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The sum of ages of 22 boys and 24 girls is 160. What is the

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The sum of ages of 22 boys and 24 girls is 160. What is the [#permalink] New post 28 Aug 2009, 05:12
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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
[Reveal] Spoiler: OA
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Re: GmatScore: Boyz&Girls [#permalink] New post 28 Aug 2009, 06:52
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
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Re: GmatScore: Boyz&Girls [#permalink] New post 28 Aug 2009, 07:20
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?
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Re: GmatScore: Boyz&Girls [#permalink] New post 28 Aug 2009, 07:40
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 re-run 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
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Re: GmatScore: Boyz&Girls [#permalink] New post 29 Aug 2009, 00:07
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20x+24y=160
5x+6y=40

suppose
x+y=t
then
5x+5y=5t or 6x+6y=6t

y=40-5t>=0
x=6t-40>=0

6.67=<t=<8
t=7

Ans C
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Re: GmatScore: Boyz&Girls [#permalink] New post 29 Aug 2009, 00:29
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.
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Re: GmatScore: Boyz&Girls [#permalink] New post 29 Aug 2009, 05:01
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.
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Re: GmatScore: Boyz&Girls [#permalink] New post 27 Feb 2012, 11:22
22b + 22g = 160
11b + 12g = 80
11(b+g) = 80-g

b+g = \frac{80-g}{11}

try g=3 (no other value is possible) and you will get b=4

ans: 7
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Re: The sum of ages of 22 boys and 24 girls is 160. What is the [#permalink] New post 27 Feb 2012, 13:05
Expert's post
CasperMonday wrote:
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


No need for complicated approaches: 22b+24g=160 --> 11b+12g=80. Notice that b must be even in order the sum to be even: b=2 doesn't give integer value of g, but b=4 does --> g=3 --> b+g=7. So as you see you need to try only two values to get the right answer.

Answer: C.
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Re: The sum of ages of 22 boys and 24 girls is 160. What is the   [#permalink] 27 Feb 2012, 13:05
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