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. 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.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 22 Sep 2010
Posts: 77

A certain fruit stand sold apples for $0.70 each and bananas
[#permalink]
Show Tags
Updated on: 03 Mar 2012, 22:43
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
Official Answer and Stats are available only to registered users. Register/ Login.
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




Math Expert
Joined: 02 Sep 2009
Posts: 52294

Re: help me to solve it.....
[#permalink]
Show Tags
30 Sep 2010, 04:22




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
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




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 \(b=7\) > \(a+b=11\). Answer: B. 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
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: \(7a+5b=63\) > \(5b=637a\) > \(5b=7(9a)\) > \(5b\) 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.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



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
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.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



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
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/integralsolutionsofaxbyc.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



Manager
Joined: 20 Dec 2010
Posts: 153
Location: Stockholm, Sweden

Re: help me to solve it.....
[#permalink]
Show Tags
21 Dec 2010, 15:58
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 95 = 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: 12032014

Re: A certain fruit stand sold apples for $0.70 each and bananas
[#permalink]
Show Tags
21 Dec 2014, 12:38
from the question we get the following equation : 0.7A+0.5B = 6.3 this can be written as : 7A+5B = 63 Now rather than randomly plugging in values , we can do the following : 5B = 63  7A ==> 5B = 7(9A)
this tells us that B should be a multiple of 7. it cannot be 14 as then the value will be greater than 63. hence B = 7 and A = 4 Ans is 11



Director
Joined: 23 Jan 2013
Posts: 559

Re: A certain fruit stand sold apples for $0.70 each and bananas
[#permalink]
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+(6328)/5=4+7=11
B



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

Re: A certain fruit stand sold apples for $0.70 each and bananas
[#permalink]
Show Tags
05 Jan 2015, 07:02
A = Apples B = Bananas
0.7A + 0.5B = 6.3 7A + 5B = 63 5B = 63  7A 5B = 7 (9  A)
Therefore, B has to be = 7 And, 5 = (9  A) i.e. A = 4
A + B = 7 + 4 = 11
Answer: B



Manager
Joined: 30 Dec 2015
Posts: 83
GPA: 3.92
WE: Engineering (Aerospace and Defense)

Re: A certain fruit stand sold apples for $0.70 each and bananas
[#permalink]
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

A certain fruit stand sold apples for $0.70 each and bananas
[#permalink]
Show Tags
Updated on: 09 Jan 2017, 14:33
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, 14:24.
Last edited by dannythor6911 on 09 Jan 2017, 14:33, edited 1 time in total.



Intern
Joined: 19 Nov 2016
Posts: 16

A certain fruit stand sold apples for $0.70 each and bananas
[#permalink]
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 ]



