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MGMAT Benchmark method for fractions

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MGMAT Benchmark method for fractions [#permalink] New post 06 May 2011, 19:49
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Hello

I am a newbie brushing up my basics on Quant. Please help. I am a bit confused with the method the bench mark values used by MGMAT guide 2. In the problem set Chapter 2 Q10

Put these fractions from the least to the greatest

9/17 , 3/6, 19/20 , 7/15

Explanation

9/17 is slightly more than 1/2
3/16 is slightly less than 1/4
19/20 is slightly less than 1
7/15 is slightly less than 1/2.

I am a bit confused with the language. For example how is 3/16 is slightly less than 1/4.

3 x 5 = 15
3 x 6 = 18

so it should fall between 1/5 and 1/6 hence it should be more than 1/4 not less (if i make any sense!)


Same with all the fractions. The language is exactly opposite what i expected it to be.

Please help clarify.
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Re: MGMAT Benchmark method for fractions [#permalink] New post 06 May 2011, 21:35
First get the half and quarter and then compare it to the other fraction.

We know this -
1/2 = 9/18 = 7/14
1/4 = 4/16 = 3/12
1 = 19/19

Now -
9/17 is slightly more than 1/2 ----> The half is 9/18. So 9/17 is more than 0.5
3/16 is slightly less than 1/4 ----> The quarter is 3/12. Hence 3/16 is less than 0.25
19/20 is slightly less than 1 -----> 1 whole is 19/19. hence 19/20 is about 0.9
7/15 is slightly less than 1/2 ----> The half is 7/14. hence 7/15 is less than 0.5

melguy wrote:
Hello

I am a newbie brushing up my basics on Quant. Please help. I am a bit confused with the method the bench mark values used by MGMAT guide 2. In the problem set Chapter 2 Q10

Put these fractions from the least to the greatest

9/17 , 3/6, 19/20 , 7/15

Explanation

9/17 is slightly more than 1/2
3/16 is slightly less than 1/4
19/20 is slightly less than 1
7/15 is slightly less than 1/2.

I am a bit confused with the language. For example how is 3/16 is slightly less than 1/4.

3 x 5 = 15
3 x 6 = 18

A good way to look is approx. ie. consider Let x = 3/16. Since 15 is a multiple of 3. Letme write x is close to 3/15 Now x will be less than this since denominator of x is > 15. Hence x is slightly less than 3/15 or 0.2

Hence x is less than 1/4 or 0.25

so it should fall between 1/5 and 1/6 hence it should be more than 1/4 not less (if i make any sense!)


Same with all the fractions. The language is exactly opposite what i expected it to be.

Please help clarify.
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Re: MGMAT Benchmark method for fractions [#permalink] New post 06 May 2011, 22:27
3/6 = 1/2

9/17 means it is greater than 9/18 as the denominator is lesser.

7/15 it is slightly lesser than 7/14 as the denominator is greater.

19/20 will have the greatest value close to 1.

thus the order is 7/15 < 3/6 < 9/17 < 19/20.
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Re: MGMAT Benchmark method for fractions [#permalink] New post 07 May 2011, 03:34
melguy wrote:
Hello

I am a newbie brushing up my basics on Quant. Please help. I am a bit confused with the method the bench mark values used by MGMAT guide 2. In the problem set Chapter 2 Q10

Put these fractions from the least to the greatest

9/17 , 3/6, 19/20 , 7/15

Explanation

9/17 is slightly more than 1/2
3/16 is slightly less than 1/4
19/20 is slightly less than 1
7/15 is slightly less than 1/2.

I am a bit confused with the language. For example how is 3/16 is slightly less than 1/4.

3 x 5 = 15
3 x 6 = 18

so it should fall between 1/5 and 1/6 hence it should be more than 1/4 not less (if i make any sense!)


Same with all the fractions. The language is exactly opposite what i expected it to be.

Please help clarify.


Another approach can be:
9/17 , 3/6, 19/20 , 7/15

Separate 3/6, 19/20 , 7/15 from 9/17
We see that 60 is the lcm for 6,20,15.

3/6, 19/20 , 7/15
Numerators will be: 30, 57, 28
Thus, 7/15 is the least among 3/6,19/20,7/15.

Now;
compare 9/17 with 7/15
7/15(less than 7/14=1/2) is less than 9/17(more than 9/18=1/2) and least among the choices.
***************************************************
7/14=1/2
If the numerator(7) is kept constant:
Increase in denominator will decrease the value of the fraction.
Decrease in denominator will increase the value of the fraction.

If the denominator(14) is kept constant:
Increase in numerator will increase the value of the fraction.
Decrease in numerator will decrease the value of the fraction.
******************************************************
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Re: MGMAT Benchmark method for fractions [#permalink] New post 07 May 2011, 07:29
given 9/17 3/6 19/20 7/15

if you look at given numbers , you should see 9/17 is close to 9/18
3/6 is 1/2
19/20 is close to 1 as numerator and denominator are pretty close.
7/15 is close to 7/14


out of 9/17 and 9/18, we can see they only differ in their denominator, greater the denominator , the smaller fraction it is. so 9/18< 9/17 => 1/2 < 9/17 . In other words we have 9/17 > 1/2
and way less than 1.

same thing with 7/15 and 7/14. if we apply the same reasoning as in the above example , we can see that 7/15 < 7/14 = > 7/15 < 1/2

so going back to our sequence of numbers 9/17 3/6 19/20 7/15

>1/2 1/2 ~=1 <1/2

so increasing order would be <1/2 1/2 >1/2 ~=1

7/15 < 3/6 < 9/17 < 19/20
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Re: MGMAT Benchmark method for fractions [#permalink] New post 11 May 2011, 05:30
To add to what fluke has suggested, to compare 9/17 with 7/15, cross multiply numerators and denominators, the fraction with the numerator giving the bigger result is greater than the other one.

So 15 * 9 = 135 and 17*7 = 119

So 9/17 > 7/15.
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Re: MGMAT Benchmark method for fractions   [#permalink] 11 May 2011, 05:30
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