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A certain fruit stand sold apples for $0.70 each and bananas

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A certain fruit stand sold apples for $0.70 each and bananas

by melguy » Sat Dec 17, 2016 7:18 pm
A certain fruit stand sold apples for $0.70 each and bananas for $0.50 each. If a customer purchased both apples and bananas from the stand for a total of $6.30, what total number of apples and bananas did the customer purchase?

(A) 10
(B) 11
(C) 12
(D) 13
(E) 14

Please help me with this question. I want to solve this question with answer plug in approach (which I could do in a minute or 1.5 mins).

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by GMATGuruNY » Sat Dec 17, 2016 7:45 pm
melguy wrote:A certain fruit stand sold apples for $0.70 each and bananas for $0.50 each. If a customer purchased both apples and bananas from the stand for a total of $6.30, what total number of apples and bananas did the customer purchase?

(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Let $B = the amount spent on bananas and $A = the amount spent on apples.

Since each banana sells for 50 cents, we get the following options for $B, in cents:
50, 100, 150, 200...

Every value in the list above ends in 50 or 00.
Implication:
Since $B + $A = 630, $A must end in either 80 or 30.

Since each apple sells for 70 cents, we get the following options for $A:
70, 140, 210, 280...

Test the value in blue.
If $A = 280, then $B = 630-280 = 350.
In this case:
Number of apples purchased = (total spent on apples)/(price per apple) = 280/70 = 4.
Number of bananas purchased = (total spent on bananas)/(price per banana) = 350/50 = 7.
Total amount of fruit purchased = 4+7 = 11.

The correct answer is B.
Last edited by GMATGuruNY on Sat Dec 17, 2016 9:04 pm, edited 1 time in total.
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by Brent@GMATPrepNow » Sat Dec 17, 2016 8:20 pm
A certain fruit stand sold apples for $0.70 each and bananas for $0.50 each. If a customer purchased both apples and bananas for a total of $6.30, what number of apples and bananas did the customer purchase.

A)10
B)11
C)12
D)13
E)14
Here's an approach where we test the POSSIBLE SCENARIOS.

FACT #1: (total cost of apples) + (total cost of bananas) = 630 CENTS
FACT #2: total cost of bananas is DIVISIBLE by 50, since each banana costs 50 cents.

Now let's start testing POSSIBLE scenarios.

Customer buys 1 apple.
1 apple costs 70 cents, which means the remaining 560 cents was spent on bananas.
Since 560 is NOT divisible by 50, this scenario is IMPOSSIBLE

Customer buys 2 apples.
2 apple costs 140 cents, which means the remaining 490 cents was spent on bananas.
Since 490 is NOT divisible by 50, this scenario is IMPOSSIBLE

Customer buys 3 apples.
3 apple costs 210 cents, which means the remaining 520 cents was spent on bananas.
Since 520 is NOT divisible by 50, this scenario is IMPOSSIBLE

Customer buys 4 apples.
4 apple costs 280 cents, which means the remaining 350 cents was spent on bananas.
Since 350 IS divisible by 50, this scenario is POSSIBLE
350 cents buys 7 bananas.
So, the customer buys 4 apples and 7 bananas for a total of 11 pieces of fruit

Answer: B

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Brent
Brent Hanneson - Creator of GMATPrepNow.com
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