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Register now and save up to $200 Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code ## Operations with Integers tagged by: Brent@GMATPrepNow This topic has 4 expert replies and 0 member replies danielanassar Newbie | Next Rank: 10 Posts Joined 02 May 2016 Posted: 2 messages #### Operations with Integers Wed Jul 06, 2016 4:20 pm Elapsed Time: 00:00 • Lap #[LAPCOUNT] ([LAPTIME]) 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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### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
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Wed Jul 06, 2016 5:13 pm
Quote:
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 Cheers, Brent _________________ Brent Hanneson – Founder of GMATPrepNow.com Use our video course along with Check out the online reviews of our course Come see all of our free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert Brent@GMATPrepNow GMAT Instructor Joined 08 Dec 2008 Posted: 10763 messages Followed by: 1212 members Thanked: 5146 times GMAT Score: 770 Wed Jul 06, 2016 5:13 pm Quote: 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
I should mention that we can't really solve this question using regular algebra.
If we let A = total cost of apples (in cents),
and let B = total cost of bananas (in cents),
we get the equation 70A + 50B = 630

In high school we learned that, if we're given 1 equation with 2 variables, we cannot find the value of either variable. However, if we restrict the variables to POSITIVE INTEGERS, then there are times when we can find the value of a variable if we're given 1 equation with 2 variables.

Here's a similar question from the Official Guide: http://www.beatthegmat.com/og-13-132-t117594.html

Cheers,
Brent

_________________
Brent Hanneson – Founder of GMATPrepNow.com
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Check out the online reviews of our course
Come see all of our free resources

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### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
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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 ### GMAT/MBA Expert Matt@VeritasPrep GMAT Instructor Joined 12 Sep 2012 Posted: 2560 messages Followed by: 113 members Thanked: 581 times Target GMAT Score: V51 GMAT Score: 780 Thu Jul 07, 2016 2:57 pm I'm going to leave you guys in the shade here 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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