List M consists of 50 decimals, each of which has a value between

Let's examine the EXTREME CASES

S - T = x percent of T
So, S - T = (x/100)T
Divide both sides by to get: (S - T)/T = x/100
Multiply both sides by 100 to get: x = 100(S - T)/T

First, we we'll MINIMIZE the value of x by minimizing the value of S - T and maximizing the value of T.
This occurs when list M = {9.11, 9.11, 9.11, 9.11, 9.11, 9.11, . . . . .9.11, 9.11}
So, S = (50)(9.11)
And T = (50)(9)

So, S - T = (50)(9.11) - (50)(9)
= (50)(9.11 - 9)
= (50)(0.11)

Plug these values into the above equation to get x =100(50)(0.11)/(50)(9)
= 100(0.11)/9
= 11/9
≈1.2222...
So, the MINIMUM value of x is approximately 1.22%

First, we we'll MAXIMIZE the value of x by maximizing the value of S - T and minimizing the value of T.
This occurs when list M = {1.99, 1.99, 1.99, 1.99, 1.99, . . . 1.99, 1.99}
So, S = (50)(1.99)
And T = (50)(1)

So, S - T = (50)(1.99) - (50)(1)
= (50)(1.99 - 1)
= (50)(0.99)

Plug these values into the above equation to get x =100(50)(0.99)/(50)(1)
= 100(0.99)/1
= 99
So, the MAXIMUM value of x is 99%

Combine the results to get: 1.22% < x ≤ 99%
All three values (2%, 34% and 99%) fall within this range of x-values.

Answer: E

Cheers,
Brent

IMO Answer is E.

Here is why:

Given is the expression (S-T)/T = ((S/T) - 1)

Where S - Sum of 50 decimals
T - Sum of the 50 truncated decimals

Let’s test each answer choice:

i) 2%

((S/T)-1) = 2/100

S/T = (2/100)+1 = 102/100

Simplified to S/T = 51/50

Certainly a possibility if each decimal in S is 1.02, added 50 times & hence each decimal in T is 1, added 50 times.

So i) is possible.

ii) 34%

((S/T)-1) = 34/100

S/T = (34/100) + 1 = 134/100

Simplified to S/T = 67/50

Certainly possible if each decimal in S is 1.34, added 50 times & hence each decimal in T is 1, added 50 times.

So ii) is possible


iii) 99%


((S/T)-1) = 99/100

S/T = (99/100) + 1 = 199/100

Simplified to S/T = 99.5/50

Certainly possible if each decimal in S is 1.99, added 50 times & hence each decimal in T is 1, added 50 times.

So iii) is possible.

Answer is choice E.

I may have gone horribly stupid wrong here, since it’s past 2 am & I am half sleepy, with slightly drunk from my birthday party. Thanks if you wished me.

Gump.



Sent from my iPhone using GMAT Club Forum

C according to me,
can be checked by taking values for eg (reducing the cardinal no of set M):
case 1: M={1.96,1.97,1.98,1.99}
s-t/t =3.9/4 = 97.5 approx(taking only 4 maximum values)
so the % cannot be 99 in any case since 50 elements are there)

case2: M={5.12,6.02,7.03,8.04}
s-t/t is definetly <2%, so, 2 can be a possible value.

so these are the two extremes and any value b/w these % can be a ratio.

Question mention possible values:
So let find the range of \(\frac{(S - T )}{T}*100\)

Maximum percent will be when S-T will be max and T will be min
since S is in the form abc.yz and T will be x(rounded down)
List M , term will be in form a+.bc
when rounded down it will be a
subtracting both=.bc
Therefore ,S-T=.YZ
max value S-T=.99*50 when first term= 1.99 and rounded down value=1
T=1*50
\(((S-T)/T)*100=99\)

Min value when first term =9.11 and rounded value =9
S-T=.11*50
T=9*50

\(((S-T)/T)*100=1.22\)

So all three value will satisfy

option E

Just one thing in the first part of your explanation

1.02 can be possible right? given that the two decimal digits need to be non zero?

Explanation of I) 2% is not correct as we can't have 1.02 as it is mentioned in question that we have two non zero decimal digits.

Rest all is fine.
I would love to go with approach kunalcvrce has .it covers all aspects in single way

Posted from my mobile device

GMATPrepNow

Hi Brent - could you kindly explain why you took 9.11 in the first case instead of 9.99, and 1.99 in the second case instead of 1.11?
Thanks,
Pushpak

Given: x = 100(S - T)/T
To MINIMIZE the value of x we must minimize the value of S - T and maximizing the value of T.
9.99 rounds down to 9, and also 9.11 rounds down to 9. So, T is the same in both cases.
However, if we use 9.99, then S - T = 9.99 - 9 = 0.99, so (S-T)/T = 0.99/9
If we use 9.11, then S - T = 9.11 - 9 = 0.11, so (S-T)/T = 0.11/9

0.11/9 < 0.99/9
So, (S - T)/T is minimized when we use 9.11

Does that help?

Ok! Now it makes sense! Thank you!

There is a slight error indeed. The question clearly says here that there are two 'non-zero' digits after the decimal. In your solution you have mentioned '1.02' as a possibility for statement I.

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