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Intern
Joined: 31 Oct 2011
Posts: 30
Given Kudos: 11
Location: India
Set S contains the following numbers 10, 14, 19, 27, 36, 49, 67, 70
[#permalink]
14 Dec 2011, 07:30
14 Dec 2011, 07:30
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Difficulty:
75%
(hard)
Question Stats:
59% (02:25) correct
41%
(02:31)
wrong
based on 141
sessions
Set S contains the following numbers 10, 14, 19, 27, 36, 49, 67, 70, 94. It was found that Mark had inadvertently interchanged the digits of one of the numbers. Steve, in charge of statistics, rectifies this error. As a result, the median changed and the average shifted by 5. Find the number that was incorrectly noted.
A. 36
B. 49
C. 94
D. 27
E. 41
A. 36
B. 49
C. 94
D. 27
E. 41
Manager
Joined: 29 Jul 2011
Status:Disbelief! The Countdown Begins
Affiliations: CFA
Posts: 214
Given Kudos: 7
Concentration: Finance, Economics
Schools: Johnson '15 (M)
GMAT 1: 600 Q45 V28
GMAT 2: 670 Q44 V39
GMAT 3: 750 Q49 V42
GPA: 3.5
WE:Accounting (Insurance)
Re: Set S contains the following numbers 10, 14, 19, 27, 36, 49, 67, 70
[#permalink]
14 Dec 2011, 09:22
14 Dec 2011, 09:22
7
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1
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This is a little cumputational for GMAT math, but average the orignal set of numbers.
10+14+19+27+36+49+67+70+94 = 386
386/9 = 42.888
New mean had to be either 37.888 or 47.888
A 5 point swing means you need to either add 5*9 - 45 to the original total of 386 or subtract 45 from it.
What number when transposed has a difference of 45. 27 does.
72-27 = 45
If you are familiar enough with the concept of mean, you can skip all the nonsense above and just see there is 9 terms that go into the average, and if you mean changes by 5 you know that the total of all the numbers must have changed by 45 (9*5). Then guess and check to see which number when transposed yields a difference of 45.
10+14+19+27+36+49+67+70+94 = 386
386/9 = 42.888
New mean had to be either 37.888 or 47.888
A 5 point swing means you need to either add 5*9 - 45 to the original total of 386 or subtract 45 from it.
What number when transposed has a difference of 45. 27 does.
72-27 = 45
If you are familiar enough with the concept of mean, you can skip all the nonsense above and just see there is 9 terms that go into the average, and if you mean changes by 5 you know that the total of all the numbers must have changed by 45 (9*5). Then guess and check to see which number when transposed yields a difference of 45.
General Discussion
Re: Set S contains the following numbers 10, 14, 19, 27, 36, 49, 67, 70
[#permalink]
14 Dec 2011, 11:49
14 Dec 2011, 11:49
Dbalks wrote:
This is a little cumputational for GMAT math, but average the orignal set of numbers.
10+14+19+27+36+49+67+70+94 = 386
386/9 = 42.888
New mean had to be either 37.888 or 47.888
A 5 point swing means you need to either add 5*9 - 45 to the original total of 386 or subtract 45 from it.
What number when transposed has a difference of 45. 27 does.
72-27 = 45
If you are familiar enough with the concept of mean, you can skip all the nonsense above and just see there is 9 terms that go into the average, and if you mean changes by 5 you know that the total of all the numbers must have changed by 45 (9*5). Then guess and check to see which number when transposed yields a difference of 45.
10+14+19+27+36+49+67+70+94 = 386
386/9 = 42.888
New mean had to be either 37.888 or 47.888
A 5 point swing means you need to either add 5*9 - 45 to the original total of 386 or subtract 45 from it.
What number when transposed has a difference of 45. 27 does.
72-27 = 45
If you are familiar enough with the concept of mean, you can skip all the nonsense above and just see there is 9 terms that go into the average, and if you mean changes by 5 you know that the total of all the numbers must have changed by 45 (9*5). Then guess and check to see which number when transposed yields a difference of 45.
Nice way to solve the problem. I confess I was stuck at this problem for very long (over 3 mins) without luck anyway.
I want to know if this is the best way to solve such problems. Calculating the sum and average of 9 numbers might be a little time consuming, although 700-level questions might have such calculations. But I wonder if we will be able to accomplish such a feat within 2 minutes. Even if we were to use the shortcut method of using the concept of the mean, finding 9 differences between the transposed number and the original number would take time. In the worst case scenario, we would have to compute at least 8 differences before we get to the right answer. Of course, with the presence of options, this number would come down to 4. I still wonder if there is another shortcut and more effective way to solve the problem.
Appreciate your solution and approach nonetheless. Congrats for your Kudos.
