwiches sold yesterday were tuna melts, and \(\frac{1}{3}\) of all customers yesterday were male.

(2) Yesterday, twice as many tuna melts were bought by females as there were veggie melts bought by males.
[Reveal] Spoiler: OA

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New post 16 Sep 2014, 00:53
Official Solution:


In this overlapping sets problem, there are two kinds of sandwiches (tuna melts and veggie melts, abbreviated T and V). There are also two kinds of customers: male and female. Since each customer buys exactly one sandwich, customers and sandwiches are interchangeable. Thus, we can set up one table to keep track of both type of sandwich and type of customer, as follows:
M F Total T V Total 300
We are looking for the ratio of two numbers on this chart: veggie melts bought by females and the total number of veggie melts.

Statement (1): INSUFFICIENT. We can fill in the chart's total row and total columns, but the four cells in the upper left remain unknown.
M F Total T 150 (\(\frac{1}{2}\) of 300) V 150 Total 100 200 300
Thus, we cannot figure out the needed ratio.

Statement (2): INSUFFICIENT. We can use the relationship between "female tuna melts" and "male veggie melts," introducing a variable as follows:
M F Total T \(2x\) V \(x\) Total 300
However, without more information, we cannot find the needed ratio.

Statements (1) and (2) together: SUFFICIENT. Combining the tables above, we get the following:

We can fill in the remaining cells with expressions -- for instance, "female veggie melts" can be written as \(150 - x\), since the veggie row must sum to 150. Now we can add up the female column and solve for \(x\):
\(2x + (150 - x) = 200\)
\(x + 150 = 200\)
\(x = 50\)

We see that \(\frac{100}{150}\), or \(\frac{2}{3}\), of the veggie melts sold yesterday were bought by female customers.

Note that we could have addressed this problem without knowing the total number of customers (300). We are only looking for a ratio between two numbers on the chart.


Answer: C
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Re: S99-19 [#permalink]

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New post 16 Apr 2017, 15:11
1 should be sufficient

1/2 amount of all sandwiches were tuna , so 150 are veggie melts
1/3 were men , thats 1/3x300= 100, so Women are 200

150/200=3/4

Am i wrong?

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Re: S99-19 [#permalink]

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New post 16 Apr 2017, 23:10
sammuthappa wrote:
1 should be sufficient

1/2 amount of all sandwiches were tuna , so 150 are veggie melts
1/3 were men , thats 1/3x300= 100, so Women are 200

150/200=3/4

Am i wrong?


Yes. That's not correct.

From (1): 1/2 of all sandwiches sold yesterday were tuna melts, and 1/3 of all customers yesterday were male.

150 were tuna and the rest, so 150, were veggie.
100 customers were male and the rest, so 200, were female.

The question asks: what fraction of veggie melts sold yesterday were bought by female customers? So, what fraction of 150 veggie sandwiches sold yesterday were bought by female customers? How do you know what sandwiches did males and females buy? We just know the total number of each kind that were bought.

Check other solutions of this questions here: https://gmatclub.com/forum/the-farmer-i ... 88784.html

Hope it helps.
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New to the Math Forum?
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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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Kudos [?]: 135771 [0], given: 12708

Re: S99-19   [#permalink] 16 Apr 2017, 23:10
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