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

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List M consists of 50 decimals, each of which has a value between [#permalink]

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GST Week 5 Day 3 Manhattan Prep Question 3


Give your best shot at writing a top notch explanation and you will have the chance to win GMAT Club tests daily and 6 Practice Tests + 9 Question Banks + Challenge Problem Archive + GMAT Navigator from Manhattan Prep. See the GMAT Spring Training Thread for all details


List M consists of 50 decimals, each of which has a value between 1 and 10 and has two non-zero digits after the decimal place (e.g. 5.68 could be a number in List M). The sum of the 50 decimals is S. The truncated sum of the 50 decimals, T, is defined as follows. Each decimal in List M is rounded down to the nearest integer (e.g. 5.68 would be rounded down to 5); T is the sum of the resulting integers. If S - T is x percent of T, which of the following is a possible value of x?

I. 2%
II. 34%
III. 99%

(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, and III

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Re: List M consists of 50 decimals, each of which has a value between [#permalink]

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souvik101990 wrote:

GST Week 5 Day 3 Manhattan Prep Question 3


Give your best shot at writing a top notch explanation and you will have the chance to win GMAT Club tests daily and 6 Practice Tests + 9 Question Banks + Challenge Problem Archive + GMAT Navigator from Manhattan Prep. See the GMAT Spring Training Thread for all details


List M consists of 50 decimals, each of which has a value between 1 and 10 and has two non-zero digits after the decimal place (e.g. 5.68 could be a number in List M). The sum of the 50 decimals is S. The truncated sum of the 50 decimals, T, is defined as follows. Each decimal in List M is rounded down to the nearest integer (e.g. 5.68 would be rounded down to 5); T is the sum of the resulting integers. If S - T is x percent of T, which of the following is a possible value of x?

I. 2%
II. 34%
III. 99%

(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, and III


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.
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Re: List M consists of 50 decimals, each of which has a value between [#permalink]

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New post 10 May 2018, 11:47
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souvik101990 wrote:

GST Week 5 Day 3 Manhattan Prep Question 3


Give your best shot at writing a top notch explanation and you will have the chance to win GMAT Club tests daily and 6 Practice Tests + 9 Question Banks + Challenge Problem Archive + GMAT Navigator from Manhattan Prep. See the GMAT Spring Training Thread for all details


List M consists of 50 decimals, each of which has a value between 1 and 10 and has two non-zero digits after the decimal place (e.g. 5.68 could be a number in List M). The sum of the 50 decimals is S. The truncated sum of the 50 decimals, T, is defined as follows. Each decimal in List M is rounded down to the nearest integer (e.g. 5.68 would be rounded down to 5); T is the sum of the resulting integers. If S - T is x percent of T, which of the following is a possible value of x?

I. 2%
II. 34%
III. 99%

(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, and III


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
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Re: List M consists of 50 decimals, each of which has a value between [#permalink]

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New post 10 May 2018, 14:14
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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.



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Re: List M consists of 50 decimals, each of which has a value between [#permalink]

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New post 12 May 2018, 11:10
gump2020 wrote:
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.



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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?
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Re: List M consists of 50 decimals, each of which has a value between [#permalink]

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New post 26 May 2018, 22:11
gump2020 wrote:
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


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

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Re: List M consists of 50 decimals, each of which has a value between   [#permalink] 26 May 2018, 22:11
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