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Which of the following is greater than 3/4 ?

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Which of the following is greater than 3/4 ?

by gmattesttaker2 » Sat Oct 05, 2013 12:07 am
Hello,

This is from MGMAT CAT:

Which of the following is greater than 3/4?

A) (3/4)^2
B) (7/9)^2
C) 31/42
D) 16/21
E) sq.root (1/2)

OA: D

I was able to get the correct answer but I was'nt sure if my method was the best. Here is my approach:

A) (3/4)^2 has to be less than 3/4 - Hence A ruled out

B) Convert 3/4 and 7/9 to common base i.e. 27/36 and 28/36. My reasoning was 28/36 is slightly more than 27/36 but because we square 28/36 it will be at least as small as 27/36. (Not sure if this reasoning is correct though.)

E) sq. root ( 1/2) = 1/1.4 = 10/14 = 5/7 = 0.71. Hence ruled out


I was stuck between C and D. I think I manually calcuated both of them to get the correct answer. Is there a better way to solve this problem? Thanks for your help.

Best Regards,
Sri
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by theCodeToGMAT » Sat Oct 05, 2013 12:26 am
3/4 = .75
A) (3/4)^2 --> (.7_)^2 = 0.4_ to 0.5_

B) (7/9)^2 --> (.7_)^2 = 0.4_ to 0.5_

C) 31/42 --> 31/40 = ~0.77 (rough approx by 31/4) ... since we are increasing denominator by 3.. so value will further decrease..

D) 16/21 --> 16/20 = 8 .. so little less than 8

E) sq.root (1/2) --> 1/1.4 = 10/14 = 5/7 = 0.71
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by daddymention2 » Sat Oct 05, 2013 12:43 am
Looking at C (31/42) and D (16/21) it was quickly apparent to me that D > C, because by doubling the denominator of D to 42 you can see 32>31.

I'm not sure how you calculated C and D manually, but the quickest way I thought of was working out what three quarters of 42 and 21 were (31.5 and 15.75), and comparing these to the denominators.
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by daddymention2 » Sat Oct 05, 2013 12:43 am
Looking at C (31/42) and D (16/21) it was quickly apparent to me that D > C, because by doubling the denominator of D to 42 you can see 32>31.

I'm not sure how you calculated C and D manually, but the quickest way I thought of was working out what three quarters of 42 and 21 were (31.5 and 15.75), and comparing these to the denominators.
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by vinay1983 » Sat Oct 05, 2013 1:01 am
gmattesttaker2 wrote:Hello,

This is from MGMAT CAT:

Which of the following is greater than 3/4?

A) (3/4)^2
B) (7/9)^2
C) 31/42
D) 16/21
E) sq.root (1/2)

OA: D

I was able to get the correct answer but I was'nt sure if my method was the best. Here is my approach:

A) (3/4)^2 has to be less than 3/4 - Hence A ruled out

B) Convert 3/4 and 7/9 to common base i.e. 27/36 and 28/36. My reasoning was 28/36 is slightly more than 27/36 but because we square 28/36 it will be at least as small as 27/36. (Not sure if this reasoning is correct though.)

E) sq. root ( 1/2) = 1/1.4 = 10/14 = 5/7 = 0.71. Hence ruled out


I was stuck between C and D. I think I manually calcuated both of them to get the correct answer. Is there a better way to solve this problem? Thanks for your help.

Best Regards,
Sri
A rule i know as the fraction increases it tends to get nearer to 0 and the vice versa is true. So the question is 3/4 is 0.75, which of the following is greater than 0.75.

A 3/2 squared will definitely be lower than 0.75 ruled out (above rule)
B 7/9 is 0.77 but the square will result in value lesser than 0.77 so out
C 31/42 approx is 30/42=15/21=5/7=0.71 out (even after approximation, it will be less than 0.75
D 16/21 approx 16/20 approx 4/5 approx 0.8 condidate for correct answer
E 1/2 is 0.5 so square root will definitely result in less than 0.5

D for me
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by rakeshd347 » Sat Oct 05, 2013 1:35 am
gmattesttaker2 wrote:Hello,

This is from MGMAT CAT:

Which of the following is greater than 3/4?

A) (3/4)^2
B) (7/9)^2
C) 31/42
D) 16/21
E) sq.root (1/2)

OA: D

I was able to get the correct answer but I was'nt sure if my method was the best. Here is my approach:

A) (3/4)^2 has to be less than 3/4 - Hence A ruled out

B) Convert 3/4 and 7/9 to common base i.e. 27/36 and 28/36. My reasoning was 28/36 is slightly more than 27/36 but because we square 28/36 it will be at least as small as 27/36. (Not sure if this reasoning is correct though.)

E) sq. root ( 1/2) = 1/1.4 = 10/14 = 5/7 = 0.71. Hence ruled out


I was stuck between C and D. I think I manually calcuated both of them to get the correct answer. Is there a better way to solve this problem? Thanks for your help.

Best Regards,
Sri
The best approach with these comparison question is to either make numerators or denominators equal on both sides.
Here we have.
A) (3/4)^2=9/4
Say 9/16>9/16 no way its easy to it is out.
B) (7/9)^2= 49/81
49/81>3/4 cross multiply...you will get 49*4>3*81...no its wrong so out.

C) 31/42
31/42>3/4 cross multiply...you will get 31*4>3*42 or 124>126 No its wrong so out.
D) 16/21
16/21>3/4 cross multiply....you will get 64>63.....yes this is the correct answer
E) sq.root (1/2)
sq. root(1/2)>3/4...1/2>9/16 cross multiply you will get...16>18 no wrong answer so Out.

Correct answer is D

You don't have to do the decimal division if you cross multiply and if the equality sign holds true then its good otherwise ignore it. remember Multiplication is generally easier than division.
If you want to check which one of these is bigger
21/43 or 14/17
best thing is assume 21/43 is bigger than 14/17 and make the equality sign 21/43>14/17...or divide both side by 7....3/43>2/17...51>86...so equality sign doesn't hold so 14/17 is bigger than 21/43.

As you have mentioned that you eliminated all other choices but C and D. C and D are easy to sort out.
C) 31/42
D) 16/21=32/42 ( multiply and divide by 2.) you can see clearly D is bigger than C.
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by GMATGuruNY » Sat Oct 05, 2013 3:17 am
gmattesttaker2 wrote:Hello,

This is from MGMAT CAT:

Which of the following is greater than 3/4?

A) (3/4)^2
B) (7/9)^2
C) 31/42
D) 16/21
E) sq.root (1/2)

OA: D
To compare positive fractions, CROSS-MULTIPLY.

When a problem requires that all 5 answer choices be evaluated, the correct answer choice is likely to be D or E (so that the average test-taker will waste time checking all 5 answer choices).
Between D and E, D is easier to evaluate:

16/21 > 3/4
4*16 > 3*21
64 > 63.
Success!
No need to check the other answer choices.

The correct answer is D.
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by theCodeToGMAT » Sat Oct 05, 2013 3:20 am
GMATGuruNY wrote:
To compare positive fractions, CROSS-MULTIPLY.

When a problem requires that all 5 answer choices be evaluated, the correct answer choice is likely to be D or E (so that the average test-taker will waste time checking all 5 answer choices).
Between D and E, D is easier to evaluate:

16/21 > 3/4
4*16 > 3*21
64 > 63.
Success!
No need to check the other answer choices.

The correct answer is D.
Oh yeah.... I remember this method which you showed in Inequalities question..

Thanks!!!
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