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Tough OG 13 Question

by GaneshMalkar » Sat Mar 16, 2013 10:31 am
List T consist of 30 positive decimals, none of which is an integer, and the sum of the 30 decimals is S. The estimated sum of the 30 decimals, E, is defined as follows. Each decimal in T whose tenths digit is even is rounded up to the nearest integer, and each decimal in T whose tenths digits is odd is rounded down to the nearest integer. If 1/3 of the decimals in T have a tenths digit that is even, which of the following is a possible value of E - S ?

I -16
II 6
III 10

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

OA - B

Not able to find a way to do this in 2 mins ... Experts please help :(
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by Anju@Gurome » Sat Mar 16, 2013 10:55 am
GaneshMalkar wrote:List T consist of 30 positive decimals, none of which is an integer, and the sum of the 30 decimals is S. The estimated sum of the 30 decimals, E, is defined as follows. Each decimal in T whose tenths digit is even is rounded up to the nearest integer, and each decimal in T whose tenths digits is odd is rounded down to the nearest integer. If 1/3 of the decimals in T have a tenths digit that is even, which of the following is a possible value of E - S ?
To simplify the situation, let us assume the decimals are 1.a, 1.b, 1.c, etc. and rounded to tenth place.

Now, 30/3 = 10 of these decimals will be rounded up and rest 20 will be rounded down to the nearest integer. Hence, E = 10*2 + 20 = 40

Now, S will be maximum when all the decimals have tenths digit either 8 (even) or 9 (odd). Hence, maximum value of S = 30 + 10*(0.8) + 20*(0.9) = 56
Now, S will be minimum when all the decimals have tenths digit either 2 (even) or 1 (odd). Hence, maximum value of S = 30 + 10*(0.2) + 20*(0.1) = 34

Hence, maximum value of (E - S) = (40 - 34) = 6 and minimum value of (E - S) = (40 - 56) = -16
Hence, -16 ≤ (E - S) ≤ 6

The correct answer is B.
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by GMATGuruNY » Sat Mar 16, 2013 1:48 pm
List T consist of 30 positive decimals, none of which is an integer, and the sum of the 30 decimals is S. The [/u]esimated sum of the 30 decimals, E, is defined as follows. Each decimal in T whose tenths digit is even is rounded up to the nearest integer, and each decimal in T whose tenths digit is odd is rounded down to the nearest integer; E is the sum of the resulting integers If 1/3 of the decimals in T have a tenths digit that is even, which of the following is a possible value of E-S?

I. -16
II. 6
III. 10

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


Make the problem CONCRETE by plugging in easy values.
10 of the values must have a tenths digit that is EVEN, while the other 20 values must have a tenths digit that is ODD.
To make the math easy, let's not consider decimals beyond the tenths place.
Try to MAXIMIZE E-S and MINIMIZE E-S.

E-S MAXIMIZED:
To MAXIMIZE the value of E-S, we must MINIMIZE the value of S.
To minimize S, we must ROUND UP the even decimals as MUCH as possible (from .2 to the next highest integer) and ROUND DOWN the odd decimals as LITTLE as possible (from .1 to the next smallest integer).
Let S = 10(.2) + 20(.1) = 4.
In E, .2 is rounded up to 1 and .1 is rounded down to 0:
E = 10(1) + 20(0) = 10.
Thus, the MAXIMUM possible value of E-S = 10-4 = 6.

E-S MINIMIZED:
To MINIMIZE the value of E-S, we must MAXIMIZE the value of S.
To maximize S, we must ROUND UP the even decimals as LITTLE as possible (from .8 to the next highest integer) and ROUND DOWN the odd decimals as MUCH as possible (from .9 to the next smallest integer).
Let S = 10(.8) + 20(.9) = 26.
In E, .8 is rounded up to 1 and .9 is rounded down to 0:
E = 10(1) + 20(0) = 10.
Thus, the MINIMUM possible value of E-S = 10-26 = -16.

Since the MAXIMUM difference is 6 and the MINIMUM difference is -16, only I and II are possible values of E-S.

The correct answer is B.
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by coolhabhi » Sun Mar 17, 2013 11:11 am
GaneshMalkar wrote:List T consist of 30 positive decimals, none of which is an integer, and the sum of the 30 decimals is S. The estimated sum of the 30 decimals, E, is defined as follows. Each decimal in T whose tenths digit is even is rounded up to the nearest integer, and each decimal in T whose tenths digits is odd is rounded down to the nearest integer. If 1/3 of the decimals in T have a tenths digit that is even, which of the following is a possible value of E - S ?

I -16
II 6
III 10

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

OA - B

Not able to find a way to do this in 2 mins ... Experts please help :(
My Honest answer: Select some answer and get to the next question. It is better that way rather than banging up our heads in the exam hall on such questions. It would save time for other questions.
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