The average of 12 numbers 16. When one number is discarded and 15 is a

Question

The average of 12 numbers 16. When one number is discarded and 15 is added, the average becomes 17. What is the number that is discarded?

A. 3
B. 5
C. 6 
D. 10
E. 12

achuepnlx · Answer

A 3.

16*12 - x +15 = 17*12
192+15 -x = 204
207-204 = x
x = 3.

Abhishek009 · Answer

\frac{12*16 - x + 15}{12} = 17

192 - x + 15 = 204

Or,  x = 3

So, answer will be (A)

pushpitkc · Answer

Given data : The average of 12 number is 16, and one of the numbers(x) is removed.

The number which replaces x is 15, and this makes the overall average go up to 17(an increase of 1)
x must be 12 lesser than 15 since the replacement of the number causes the average to go up 1.
Hence,  x = 15-12 = 3(Option A)

generis · Answer

Using  (Average * number of terms) = Sum

Find the sum of first set of numbers.

Find the sum of the second set of numbers.

Set up an equation where the first sum is changed per the prompt, and equals the second sum.

1. (A)*(n) = S (the number of terms, 12, does not change)

Sum of first set of numbers: 16 * 12 = 192

Sum of second set of numbers: 17 * 12 =  204 (RHS)

2. Equation. From the first sum of 192, some number, x, is subtracted, and 15 is added  (LHS ):

192 - x + 15 = 204
-x = -3, or
x = 3

Answer A

sashiim20 · Answer

Average to 12 numbers  = 16

Sum of 12 numbers  = 16 * 12 = 192.  ---------- (i)

Average of 12 numbers (one number is discarded) and 15 is added  = 17

Sum of 12 numbers (one number is discarded) and 15 is added  = 17 * 12 = 204 -------------- (ii)

Subtracting (ii) from (i), we get;

204 - 192 = 12

Difference between 15 and number discarded is 12. Let the number be x.

15 - x = 12

x = 15 - 12 = 3.

Hence the number discarded  = 3.  Answer (A) ...

ashudhall · Answer

Sum of 12 numbers=16*12=192
When one number is discarded and 15 is added then sum= 17*12=204
Let the number discarded be x
192-x+15=204
207-x=204
Hence x=3
A

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ydmuley · Answer

Average = \frac{Sum}{Count}

12 = \frac{Sum}{16}

12 * 16 = Sum

Sum = 192

Now, we remove one number and add 15, and the new average is 17

12 = \frac{New Sum}{17}

12 * 17 = New Sum

New Sum = 204

So, difference between  Sum  and  New Sum = 204 - 192 = 12

As we have added 15, we will substract above number from  15 = 15-12 = 3 
  
Hence, the Answer is A

JeffTargetTestPrep · Answer

Since the average of 12 numbers is 16, the sum of those numbers is 12 x 16 = 192.

We can let x = the discarded number and we can create the following equation:

(192 - x + 15)/12 = 17

207 - x = 204

x = 3

Answer: A

TimeTraveller · Answer

Sum of 12 numbers =  12*16 = 192

Discarding a number (x, say) and adding 15, we get =  \frac{192 - x + 15}{12} = 17

192 - x + 15 = 204

-x = 204 - 192 - 15

x = 3 . Ans - A.

v12345 · Answer

Let discarded number be x.
Sum of 12 numbers = 16*12 = 192
Sum of new 12 numbers includes 15 = 17*12 = 204

192 + 15 - x = 204
x = 3
Hence, OA is (A).

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The average of 12 numbers 16. When one number is discarded and 15 is a

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