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# Connie has a number of gold bars, all of different weights. She gives the 24 lightest bars, which weigh 45% of the total weight, to Brennan. She gives the 13 heaviest bars, which weigh 26% of the total weight, to Maya. She gives the rest of the bars to Blair. How many bars did Blair receive?

A. 14

B. 15

C. 16

D. 17

E. 18

### Solution(By Examveda Team)

The average weight of the bars given to Brennan (light) < the average weight of the bars given to Blair < the average weight of the bars given to Maya (heavy).
Let the total weight of all the bars be X.
The weight of the bars given to Brennan,
= 45% of X = 0.45X
The weight of the bars given to Maya,
= 26% of X = 0.26X
The weight of the bars given to Claire = rest = 29% of X = 0.29X
The average weight of the bars given to Brennan,
$$= \frac{{{\text{Weight}}}}{{{\text{Number}}\,{\text{of}}\,{\text{bars}}}} = \frac{{0.45{\text{X}}}}{{24}}$$
The average weight of the bars given to Maya = Weight / number of bars = $$\frac{{0.26{\text{X}}}}{{13}}$$
Similarly, if the number of bars given to Blair = B,
then the average weight of the bars given to Blair = $$\frac{{0.29{\text{X}}}}{{\text{B}}}$$
As, the average weight of the bars given to Brennan (light) < the average weight of the bars given to Blair < the average weight of the bars given to Maya
So , Option (B) is the right answer
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