Which of the following is closest to \(\frac{(998*0.02 + 4.97)}{(1002*0.02 + 5.03)}\) ?

(A) 0.50
(B) 0.89
(C) 0.98
(D) 1.02
(E) 1.05


Source: GMAT Club Tests - hardest GMAT questions

The OE is not clear..i did it without rounding it off and not getting the answer:(

(1000 - 2) x .02 + 4.97 = 20 -.04 + 4.97 = 24.93
(1000 + 2) x .02 +5.03 = 20 + .04 + 5.03= 25.07

It is less that 1.

10% of 25.07 = 2.507

so it cant be .89 or lower.

So we are left with .98.

Bad at rounding..
Got till 2493/2507.if you round this too the nearest round figure we'll get 2500/2500 =1

The question asks for the "closest" option. It's clear that the fraction is less than 1. If we know that it's less than 1, we choose 0.98 over 1.02 as the fraction is closer to 0.98 than to 1.02.

Hope it helps.

Sorry I did'nt ask the question properly..HOW do we confirm its less than one?'Cos while timing myself i did the careless error and mistook it as more than one..just trying to cut down on my errors..sorry if the question is too amateur

OK. The fraction is less than 1 when it's numerator is less than its denominator. Now let's take a look at the fraction from the stem:
\(\frac{(998*0.02 + 4.97)}{(1002*0.02 + 5.03)}\)
We know that \(4.97 \lt 5.03\). Likewise, \(998*0.02 \lt 1002*0.02\). Now we're sure that the numerator is less than the denominator in this fraction. You don't even have to multiply the figures.
Is it a bit clearer now?

Let’s use some logic..

By observation, numerator is very close too denominator.

D/E are out as numerator cannot be > denominator.
A is also out because numerator is substantially > 1/2(denominator).
B is equivalent to 90% i.e. numerator < 90% (denominator) where as .

So left with C.

Alternatively:

= \(\frac{(998*0.02 + 4.97)}{(1002*0.02 + 5.03)}\)
= \(\frac{(1000 - 2) *0.02 + 4.97)}{(1000+2)*0.02 + 5.03)}\)
= \(\frac{(20 - 0.04) + 4.97)}{(20 + 0.04) + 5.03)}\)
= \(\frac{(19.96 + 4.97)}{(20.04) + 5.03)}\)
= \(\frac{(24.93)}{(25.07)}\)
= equivalent to 1 but < 1, which is 0.98....

In 30 second, it is known that OA is C....

i guess there is no need to calculate here as it is very close to :

25/25=1 but here it is 25(-) / 25(+) where (-) means slightly below 25 and (+) slightly above 25

so the answer needs to be the closest answer to 1 and <1

so I chose 0.98

what do you think of this reasoning ?

simplified to 24.93/25.07 ~ since we can see that the numerator is smaller than the denominator we can automatically assume that the answer cannot be greater than or equal to 1 so that eliminates D & E.

After that I viewed it more as a percentage by saying what percent of 25.07 is 24.93 which is really close to 100% so I looked at the answers and went with the choice closest which is C ~ 0.98 or 98%.

I took 25.07 * .98 and got 24.5686 which is slightly smaller then 24.93 so I figured that answers A & B would put me even further away.

My answer is kind of wordy but figuring out the actual problem did not take that long.

Yes after getting 24.93/25.07 the closest choice is 0.98

I think this a 25-30 sec question
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Let's see how close to 1 is the fraction \(24.93/25.07\).
\(1-24.93/25.07=0.14/25.07<0.14/25=0.0056\)
\(1-0.98=0.02\) and \(1-0.89=0.11\)
Ans. is C.

I got C :

= 998*2+500 / 1002*2+500

=998+250/1002+250

which is slightly less then 1 , so nearest is 0.98

Basically we should not spend so much time on this question. Here is the mental math.

998 is close to 1000 (Value increased) 4.97 is close to 5 value increased.

Equation below is now completely similar to equation above. which is

1000 * .002 + 5 / 1000 (dec) * .002 + 5 (dec)

Since the values are the same which is equal to 1, and we have increased the value in numerator fractionally and similarly decreased the value in denomiator fractionally. The value has to lie close to 1 (but lesser).

which is the closest value to 1 - .98 OA C.

here is my explanation. it hardly takes a minute..

(998*0.02+4.97)/(1002*0.02+5.03)
=> (1002*0.02+5.03)-(4*0.02+2*0.03)/(1002*0.02+5.03)
=>1-((4*0.02+2*0.03)/(1002*0.02+5.03))
now, the answer can be around 1 more accurately it is less than 1.
a bit of understanding and calculation will tell you that answer is 0.98.

from observation it is clear that numerator and denominator are very close in value and also numerator is less than denominator. So for me the closest value would be 0.98

Hence (C)

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This is equivalent to
2493/2507 . I.e <1 and Close to 1.

Answer is c.

Posted from my mobile device

Simplifies down to 24.93/25.07
It is less than 1 and more than 0.90.

OA is C.

[(1000-2)*2%+(5-3%)][/(1000+2)*2%+(5+3%)]
=[1005-7%]/[1005+7%]
=1004.03/1005.07
=100%-1.04/1005.07
=98%(approx)
The ans is C

(998*0.02+4.97)/(1002*0.02+5.03)
={(1002-4)*0.02+(5.03-0.06)}/(1002*0.02+5.03)
={(1002*0.02+5.03) - (4*0.02+0.06)}/(1002*0.02+5.03)
=1-0.14/25.07
=1-0.004(approx)
hence C which is close to it
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ditto, spottted that both top+bottom are incredibly close to each other (certainly closer than a 10% margain, eliminating anything below 0.9) and that the top is slightly smaller than the bottom (so has to be less than 1). 30 second solve, C as closest educated guess