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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

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by BTGmoderatorDC » Fri Aug 21, 2020 5:57 pm

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Answers

A

B

C

D

E

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Difficulty—

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



OA A

Source: e-GMAT
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Source: — Data Sufficiency |
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Re: Joan spent $10 to buy at least one piece each of apples and oranges at a store where each apple cost $2 and each ora

by Targt780 » Sat Aug 22, 2020 2:46 am
Let the number of apples be A and the number of oranges be O

We know that A>0 and O>0 and since we cannot purchase fractions of fruit we can safely assume that both are A and O are integers

Total amount spent = $10
Cost of each apple = $2
Cost of each orange = $1

The question stem translates to 2A+O=10

(1) Given that O=6
Substituting it in the above equation we get

2A+6=10
2A=4
A=2

(1) is sufficient

(2) O<10

O can be anything 8,6,4

Substituting O =8

2A+8=10
A=1

Substituting O=6
2A+6=10
A=2
.
.
.

Hence we get different values of A for different values of O

(2) Insufficient

Hence Statement (1) is alone sufficient
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Re: Joan spent $10 to buy at least one piece each of apples and oranges at a store where each apple cost $2 and each ora

by Brent@GMATPrepNow » Sat Aug 22, 2020 5:50 am
BTGmoderatorDC wrote: ↑
Fri Aug 21, 2020 5:57 pm
 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



OA A

Source: e-GMAT
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 i) 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
Brent Hanneson - Creator of GMATPrepNow.com
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