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

1. $15 is enough to buy 7 muffins and 11 brownies
2. $15 is enough to buy 10 muffins and 8 brownies

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. 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.

Suggested GMAT Data Sufficiency Samples

• GMAT Data Sufficiency- What is the value of x? (1) x^2 – 5 x + 6 = 0 (2) x > 0
• GMAT Data Sufficiency- What is the value of x? 1) x^2 + x + 10 = 16 2) x = 4y^4+2y^2+2
• GMAT Data Sufficiency- A terminating decimal is defined as a decimal that has a finite number of nonzero digits
• GMAT Data Sufficiency- A rectangular solid has length, width, and height of L cm, W cm, and H cm, respectively
• GMAT Data Sufficiency- What is the circumference of circle C ? (1) The radius of circle C is 2π.
• GMAT Data Sufficiency- Triangle ABC is right angled at B. BD, the median to hypotenuse AC, is 5 units
• GMAT Data Sufficiency- If each side of parallelogram P has length 1, what is the area of P ?
• GMAT Data Sufficiency- Is the positive integer n a multiple of 24?
• GMAT Data Sufficiency- Did Insurance Company K have More than $300 Million in Total Net Profits Last Year?
• GMAT Data Sufficiency- What is the Remainder when 333^222 is Divided by 7?
• GMAT Data Sufficiency- Is 1/(a - b) > b - a ?
• The cardinality of a finite set is the number of elements in the set. What is the cardinality of set A ? GMAT Data Sufficiency
• The Average Price of Three Stocks is $25 per Share GMAT Data Sufficiency
• Max purchased a guitar for a total of $624,which consisted of the price of the guitar and the sales tax. GMAT Data Sufficiency
• In the figure shown, point O is the center of the semicircle and points B, C, D lie on the semicircle GMAT Data Sufficiency
• Is 500 the average (arithmetic mean) score on the GMAT? GMAT Data Sufficiency
• If 4x = 5y = 10z, what is the value of x + y + z ? (1) x - y = 6 (2) y + z = 36 GMAT Data Sufficiency
• Figure ABCD is a rectangle with sides of length x centimeters and width y centimeters, and a diagonal of length z centimeters. GMAT Data Sufficiency
• Can the Positive Integer p be Expressed as the Product of Two Integers GMAT Data Sufficiency
• A School Administrator will Assign each Student in a Group GMAT Data Sufficiency
• Is quadrilateral PQRS a parallelogram? (1) Adjacent sides PQ and QR have the same length. (2) Adjacent sides RS and SP have the same length. GMAT Data Sufficiency
• GMAT Data Sufficiency- A Certain Truck Uses 1 12 + k v 2 Gallons of Fuel Per Mile GMAT Data Sufficiency
• What is the value of x? (1) x^2 – 5 x + 6 = 0 (2) x > 0 GMAT Data Sufficiency
• What is the value of x? 1) x^2 + x + 10 = 16 2) x = 4y^4+2y^2+2 GMAT Data Sufficiency
• For a Class of 50 Students, The Table Above Reports The Number of Students GMAT Data Sufficiency
• A Terminating Decimal is Defined as a Decimal GMAT Data Sufficiency
• A Rectangular Solid has Length, Width, and Height of L cm, W cm, and H cm, Respectively GMAT Data Sufficiency
• What is the circumference of circle C ? (1) The radius of circle C is 2π. (2) The center of circle C is located at point (7,8) in the xy-plane. GMAT Data Sufficiency
• If √3+√x−1=43+x−1=4 , what is the value of x? GMAT Data Sufficiency
• What is the Sum of a, b, and c? GMAT Data Sufficiency
• What is the Probability of Getting a Jack from a 52-Card Deck GMAT Data Sufficiency
• Is P – 1 Even? GMAT Data Sufficiency
• GMAT Data Sufficiency- If x is the Product of Three Consecutive Positive Integers, Which of the Following Must be True?
• GMAT Data Sufficiency- In the Figure Above, What is the Area of Semicircle DPA?
• GMAT Data Sufficiency- Is |x-10| > |x-30|
• GMAT Data Sufficiency- What is The Value of (a!+b!)(c!+d!)?
• GMAT Data Sufficiency- If xy = - 6, What is the Value of xy(x + y)?
• GMAT Data Sufficiency- A Drawer Contains 8 Socks, and 2 Socks are Selected at Random Without Replacement
• GMAT Data Sufficiency- The Average Price of Three Stocks is $25 per Share
• GMAT Data Sufficiency- Given k is a Nonzero Integer, is k>0?
• GMAT Data Sufficiency- If J≠0, What Is The Value Of J?
• If |m + 4| = 2, what is the value of m? GMAT Data Sufficiency
• How Many Integers are There Between, But Not Including, Integers r and s ? GMAT Data Sufficiency
• Given k is a Nonzero Integer, is k>0? GMAT Data Sufficiency
• Is the Average of a Set of 5 Distinct Positive Integers {a, b, 6, 4, 2} GMAT Data Sufficiency
• If a, b, and c are distinct positive integers, is(abc)(abc)an integer? GMAT Data Sufficiency
• If a > b, How much Greater than b is a? GMAT Data Sufficiency
• What is the Radius of the Circle above with Center O? GMAT Data Sufficiency
• The Cardinality of a Finite Set is the Number of Elements in the Set. GMAT Data Sufficiency
• P and Q are Prime Numbers Less than 70. What is the Units Digit of P*Q? GMAT Data Sufficiency