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

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Current Student
Joined: 19 Mar 2012
Posts: 4310
Location: India
GMAT 1: 760 Q50 V42
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WE: Marketing (Non-Profit and Government)
List M consists of 50 decimals, each of which has a value between  [#permalink]

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10 May 2018, 11:15
1
29
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Difficulty:

95% (hard)

Question Stats:

32% (02:38) correct 68% (02:52) wrong based on 263 sessions

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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

_________________
Intern
Joined: 02 May 2018
Posts: 3
Re: List M consists of 50 decimals, each of which has a value between  [#permalink]

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10 May 2018, 14:14
5
3

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

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.

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
##### General Discussion
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Joined: 20 Jan 2018
Posts: 18
Location: India
Schools: ISB '20 (A)
GMAT 1: 620 Q50 V24
GMAT 2: 710 Q51 V34
GPA: 3.9
Re: List M consists of 50 decimals, each of which has a value between  [#permalink]

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10 May 2018, 11:42
1
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.
Manager
Joined: 05 Feb 2016
Posts: 166
Location: India
Concentration: General Management, Marketing
WE: Information Technology (Computer Software)
Re: List M consists of 50 decimals, each of which has a value between  [#permalink]

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10 May 2018, 11:47
1
1
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
Intern
Joined: 13 Nov 2017
Posts: 3
Re: List M consists of 50 decimals, each of which has a value between  [#permalink]

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12 May 2018, 11:10
gump2020 wrote:

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

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.

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

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?
Director
Joined: 02 Oct 2017
Posts: 705
Re: List M consists of 50 decimals, each of which has a value between  [#permalink]

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26 May 2018, 22:11
gump2020 wrote:

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

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.

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

Posted from my mobile device
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 4234
Re: List M consists of 50 decimals, each of which has a value between  [#permalink]

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29 Sep 2018, 07:46
3
Top Contributor
1
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

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.

Cheers,
Brent
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Posts: 3
List M consists of 50 decimals, each of which has a value between  [#permalink]

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22 Oct 2019, 09:46
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
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 4234
Re: List M consists of 50 decimals, each of which has a value between  [#permalink]

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22 Oct 2019, 12:02
1
Top Contributor
pushpakb wrote:
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?
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Re: List M consists of 50 decimals, each of which has a value between  [#permalink]

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22 Oct 2019, 12:09
GMATPrepNow wrote:
pushpakb wrote:

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!
Re: List M consists of 50 decimals, each of which has a value between   [#permalink] 22 Oct 2019, 12:09
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