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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
List M consists of 50 decimals, each of which has a value between 1 an
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31 Mar 2021, 22:26
31 Mar 2021, 22:26
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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
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
List M consists of 50 decimals, each of which has a value between 1 an
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04 Apr 2021, 21:23
04 Apr 2021, 21:23
1
This question busts the type of questions we can often expect in quants. Indeed this is a hard question.
At this point, we must interpret the question.
\(x = \frac{S-T}{T}\)
If you recall how you calculate percentage changes, you can use that knowledge here. x is basically how much the real sum S is greater than the rounded down sum T.
Here you may guess that for each decimal number, the difference S-T for each decimal number in list M will produce the values that were reduced when the rounded down. Minimum of these values can be 0.11 while maximum of these values can be 0.99 because each decimal in list M has two non-zero digits after the decimal place. This is just to estimate. Total S-T will be between 0.11 * 50 and 0.99 * 50.
Similarly, you may guess that each value contributing to the sum T will be between 1 and 9 because each decimal in list M has a value between 1 and 10.
So, T will be between 1 * 50 and 9 * 50.
Now you can imagine how much x can be by putting these estimates into \(x = \frac{S-T}{T}\).
Putting aside 50 as it can be cancelled out in estimation, we can find that x can be somewhere from 0.012 to 0.99, or 1.2% to 99%.
Hence, E is the correct answer.
Quote:
If S - T is x percent of T, which of the following is a possible value of x?
At this point, we must interpret the question.
\(x = \frac{S-T}{T}\)
If you recall how you calculate percentage changes, you can use that knowledge here. x is basically how much the real sum S is greater than the rounded down sum T.
Quote:
... each of which has a value between 1 and 10 and has two non-zero digits after the decimal place.
Here you may guess that for each decimal number, the difference S-T for each decimal number in list M will produce the values that were reduced when the rounded down. Minimum of these values can be 0.11 while maximum of these values can be 0.99 because each decimal in list M has two non-zero digits after the decimal place. This is just to estimate. Total S-T will be between 0.11 * 50 and 0.99 * 50.
Similarly, you may guess that each value contributing to the sum T will be between 1 and 9 because each decimal in list M has a value between 1 and 10.
So, T will be between 1 * 50 and 9 * 50.
Now you can imagine how much x can be by putting these estimates into \(x = \frac{S-T}{T}\).
Putting aside 50 as it can be cancelled out in estimation, we can find that x can be somewhere from 0.012 to 0.99, or 1.2% to 99%.
Hence, E is the correct answer.
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Joined: 10 Apr 2015
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Re: List M consists of 50 decimals, each of which has a value between 1 an
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05 Apr 2021, 06:01
05 Apr 2021, 06:01
1
GeminiHeat wrote:
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
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
