GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 25 Mar 2019, 09:06

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

A certain fruit stand sold apples for $0.70 each and bananas for$0.50

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 53831
A certain fruit stand sold apples for $0.70 each and bananas for$0.50  [#permalink]

Show Tags

Updated on: 20 Feb 2019, 04:26
6
65
00:00

Difficulty:

25% (medium)

Question Stats:

80% (02:12) correct 20% (02:24) wrong based on 1834 sessions

HideShow timer Statistics

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 _________________ Originally posted by Bunuel on 30 Sep 2010, 05:08. Last edited by Bunuel on 20 Feb 2019, 04:26, edited 2 times in total. Updated. Most Helpful Expert Reply Math Expert Joined: 02 Sep 2009 Posts: 53831 Re: A certain fruit stand sold apples for$0.70 each and bananas for $0.50 [#permalink] Show Tags 30 Sep 2010, 05:22 8 17 pzazz12 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. 15

Given: $$0.7b+0.5a=6.3$$ Question: $$a+b=?$$

$$0.7a+0.5b=6.3$$ --> $$7a+5b=63$$. After some trial and error you'll get that only two integer pairs of (a,b) satisfy this equation: (9,0) and (4,7) as we are told that "a customer purchased both apples and bananas" then the first pair is out and we'll have: $$a=4$$ and $$b=7$$ --> $$a+b=11$$.

_________________
Senior Manager
Status: Time to step up the tempo
Joined: 24 Jun 2010
Posts: 353
Location: Milky way
Schools: ISB, Tepper - CMU, Chicago Booth, LSB
Re: A certain fruit stand sold apples for $0.70 each and bananas for$0.50  [#permalink]

Show Tags

30 Sep 2010, 19:49
20
9
pzazz12 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. 15 Without calculating anything in paper you could approach this problem. Know -- Some multiple of 7 + Some multiple of 5 should yield 63. To get to a some multiple of 5, we should ensure that a 3 or 8 (5+3) should be a multiple of 7. 63 is a direct multiple of 7, however in this case there won't be any bananas. Hence the next option is to look for a multiple of 7 that has 8 as the unit digit. 28 satisfies this hence no. of apples is 4 and no of bananas is 7 -- Answer 11 (B). -- 35 seconds straight. _________________ Support GMAT Club by putting a GMAT Club badge on your blog General Discussion Manager Joined: 22 Sep 2010 Posts: 76 Re: A certain fruit stand sold apples for$0.70 each and bananas for $0.50 [#permalink] Show Tags 01 Oct 2010, 05:06 Bunuel wrote: pzazz12 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. 15

Given: $$0.7b+0.5a=6.3$$ Question: $$a+b=?$$

$$0.7a+0.5b=6.3$$ --> $$7a+5b=63$$. After some trial and error you'll get that only two integer pairs of (a,b) satisfy this equation: (9,0) and (4,7) as we are told that "a customer purchased both apples and bananas" then the first pair is out and we'll have: $$a=4$$ and $$b=7$$ --> $$a+b=11$$.

thank you, but can you explain me how this (9,0) and (4,7) to be solve...
Math Expert
Joined: 02 Sep 2009
Posts: 53831
Re: A certain fruit stand sold apples for $0.70 each and bananas for$0.50  [#permalink]

Show Tags

01 Oct 2010, 05:49
9
8
pzazz12 wrote:
Bunuel wrote:
pzazz12 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. 15 Given: $$0.7a+0.5b=6.3$$ Question: $$a+b=?$$ $$0.7a+0.5b=6.3$$ --> $$7a+5b=63$$. After some trial and error you'll get that only two integer pairs of (a,b) satisfy this equation: (9,0) and (4,7) as we are told that "a customer purchased both apples and bananas" then the first pair is out and we'll have: $$a=4$$ and $$b=7$$ --> $$a+b=11$$. Answer: B. thank you, but can you explain me how this (9,0) and (4,7) to be solve... Trial and error would be good for it, but here is another way: $$7a+5b=63$$ --> $$5b=63-7a$$ --> $$5b=7(9-a)$$ --> $$5b$$ must be multiple of 7 --> $$b$$ must be multiple of 7 --> $$b$$ can not be 0 (as "a customer purchased both apples and bananas") or >14 (as $$5b$$ in this case would be more than$6.30), so $$b=7$$ --> $$a=4$$.

Hope it's clear.
_________________
Intern
Joined: 31 Oct 2010
Posts: 28
Re: A certain fruit stand sold apples for $0.70 each and bananas for$0.50  [#permalink]

Show Tags

10 Dec 2010, 20:14
ezhilkumarank wrote:
pzazz12 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. 15 Without calculating anything in paper you could approach this problem. Know -- Some multiple of 7 + Some multiple of 5 should yield 63. To get to a some multiple of 5, we should ensure that a 3 or 8 (5+3) should be a multiple of 7. 63 is a direct multiple of 7, however in this case there won't be any bananas. Hence the next option is to look for a multiple of 7 that has 8 as the unit digit. 28 satisfies this hence no. of apples is 4 and no of bananas is 7 -- Answer 11 (B). -- 35 seconds straight. i get some multipule of 5 and 7 make 63... but why the multiple of 7 with a 3 or 8? Math Expert Joined: 02 Sep 2009 Posts: 53831 Re: A certain fruit stand sold apples for$0.70 each and bananas for $0.50 [#permalink] Show Tags 11 Dec 2010, 00:01 4 2 mmcooley33 wrote: ezhilkumarank wrote: pzazz12 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. 15

Without calculating anything in paper you could approach this problem.

Know -- Some multiple of 7 + Some multiple of 5 should yield 63. To get to a some multiple of 5, we should ensure that a 3 or 8 (5+3) should be a multiple of 7.

63 is a direct multiple of 7, however in this case there won't be any bananas. Hence the next option is to look for a multiple of 7 that has 8 as the unit digit. 28 satisfies this hence no. of apples is 4 and no of bananas is 7 -- Answer 11 (B). -- 35 seconds straight.

i get some multipule of 5 and 7 make 63... but why the multiple of 7 with a 3 or 8?

ezhilkumarank means that as multiple of 5 ends with 5 or 0 then multiple of 7 must end with 8 or 3 in order their sum to end with 3 (63). There is another approach in my previous post.

Hope it's clear.
_________________
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9013
Location: Pune, India
Re: A certain fruit stand sold apples for $0.70 each and bananas for$0.50  [#permalink]

Show Tags

12 Dec 2010, 05:30
1
3
ajit257 wrote:
A certain fruit stand sold apples for $0.70 each and bananas for$0.50 each. If a customer

Show Tags

15 Oct 2012, 04:51
7
2
Let the no of apples sold = a
no of bananas sold = b
Question is a+b=?
Thus 70a + 50b = 630
7a + 5b = 63
Quick Tip- In order to find out the value of a & b its better to find the value of 'a' as "63- 7a" must leave a number which will end either with 0 or
with 5. (Think about it for a second)
Thus the only value which satisfies above equation is a=4 & b=7
a+b=11 (Other values of a & b will lie outside the answer choices)
_________________
If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS.
Kudos always maximizes GMATCLUB worth
-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply
Intern
Joined: 05 Jun 2012
Posts: 6

Show Tags

15 Oct 2012, 10:50
4
To solve this question -
we can take numbers, as price of apple 7, 5 for Banana and 63 total for ease.
Now we can determine quickly that total number should range between 63/7 <= N <=63/5, so ans should be between 9 and 12.

Now solving the expression
7A+5B =63

first possibility with 9 apples, 0 banana we get 6.30 total amount, but question says customer purchased both, apple and banana. so not correct.

So next choice, for 7A+5B =63 would come by decreasing 63 in multiple of 5 and checking divisibility of that number by 7. this way we get
4 Apples *0.70 + 7 banana *050 = 6.30

Hence total number is 7+4 =11

Ans B

Bunuel wrote:
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

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 Practice Questions Question: 64 Page: 161 Difficulty: 600 GMAT Club is introducing a new project: The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project Each week we'll be posting several questions from The Official Guide for GMAT® Review, 13th Edition and then after couple of days we'll provide Official Answer (OA) to them along with a solution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you! _________________ Lets Kudos!!! Black Friday Debrief Manager Joined: 21 Sep 2012 Posts: 195 Re: A certain fruit stand sold apples for$0.70 each and bananas  [#permalink]

Show Tags

16 Oct 2012, 03:53
5
1
so apples is 0.70 * A

Bananas 0.50 * B

then 0.70A + 0.50B = 6.30

multiply by 10 we get

7A + 5B = 63

5B = 63 - 7A
B = 7(9-A)/5

now to satisfy this equation we need 9 - A = 5 only then it will be divisible by 5
therefore A is 4 and when solve we get B is 7

7(9-4)/5 = 7*5/5 then we need the sum of A + B = 7 + 4 = 11

Director
Status: Professional GMAT Tutor
Affiliations: AB, cum laude, Harvard University (Class of '02)
Joined: 10 Jul 2015
Posts: 677
Location: United States (CA)
Age: 39
GMAT 1: 770 Q47 V48
GMAT 2: 730 Q44 V47
GMAT 3: 750 Q50 V42
GRE 1: Q168 V169
WE: Education (Education)
Re: A certain fruit stand sold apples for $0.70 each and bananas [#permalink] Show Tags 17 May 2016, 19:54 3 Attached is a visual that should help. Attachments Screen Shot 2016-05-17 at 7.43.35 PM.png [ 103.29 KiB | Viewed 8780 times ] _________________ Harvard grad and 99% GMAT scorer, offering expert, private GMAT tutoring and coaching worldwide since 2002. One of the only known humans to have taken the GMAT 5 times and scored in the 700s every time (700, 710, 730, 750, 770), including verified section scores of Q50 / V47, as well as personal bests of 8/8 IR (2 times), 6/6 AWA (4 times), 50/51Q and 48/51V (1 question wrong). You can download my official test-taker score report (all scores within the last 5 years) directly from the Pearson Vue website: https://tinyurl.com/y7knw7bt Date of Birth: 09 December 1979. GMAT Action Plan and Free E-Book - McElroy Tutoring Contact: mcelroy@post.harvard.edu (I do not respond to PMs on GMAT Club.) ...or find me on Reddit: http://www.reddit.com/r/GMATpreparation GMAT Tutor Joined: 01 Oct 2016 Posts: 10 Re: A certain fruit stand sold apples for$0.70 each and bananas for $0.50 [#permalink] Show Tags Updated on: 09 Jan 2017, 15:33 5 The algebraic explanations in this thread are valid but needlessly complicated. Plus, it is unlikely that you will be able to come up with a similar approach to such a problem on your own. There is a much simpler and more broadly applicable approach that doesn't require trial and error. Because the numbers of apples and bananas have to be integers, the easiest thing to do here is start with the total of 6.3 and subtract off .7 until you arrive at a multiple of .5. 6.3 - .7 = 5.6 5.6 - .7 = 4.9 4.2 - .7 = 4.2 4.2 - .7 = 3.5 We are now at a multiple of .5, having subtracted off 4 apples. Because the bananas are 50 cents each, this gives us 7 bananas, for a total of 11 pieces of fruit. _________________ Dan the GMAT Man Offering tutoring and admissions consulting in the NYC area and online danthegmatman.squarespace.com danthegmatman@gmail.com Originally posted by dannythor6911 on 05 Jan 2017, 15:24. Last edited by dannythor6911 on 09 Jan 2017, 15:33, edited 1 time in total. Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 5435 Location: United States (CA) Re: A certain fruit stand sold apples for$0.70 each and bananas for $0.50 [#permalink] Show Tags 09 Jan 2017, 10:33 pzazz12 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. 15

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.

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? The only 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.

_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

CEO
Joined: 12 Sep 2015
Posts: 3520
Re: A certain fruit stand sold apples for $0.70 each and bananas for$0.50  [#permalink]

Show Tags

07 Oct 2017, 06:43
Top Contributor
pzazz12 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. 15 Here's an approach where we test the POSSIBLE CASES. 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: Cheers, Brent _________________ Test confidently with gmatprepnow.com Manager Joined: 09 Jun 2017 Posts: 86 GMAT 1: 640 Q44 V35 Re: A certain fruit stand sold apples for$0.70 each and bananas  [#permalink]

Show Tags

26 May 2018, 07:46
1
After I thought of an alternative method to solve this type of problems ( an equation with two variables and constraints )
I found this method :
this equation 7x+5y= 63 represents a line
draw the line (by choosing two points , the easiest is when x=0 ,then y= ? ; when y=0,then x=? )
after drawing the line , search for a point that has x ,y integers
it's (4,7)
However , this method is not practical because it requires precise drawing , but it may give you an indication ( for example , plug and try values of x , not y because x has fewer values )
Attachments

dddd.JPG [ 67.09 KiB | Viewed 3691 times ]

_________________
Hope this helps
Give kudos if it does
Senior Manager
Joined: 04 Aug 2010
Posts: 389
Schools: Dartmouth College
Re: A certain fruit stand sold apples for $0.70 each and bananas [#permalink] Show Tags 15 Jan 2019, 04:39 Consider the following equation: 2x + 3y = 30. If x and y are nonnegative integers, the following solutions are possible: x=15, y=0 x=12, y=2 x=9, y=4 x=6, y=6 x=3, y=8 x=0, y=10 Notice the following: The value of x changes in increments of 3 (the coefficient for y). The value of y changes in increments of 2 (the coefficient for x). This pattern will be exhibited by any fully reduced equation that has two variables constrained to nonnegative integers. Bunuel 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

70x + 50y = 630
7x + 5y = 63

In accordance with the pattern illustrated above, we get the following nonnegative solutions for x and y:
x=9, y=0
x=4, y=7

Here -- since apples and bananas are both purchased -- x and y must both be positive.
Thus, only the option in green is viable, with the result that x+y = 4+7 = 11.

_________________
GMAT and GRE Tutor
Over 1800 followers
GMATGuruNY@gmail.com
New York, NY
If you find one of my posts helpful, please take a moment to click on the "Kudos" icon.
Available for tutoring in NYC and long-distance.