Set S contains the following numbers 10, 14, 19, 27,

Question

GMATBusters’ Quant Quiz Question -1

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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. 19
B. 27
C. 36
D. 49
E. 70

Raxit85 · Answer

1 number interchanged out of 9 numbers. Average shifted by 5 and median also changed.
Suppose, actual no = xy but noted as yx.
Here, average moved by 5, so total shall also shift by 45 (9*5).
This shift in sum = (xy-yz) = 45
So, (10x+y – 10y-x) = 45
(x-y) = 5 means difference between digits of no. is 5. 
There are only 3 options, i.e. 49,94,27. So, A, C & E out.
The median of 10,14,19,27,36,49,67,70,94 is 36.

If 49 is that no., then 10,14,19,27,36,49,67,70,94, then median is 36. So, it’s not changed. So D is out.
If 27 is that no., then 10,14,19,36,49,67,70,72, 94, then median is 49. So, it is that no.

Imo. B

uc26 · Answer

The mean of the set S is roughly 366/9= 40
For the median to change and the mean to move by 5, we need to have an impact of about + or - 45 (9*5) from the current mean.
The only answer choice that has such an impact is 27 because (72-27=45) which will change the median of the set as well.

Answer: B

Archit3110 · Answer

for given set 10, 14, 19, 27, 36, 49, 67, 70, 94
median is 36 and avg is 42.88 ( 386/9)
now its given that numbers got interchanged and the median changed and the average shifted by 5
i.e the number has to be <36 left with options A,B 
for B ; 27 we see that median then becomes 49 and avg = 431/9 ; 47.8 i.e 5 more than Set of Mark 
Set of number should be 10, 14, 19, 36, 49, 67, 70,72, 94 
OPTION B

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. 19
B. 27
C. 36
D. 49
E. 70

chetan2u · Answer

Without getting into any calculations, you can answer the question..

There are 9 numbers and by interchanging the digits, the average shifts ( could be up or down) by 5, so the number and the number formed by interchanging the digits should have a difference of 9*5 or 45.

A glance at choices tells you that only 27 and 49 are left.

Now median is 36.
27 <36 but the new number 72>36, so median will change
49>36 and its opposite 94>36, so the median will not change.

27 is the answer.

yashikaaggarwal · Answer

Set S average= 386(10+14+19+27+36+49+67+70+94)/9 = 42.88 
Shift in average with correct no. = 47.88 or 37.88

A. 19 = 386-19+91/9 = 50.88
B. 27 = 386-27+72/9 = 47.88 (MATCHING)
C. 36 = 386-36+63/9 = 45.88
D. 49 = 386-49+94 = 47.88 ( Matching)
E. 70 = 386-70+07/9 = 35.88

Now with two no. Put both correct no. In set S
Set S = 10,14,19,27,36,49,67,70,94
MEDIAN = 36

Correction 27 ->>>>> 72
SET S' = 10,14,19,36,49,67,70,72,94
MEDIAN = 49 (Matching the criteria)
Correction 49 ->>>>>> 94
Set S'' = 10,14,19,27,36,67,70,94,94
Median = 36

Answer is B

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SohGMAT2020 · Answer

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. 19
B. 27
C. 36
D. 49
E. 70

Solution:

Here the average shifted by 5. Since there are 9 terms the total sum shifted by +/- 45.

From the options, if we interchange the digits and find the difference we get,

A - 19-91 = -72 :   Incorrect 
B - 27-72 = -45
C - 36-63 = -27:   Incorrect 
D - 49-94 = -45
E - 70 - 7 = 63 :   Incorrect

now if 49 is changed to 94 the median does not change,

So the correct answer is B.

Gamerboyttt · Answer

B.
Median is changed so number should be less than or equal to 36.

Average is changed by 5 meaning overall value change of 45 of a number. We add 45 to 27 we get 72 leading to answer B

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ashwini2k6jha · Answer

Answer:B
Given average shifted by 5 means total sum shifted by =5 * 9
This shift in sum is due to error in digit ,let 10x+y be correct number and interchanged as 10y+x
Hence shift in total sum due to error=10x+y-10y-x=9(x-y)= 5*9
hence x-y=5
from given option only number satisfying difference in digit as 5 are 27 OR 49
But median change only in case of 27 Hence answer

HoneyLemon · Answer

B ,  IMO 
As per ques - (10, 14, 19, 27, 36, 49, 67, 70, 94) -- Median = 36 
Now if one number is reversed digit the mean will be shifted by 5 and median shifted .. 
That means the average will be increased or decreased by 45 . and the new number will change direction wrt the median .

Out of all the option given only 27 and 49 satisfy a value change of 45 once the digits are changed . 
However the median is getting shifted only in case of 27

Hence the ans will be 27 , ( B).

gmatway · Answer

imo B 
step1 = find avg of given set = 386/9 = 42.88 
step 2 the diffrence in new avg is of 5 so the new avg will be increase if interchanged number is greater than current one and decrease if interchnaged no. is less than current wrong no. so new avg could be either 42.88-5= 37.88
 or 42.88+5=47.88
step 3 = check options = opt A says wrong no. 19 .. the interchanged no. would be 91 which is greater than 19 and hence the avg would increase so 386-19+91 = 458/9 =50.88 REJECT (the difference between interchanged no. ab-ba is a multiple of 9 )

opt B 386-27+72=431/9 = 47.88 this is equal to +5 increase in earlier avg .HENCE this is our ans .

bM22 · Answer

Set S: {10, 14, 19, 27, 36, 49, 67, 70, 94}
Median: 36
Average: 42.8

Now lets go option wise:

A. 19 - if we reverse 19, we get the set as: {10, 14, 27, 36, 49, 67, 70, 91, 94}
New Median: 49
New Average: (386 - 19 + 91)/9 = 50.8
Did the median change yes, but did the average also shift by 5 - No
So A is incorrect.

B. 27 - if we reverse 27, we get the set as: {10, 14, 19, 36, 49, 67, 70, 72, 94}
New Median: 49
New Average: (386 - 27 + 72)/9 = 47.8
Did the median change yes, but did the average also shift by 5 - No
 So B is Correct.
 
C. 36 - if we reverse 36, we get the set as: {10, 14, 19, 27, 49, 63, 67, 70, 94}
New Median: 49
New Average: (386 - 36 + 63)/9 = 38.8
Did the median change yes, but did the average also shift by 5 - Yes
So C is also Incorrect.

D. 49 - if we reverse 49, we get the set as: {10, 14, 19, 27, 36, 67, 70, 94, 94}
New Median: 36
New Average: (386 - 49 + 94)/9 = 47.8
Did the median change No, and did the average also shift by 5 - No
So D is also incorrect.

E. 70 - if we reverse 70, we get the set as: {07, 10, 14, 19, 27, 36, 49, 67, 94}
New Median: 27
New Average: (386 - 70 + 7)/9 = 35.6
Did the median change No, and did the average also shift by 5 - No
So E is also incorrect.

Answer B.

tejas29d · Answer

the average has shifted by 5 as the total numbers are 9, shift due to shift in average shall be +-45 (9*5) wee have to only find the numbers in which difference after interchanging of digits is +-45 there are only three such numbers 27, 49, 94 However, please note that it is mentioned that "median has changed" Even if digits of 49,94 are interchanged, median will not change, hence correct answer is 27

Kinshook · Answer

Given: 
1. Set S contains the following numbers 10, 14, 19, 27, 36, 49, 67, 70, 94. 
2. It was found that Mark had inadvertently interchanged the digits of one of the numbers. 
3. Steve, in charge of statistics, rectifies this error. 
4. As a result, the median changed and the average shifted by 5.

Asked: Find the number that was incorrectly noted.

S = {10, 14, 19, 27, 36, 49, 67, 70, 94}
Average = 36 + (-26 - 22 - 17 - 9 + 0 + 13 + 31 + 34 + 58)/9 = 42.89

Since average shifted by 5, difference between number = 5*9 = 45
10 - 01 = 9
41 - 14 = 27
91 - 19 = 72
 72 - 27 = 45

The number is 27.
Median changed from 36 to 49
and average shifted from 42.89 to 47.89

IMO B

coreyander · Answer

10, 14, 19, 27,  36 , 49, 67, 70, 94
Median = 36.

Given: The average shifted by 5.
The digits get interchanged  
 
Let X be the Sum of Set S.

Before rectification of error:

\frac{X}{9} = Average  .....(1)

After rectification of error:

Let Y be the Latest Sum of Set S.

\frac{Y}{9} = Average \pm 5

Thus,  Y=(9*Average) \pm (9*5) . ...(We know that  9*Average = X  from (1))
-->  Y = X \pm 45

Question Stem tells us that only one number was changed. 
Thus, this number must be the cause of  \pm 45  in the Total Sum. ...(2)

--> Adding or Subtracting 45 from the number should result in the digits interchanging their positions.  
Do a quick check on the elements in the set for the above.

There are only three numbers in the above Set S that satisfy the above condition -->  27,49,94.

Question Stem tells that the median is changed when the number is interchanged.

Only when you interchange 27 to 72, the median gets changed from 36 to 49.
When you interchange 49<-->94, the median remains 36.

Thus, (B) 27 is our answer.

+1 Kudos if you like my explanation

rxb266 · Answer

There is a simple wayto do it..

Look at the ans options..

The number and its reverse when divided by 9 should give a difference of 5 (since the difference of averageis 5).. The only answer option that does it is B

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rxb266 · Answer

There is a simple wayto do it..

Look at the ans options..

The number and its reverse when divided by 9 should give a difference of 5 (since the difference of averageis 5).. The only answer option that does it is B

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Vatsal107 · Answer

The average changes by 5. There are 9 nos. therefore, the net increase will be 9X5 i.e 45. One look at the options reveals that if we interchange 49 , we get 94 which is 45(=94-49) greater than 49. Hence , 49 is the answer

Set S contains the following numbers 10, 14, 19, 27,

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