Alice has $15, Which is enough to Buy 11 Muffins and 7 Brownies GMAT Data Sufficiency

bySayantani Barman Experta en el extranjero

Question: Alice has $15, which is enough to buy 11 muffins and 7 brownies, is $45 enough to buy 267 muffins and 27 brownies?

$15 is enough to buy 7 muffins and 11 brownies
$15 is enough to buy 10 muffins and 8 brownies

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.

Solution and Explanation:

Approach Solution (1):

Muffin: M; Brownie: B

11 M + 7 B <= 15

Question: 27(M + B) <= 45 or M + B <= $\frac{5}{3}$

S1: 7 M + 11 B <= 15 --- (1)
Given: 11 M + 7 B <= 15 --- (2)
Add equation (1) and (2), we get:

18 M + 18 B <= 30 or M + B <= $\frac{5}{3}$(Enough)
S2: 10 M + 8 B <= 15 --- (3)
Adding S2 and S3, we get: 21 M + 15 B <= 30; or
7M + 5B <= 10 --- (4)

Now if M + B <= $\frac{5}{3}$

Then 7 M + 7 B <= $\frac{35}{3}$--- (5)

Subtract equation (4) from equation (5), we get: 2 B <=$\frac{5}{3}$which do not know so only A is the answer

Correct Option: A

Approach Solution (2):

10m + 8b <= 15
Also 11m + 7b <= 15
In both number of m is more than b and total is 18
So if all 18 terms are so cheap that they all are for $1, you can buy 15 times the given number.
Also if they just get equal $15 and price of m is more than b
So when you replace m with b in 10m + 8b to make it 9 of each, it is possible
But if b is more than m and their combined price equals exactly 15, change of B to m will take it above 15, hence not possible
So S2 is insufficient
In S1, it gives you more b than m and main statement gives you more m than b, so equal number of both is possible

Hence sufficient

Correct Option: A

Approach Solution (3):

Given: 11m + 7b <= 15, where m and b are prices of one muffin and one brownie respectively.

Question: Is 27m + 27b <= 45? Reduce by 3: 9m + 9b <= 15. The question basically asks whether we can substitute 2 muffins with 2 brownies

Now, If m > b, we can easily substitute 2 muffins with 2 brownies. But if m < b, we don’t know this for sure.

But consider the case when we are told that we can substitute 3 muffins with 3 brownies. In both cases (m > b or m < b) it would mean that we can substitute 2 muffins with 2 brownies, but again we won’t be sure whether we can substitute 4 muffins with 4 brownies.

(1) $15 is enough to buy 7 muffins and 11 brownies. 7m + 11b <= 15: we can substitute 4 muffins with 4 brownies, so according to the above, we can surely substitute 2 muffins with 2 brownies.
Sufficient

(2) $15 is enough to buy 10 muffins and 8 brownies. 10m + 8b <= 15; we can substitute 1 muffin with 1 brownie, so according to the above, this does not ensure that we can substitute 2 muffins with 2 brownies.
Not sufficient

Correct Option: A

“Alice has $15, which is enough to buy 11 muffins and 7 brownies, is $45 enough to buy 267 muffins and 27 brownies?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

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Alice has $15, Which is enough to Buy 11 Muffins and 7 Brownies GMAT Data Sufficiency

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