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Operations with Integers

This topic has 4 expert replies and 0 member replies
danielanassar Newbie | Next Rank: 10 Posts Default Avatar
Joined
02 May 2016
Posted:
2 messages

Operations with Integers

Post Wed Jul 06, 2016 4:20 pm
Could you please help me understand how to solve this problem:

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?

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Post Thu Jul 07, 2016 2:57 pm
I'm going to leave you guys in the shade here Very Happy

We know a + b < 13, since 13 * 50¢ is too much money.

We know a + b > 9, since 9 * 70¢ = $6.30, and we were told that we didn't only buy apples.

So a + b = 10, 11, or 12.

We also know that 7a + 5b = 63. If a and b are both odd, then we'd have Odd + Odd, which = Even. But we're told that 7a + 5b = Odd. Hence a = even and b = odd, or vice versa.

Since Even + Odd = Odd, we know the only answer is 11.

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Post Wed Jul 06, 2016 9:06 pm
Hi danielanassar,

In the future, you should make sure to post the entire prompt (including the 5 answer choices). In many cases, the answer choices provide a 'hint' as to how you might go about solving the problem. Here, the answer choices are relatively small and 'close together', so we can use a bit of 'brute force' to get to the correct answer:

We know that there will be no fewer than 10 total pieces of fruit and no more than 14 total pieces of fruit that will total $6.30, so I'm going to list out the first several multiples of apple prices and banana prices:

Apples:
$0.70
$1.40
$2.10
$2.80
$3.50
$4.20
$4.90
$5.60
Etc.

Bananas:
$0.50
$1.00
$1.50
$2.00
$2.50
$3.00
$4.00
$4.50
Etc.

Now we just have to find a pair of numbers (one from each group) that will total $6.30. It's not too much work to find that $2.80 and $3.50 total $6.30, so the total number of pieces of fruit is 7+4 = 11

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

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GMAT/MBA Expert

Matt@VeritasPrep GMAT Instructor
Joined
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Posted:
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GMAT Score:
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Post Thu Jul 07, 2016 2:57 pm
I'm going to leave you guys in the shade here Very Happy

We know a + b < 13, since 13 * 50¢ is too much money.

We know a + b > 9, since 9 * 70¢ = $6.30, and we were told that we didn't only buy apples.

So a + b = 10, 11, or 12.

We also know that 7a + 5b = 63. If a and b are both odd, then we'd have Odd + Odd, which = Even. But we're told that 7a + 5b = Odd. Hence a = even and b = odd, or vice versa.

Since Even + Odd = Odd, we know the only answer is 11.

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Post Wed Jul 06, 2016 9:06 pm
Hi danielanassar,

In the future, you should make sure to post the entire prompt (including the 5 answer choices). In many cases, the answer choices provide a 'hint' as to how you might go about solving the problem. Here, the answer choices are relatively small and 'close together', so we can use a bit of 'brute force' to get to the correct answer:

We know that there will be no fewer than 10 total pieces of fruit and no more than 14 total pieces of fruit that will total $6.30, so I'm going to list out the first several multiples of apple prices and banana prices:

Apples:
$0.70
$1.40
$2.10
$2.80
$3.50
$4.20
$4.90
$5.60
Etc.

Bananas:
$0.50
$1.00
$1.50
$2.00
$2.50
$3.00
$4.00
$4.50
Etc.

Now we just have to find a pair of numbers (one from each group) that will total $6.30. It's not too much work to find that $2.80 and $3.50 total $6.30, so the total number of pieces of fruit is 7+4 = 11

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

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