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Joan spent $10 to buy

This topic has 2 expert replies and 0 member replies

Joan spent $10 to buy

Post Sun Sep 24, 2017 3:52 am
Joan spent $10 to buy at least one piece each of apples and oranges at a store where each apple cost $2 and each orange cost $1. How many apples did she buy?

(1) She spent more than $6 on buying oranges

(2) She spent less than $10 on buying oranges

Which of the statements is the correct answer?Why can't the both statements be the right Option?

OA A

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Post Sun Sep 24, 2017 4:44 am
lheiannie07 wrote:
Joan spent $10 to buy at least one piece each of apples and oranges at a store where each apple cost $2 and each orange cost $1. How many apples did she buy?

(1) She spent more than $6 on buying oranges

(2) She spent less than $10 on buying oranges

Which of the statements is the correct answer?Why can't the both statements be the right Option?

OA A
Statement 1: She spent more than $6 on buying oranges

=> She spent 7, 8, or 9 dollars on buying oranges. Excluded $10 as then we would not have any money to buy an apple.

Case 1: She spent $7 on buying oranges.
=> She spent $3 on buying apples. But this is not possible since in $3 she can only buy one apple and $1 would be left. Not a possible case.

Case 2: She spent $8 on buying oranges.
=> She spent $2 on buying an apple. A possible case.

Case 1: She spent $9 on buying oranges.
=> She spent $1 on buying apples. But this is not possible since in $1 she cannot buy at least one apple. Not a possible case.

Thus, she bought one apple. Sufficient.

Statement 2: She spent less than $10 on buying oranges

Case 1: She spent $8 on buying oranges.
=> She spent $2 on buying an apple. She bought one apple.

Case 2: She spent $6 on buying oranges.
=> She spent $4 on buying apples. She bought two apples.

No unique answer. Insufficient.

The correct answer: A

Hope this helps!

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GMAT/MBA Expert

Post Sun Sep 24, 2017 6:09 am
lheiannie07 wrote:
Joan spent $10 to buy at least one piece each of apples and oranges at a store where each apple cost $2 and each orange cost $1. How many apples did she buy?

(1) She spent more than $6 on buying oranges
(2) She spent less than $10 on buying oranges
Target question: How many apples did Joan buy?

Given: Joan spent $10 to buy at least one piece each of apples and oranges at a store where each apple cost $2 and each orange cost $1.
Since there are only a handful of possible outcomes, we might benefit from quickly listing them:
i) Joan buys 1 apple (for $2) and 8 oranges (for $8)
ii) Joan buys 2 apples (for $4) and 6 oranges (for $6)
iii) Joan buys 3 apples (for $6) and 4 oranges (for $4)
iv) Joan buys 4 apple (for $8) and 2 oranges (for $2)


Statement 1: She spent more than $6 on buying oranges
When we check our list of possible outcomes, we see that only one outcome (case iv) satisfies statement 1.
So, it MUST be the case that Joan bought 4 apples
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: She spent less than $10 on buying oranges
When we check our list of possible outcomes, we see that ALL 4 outcomes satisfy statement 2.
So, it's possible that Joan bought 1 apple, 2 apples, 3 apples OR 4 apples
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

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