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

 It is currently 20 Jan 2019, 00:02

### 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

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### FREE Quant Workshop by e-GMAT!

January 20, 2019

January 20, 2019

07:00 AM PST

07:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.
• ### GMAT Club Tests are Free & Open for Martin Luther King Jr.'s Birthday!

January 21, 2019

January 21, 2019

10:00 PM PST

11:00 PM PST

Mark your calendars - All GMAT Club Tests are free and open January 21st for celebrate Martin Luther King Jr.'s Birthday.

### Show Tags

Updated on: 03 Mar 2012, 22:43
6
57
00:00

Difficulty:

25% (medium)

Question Stats:

80% (01:59) correct 20% (02:00) wrong based on 2343 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. 15 Originally posted by pzazz12 on 30 Sep 2010, 04:08. Last edited by Bunuel on 03 Mar 2012, 22:43, edited 1 time in total. Edited the question ##### Most Helpful Expert Reply Math Expert Joined: 02 Sep 2009 Posts: 52294 Re: help me to solve it..... [#permalink] ### Show Tags 30 Sep 2010, 04:22 7 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: 360
Location: Milky way
Schools: ISB, Tepper - CMU, Chicago Booth, LSB
Re: help me to solve it.....  [#permalink]

### Show Tags

30 Sep 2010, 18:49
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: 77 Re: help me to solve it..... [#permalink] ### Show Tags 01 Oct 2010, 04:06 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: 52294
Re: help me to solve it.....  [#permalink]

### Show Tags

01 Oct 2010, 04:49
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: 29
Re: help me to solve it.....  [#permalink]

### Show Tags

10 Dec 2010, 19:14
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: 52294 Re: help me to solve it..... [#permalink] ### Show Tags 10 Dec 2010, 23:01 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.
_________________
Intern
Joined: 31 Oct 2010
Posts: 29
Re: help me to solve it.....  [#permalink]

### Show Tags

11 Dec 2010, 07:20
haha crystal as usual.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8795
Location: Pune, India
Re: A certain fruit stand sold apples for $0.70 [#permalink] ### Show Tags 12 Dec 2010, 04:30 1 3 ajit257 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

Is there a faster way to do these problems other than brute force ?

The first solution will invariably involve some brute force. But (9, 0) is easy to get since 63 is a multiple of 7.
Check out this post for clarification on these type of questions:
http://gmatquant.blogspot.com/2010/11/integral-solutions-of-ax-by-c.html
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

Math Expert
Joined: 02 Sep 2009
Posts: 52294
Re: Alternate approaches to OG 12 PS #65?  [#permalink]

### Show Tags

21 Dec 2010, 15:20
3
15
Manager
Joined: 20 Dec 2010
Posts: 153
Location: Stockholm, Sweden
Re: help me to solve it.....  [#permalink]

### Show Tags

21 Dec 2010, 15:58
11
1
Maybe it could be of any help to realise that

0.7y + 0.5x = 6.3 is a straight line, we want the 'y' on the left side, rewriting gives:
7y + 5x = 63
y = 9 - (5/7)x

Almost instantly you should see that the right term (5/7) can only be an integer if X is either 7, 14, 28 and so forth.
Ruling out fourteen we only have 7 left which gives 9-5 = 4 +7 fruits.
_________________

12/2010 GMATPrep 1 620 (Q34/V41)
01/2011 GMATPrep 2 640 (Q42/V36)
01/2011 GMATPrep 3 700 (Q47/V39)
02/2011 GMATPrep 4 710 (Q48/V39)
02/2011 MGMAT CAT 1 650 (Q46/V32)
02/2011 MGMAT CAT 2 680 (Q46/V36)
02/2011 MGMAT CAT 3 710 (Q45/V41)

Manager
Joined: 12 Jan 2013
Posts: 152
Re: A certain fruit stand sold apples for $0.70 each and bananas [#permalink] ### Show Tags 17 Dec 2013, 02:46 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

He buys both, and the only combination of multiples of 5 and 7 that end in the single digit 3 is the single digits of the respective multiples ending in 8 and 5, which means 28 = 4*7 for bananas, and 7*5 = 35 for apples.. From here you can simply just add a decimal inbetween so that the restriction is upheld.

4 bananas and 7 apples gives us 11 fruits.
Intern
Joined: 06 Nov 2014
Posts: 10
Re: A certain fruit stand sold apples for $0.70 each and bananas [#permalink] ### Show Tags 24 Nov 2014, 09:29 I just started by thinking ok at least 5*7 and 7*5 is an easy approach to start with to find multiples. If you look at the answer choices that would be 12 fruits, so somewhere in the middle of your options. In total that would be 70 (or$7), so clearly "one seven less" is 63, so that's 4*7 + 7*5 = fruits 4+7=11.
Manager
Joined: 07 Dec 2009
Posts: 91
GMAT Date: 12-03-2014

### Show Tags

21 Dec 2014, 23:51
7x+5y=63

multiple of 5 gives numbers only ending 0 or 5, so multiple of 7 should end 3 or 8 respectively.
7*9=63 (eliminate - no option for 5)
7*8=56
7*7=49
7*6=42
7*5=35
7*4=28
7*3=21
7*2=14
7*1=7

it is 4+(63-28)/5=4+7=11

B
Manager
Joined: 03 Jan 2015
Posts: 61
Concentration: Strategy, Marketing
WE: Research (Pharmaceuticals and Biotech)

### Show Tags

08 Oct 2016, 19:18

_________________

If you analyze enough data, you can predict the future.....its calculating probability, nothing more!

GMAT Tutor
Joined: 01 Oct 2016
Posts: 10

### Show Tags

05 Jan 2017, 16:48
My approach:
A-->Apples:0.70
B-->Bananas: 0.50
so..
Bought Spent
1A+1B= 1.20
2A+2B= 2.40
3A+3B= 3.60
4A+4B= 4.80
5A+5B= 6.00 -> 5+5 =10 but still have 0,30 that were spent so it cant be (A), the next possible value is 11 according to the answers (B)
I hope that works!
Manager
Joined: 25 Mar 2013
Posts: 240
Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.5
Re: A certain fruit stand sold apples for $0.70 each and bananas [#permalink] ### Show Tags 06 Jan 2017, 17:34 0.7a + 0.5 b = 6.30$
Assume a = 5, b = 5
3.5 + 2.5 = 6.0$more 0.3$
more 10
11
B
_________________

I welcome analysis on my posts and kudo +1 if helpful. It helps me to improve my craft.Thank you

Re: A certain fruit stand sold apples for $0.70 each and bananas &nbs [#permalink] 06 Jan 2017, 17:34 Go to page 1 2 Next [ 31 posts ] Display posts from previous: Sort by # A certain fruit stand sold apples for$0.70 each and bananas

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.