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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