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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danielanassar
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Brent@GMATPrepNow
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Here's an approach where we test the POSSIBLE SCENARIOS.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
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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I should mention that we can't really solve this question using regular algebra.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
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: https://www.beatthegmat.com/og-13-132-t117594.html
Cheers,
Brent
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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
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
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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.
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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Jeff@TargetTestPrep
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We are given that apples were sold for $0.70 each and that bananas were sold for $0.50 each. We can set up variables for the number of apples sold and the number of bananas sold.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
b = number of bananas sold
a = number of apples sold
With these variables, it follows that:
0.7a + 0.5b = 6.3
We can multiply this equation by 10 to get:
7a + 5b = 63
Notice that we do not have any other information to set up a second equation, as we sometimes do for problems with two variables. So, we must use what we have. Keep in mind that variables a and b MUST be whole numbers, because you can't purchase 1.4 apples, for example. Notice also that 7 and 63 have a factor of 7 in common. Thus, we can move 7a and 63 to one side of the equation and leave 5b on the other side of the equation, and scrutinize the new equation carefully:
5b = 63 - 7a
5b = 7(9 - a)
b = [7(9 - a)]/5
Remember that a and b MUST be positive whole numbers here. Thus, 5 must evenly divide into 7(9 - a). Since we know that 5 DOES NOT divide evenly into 7, it MUST divide evenly into (9 - a). We can ask the question: What must a equal so that 5 divides into 9 - a? Of course, a could equal 9; but that would produce a zero for b and since the question states apples AND bananas were purchased, b cannot equal zero. The only other value a can be is 4. We can check this:
(9 - a)/5 = ?
(9 - 4)/5 = ?
5/5 = 1
Since we know a = 4, we can use that to determine the value of b.
b = [7(9 - 4)]/5
b = [7(5)]/5
b = 35/5
b = 7
Thus a + b = 4 + 7 = 11.
Answer: B
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Let $B = the amount spent on bananas and $A = the amount spent on apples.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
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.
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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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