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

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souvik101990
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List M consists of 50 decimals, each of which has a value between [#permalink] New post   10 May 2018, 11:15
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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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GST Week 5 Day 3 Manhattan Prep Question 3


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BrentGMATPrepNow
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Re: List M consists of 50 decimals, each of which has a value between [#permalink] New post   29 Sep 2018, 07:46
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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


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
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Re: List M consists of 50 decimals, each of which has a value between [#permalink] 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] New post   10 May 2018, 11:42
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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] 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] 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.



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?
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Re: List M consists of 50 decimals, each of which has a value between [#permalink] 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] New post   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
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Re: List M consists of 50 decimals, each of which has a value between [#permalink] New post   22 Oct 2019, 12:02
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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] New post   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!
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Re: List M consists of 50 decimals, each of which has a value between [#permalink] New post   18 Mar 2021, 02:40
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


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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Re: List M consists of 50 decimals, each of which has a value between [#permalink] New post   15 Oct 2023, 10:07
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