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Which expression has the greatest value?
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Bunuel
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Which expression has the greatest value? [#permalink] New post  06 Feb 2020, 04:27
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A
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C
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Which expression has the greatest value?


(A) \(\frac{1977452}{1977455}\)

(B) \(\frac{1982466}{1982469}\)

(C) \(\frac{1982487}{1982490}\)

(D) \(\frac{1982456}{1982459}\)

(E) \(\frac{1982465}{1982468}\)
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shameekv1989
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Re: Which expression has the greatest value? [#permalink] New post  06 Feb 2020, 04:42
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Which expression has the greatest value?


(A) \(\frac{1977452}{1977455}\)

(B) \(\frac{1982466}{1982469}\)

(C) \(\frac{1982487}{1982490}\)

(D) \(\frac{1982456}{1982459}\)

(E) \(\frac{1982465}{1982468}\)

As the difference between Numerator and denominator is 3 in each case we can take an analogy of \(\frac{4}{5}\) = 0.8 -> \(\frac{(4-1)}{(5-1)}\) =3/4 =0.75 i.e. as we decrease equivalent value from both numerator and denominator the value of the fraction decreases

Since C has the max value in the numerator and denominator C should have the greatest value

Answer - C
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suchita2409
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Re: Which expression has the greatest value? [#permalink] New post  20 Mar 2020, 04:07
Shameek Can u please elaborate

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shameekv1989
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Re: Which expression has the greatest value? [#permalink] New post  20 Mar 2020, 04:19
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suchita2409 wrote:
Shameek Can u please elaborate

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suchita2409
Consider comparing \(\frac{x}{y}\) to \(\frac{(x+1)}{(y+1)}\) What do we do - we cross multiply and compare. For eg. \(\frac{10}{11}\) compared to \(\frac{11}{12}\) -> 120 compared to 121 implies \(\frac{10}{11} < \frac{11}{12}\)

Therefore \(\frac{x}{y}\) compared to \(\frac{(x+1)}{(y+1)}\) (Or any positive number added to numerator and denominator)
x(y+1) compared to y(x+1) which is nothing but x compared to y

Thus if x < y then \(\frac{(x+1)}{(y+1)} > \frac{x}{y}\)
If x > y then \(\frac{(x+1)}{(y+1)} < \frac{x}{y} \)

Note x and y are nothing but Numerator and Denominators. You can check using values for x = 10 y=11 i.e. x<y and then x=11 y=10 x>y

Hope this makes better sense :)
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suchita2409
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Re: Which expression has the greatest value? [#permalink] New post  20 Mar 2020, 06:39
Thank u so much.
This problem chewed out my brain.

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fireagablast
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Re: Which expression has the greatest value? [#permalink] New post  20 Mar 2020, 13:22
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i just listed out the relavent digits and compared:

a) 9752 9755
b) 9866 9869
c) 9887 9890
d) 9856 9859
e) 9865 9868

Left divided by right should be the largest, which is C.
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prathyushaR
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Which expression has the greatest value? [#permalink] New post  20 Mar 2020, 13:31
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The expressions are all of the form \(a/(a+3)\)
for any given integer value of 'a'
as 'a' increases the value of the expression \(a/(a+3)\) increases
Check:
\(1/4 =0.25, 2/5 =0.4 , 9/12 =0.75\)

Thus in the given options the maximum value of a (the numerator) is in option C
ANSWER: C
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