Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 20 Aug 2009
Posts: 103

The sum of ages of 22 boys and 24 girls is 160. What is the
[#permalink]
Show Tags
28 Aug 2009, 06:12
Question Stats:
79% (01:41) correct 21% (02:28) wrong based on 351 sessions
HideShow timer Statistics
The sum of ages of 22 boys and 24 girls is 160. What is the sum of ages of one boy and one girl, if all the boys are of the same age and all the girls are of the same age, and only full years are counted? A. 5 B. 6 C. 7 D. 8 E. 9
Official Answer and Stats are available only to registered users. Register/ Login.




Manager
Joined: 25 Aug 2009
Posts: 168

Re: GmatScore: Boyz&Girls
[#permalink]
Show Tags
29 Aug 2009, 06:01
Let age of one boy = b & age of one girl = g
Then, We have to find out b+g
Remember, b & g can not be negative ( because these are ages) Given that,
22b + 24g = 160 ( only full years are counted is another way of saying b and g are integers)
=> 11b + 12g = 80
Now, we know that, Even + Even or odd + odd can result in even number.
80 is an even number and 12 g is also even.
So, 11b should also be even.
hence, b can take values 2,4,6 only ( from 8 onwards, 11b will exceed 80 which is not possible)
If b = 2 then g = 58/12 ( not integer) if b = 4 then g = 36/12 = 3 if b = 6 then g = 14/14 ( not integer)
Hence, only b = 4 and g = 3 satisfies all the conditions and the equation.
Therefore, b + g = 7
Hence, C is the answer.




Intern
Joined: 30 Jun 2009
Posts: 48

Re: GmatScore: Boyz&Girls
[#permalink]
Show Tags
28 Aug 2009, 07:52
Ans is C. But I am sure that I am adopting the wrong method bcse time consuming
22x + 24y = 160 let's pick x+y=7 x=1; y=6 => 22+144 = 166 x=2; y=5 => 44+120 = 164 x=3; y=4 => 66+96 = 162 x=4; y=3 => 88+72 = 160 x=5; y=2 => 110+48 = 158 x=6; y=1 => 132+24 = 156
Basically what you can also notice is that if for (x+y)=7, you take the bigger possible factor (y) for 24 and the smallest, your result will be between 156 and 166
Basically what you can also notice is that if for (x+y)=5, you take the bigger possible factor (y) for 24 and the smallest, your result will be between 112 and 118
Basically what you can also notice is that if for (x+y)=6, you take the bigger possible factor (y) for 24 and the smallest, your result will be between 134 and 142
.....
Does that makes sense



Director
Joined: 01 Apr 2008
Posts: 821
Name: Ronak Amin
Schools: IIM Lucknow (IPMX)  Class of 2014

Re: GmatScore: Boyz&Girls
[#permalink]
Show Tags
28 Aug 2009, 08:20
What is the source of this question? I do not know which concept is tested here. If we round off we get 3.5 as the age of each boy/girl.
Total is 7..but then what is the meaning of "full years are counted"? I can only think of the following..since the number of girls are higher we have to take 4 as the full years ( as the decimal will be closer to 4 ) and for boys 3. Is this what is tested here?



Manager
Affiliations: CFA Level 2 Candidate
Joined: 29 Jun 2009
Posts: 198
Schools: RD 2: Darden Class of 2012

Re: GmatScore: Boyz&Girls
[#permalink]
Show Tags
28 Aug 2009, 08:40
Sometimes an equation works less efficiently than picking numbers. This is one of the cases.
You can solve this question by testing the min/max values. Note I assume 0 cannot be a value since being 0 years old doesn't really make sense. Although if you rerun the calculations with 0 nothing is affect.
A) 5  Max 22(1) + 24(4) = 118 too low B) 6  Max 22(1) + 24(5) = 142 too low E) 9  Min 22 (8) + 24(1) = 200 too high D) 8  Min 22 (7) + 24(1) = 178 too high
C) Is really all that is left



Manager
Joined: 14 Aug 2009
Posts: 121

Re: GmatScore: Boyz&Girls
[#permalink]
Show Tags
29 Aug 2009, 01:07
20x+24y=160 5x+6y=40 suppose x+y=t then 5x+5y=5t or 6x+6y=6t y=405t>=0 x=6t40>=0 6.67=<t=<8 t=7 Ans C
_________________
Kudos me if my reply helps!



Manager
Joined: 20 Aug 2009
Posts: 103

Re: GmatScore: Boyz&Girls
[#permalink]
Show Tags
29 Aug 2009, 01:29
Thank you, guys! Flyingbunny  kudos to you) The only note is that we should use >0 equation (instead of =>0), cause if we assume that the age of a person could be equal to 0, this means that the person has not been born yet which is definitely not the case.



Manager
Status: mba here i come!
Joined: 07 Aug 2011
Posts: 230

Re: GmatScore: Boyz&Girls
[#permalink]
Show Tags
27 Feb 2012, 12:22
22b + 22g = 160 11b + 12g = 80 11(b+g) = 80g \(b+g = \frac{80g}{11}\) try g=3 (no other value is possible) and you will get b=4 ans: 7
_________________
press +1 Kudos to appreciate posts Download Valuable Collection of Percentage Questions (PS/DS)



Math Expert
Joined: 02 Sep 2009
Posts: 47977

Re: The sum of ages of 22 boys and 24 girls is 160. What is the
[#permalink]
Show Tags
27 Feb 2012, 14:05



Intern
Joined: 22 Feb 2014
Posts: 30

Re: The sum of ages of 22 boys and 24 girls is 160. What is the
[#permalink]
Show Tags
03 Aug 2014, 13:24
22*b+24*g = 160 => 22(b+g) + 2g = 160 => 11(b+g) + g = 80. Using the choices, A isn't feasible, B isn't feasible, C is, D & E overshoot 80, so C it is.



Intern
Joined: 17 Aug 2015
Posts: 7

Re: The sum of ages of 22 boys and 24 girls is 160. What is the
[#permalink]
Show Tags
26 Sep 2015, 06:11
We are looking for B + G ..?
And the stem gives us: 22B + 24G = 160.....
B + 24/22G = 160/22
Approximately:
7<B+ 12/11G<8 .... Looking at the answers we can clearly see that the summ would be around 7. Which is the right answer ! Hope it helped !



NonHuman User
Joined: 09 Sep 2013
Posts: 7748

Re: The sum of ages of 22 boys and 24 girls is 160. What is the
[#permalink]
Show Tags
13 Nov 2017, 06:14
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: The sum of ages of 22 boys and 24 girls is 160. What is the &nbs
[#permalink]
13 Nov 2017, 06:14






