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souvik101990
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12 Apr 2018, 13:26
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GST Week 1 Day 4 Exampal Question 1
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In a group of 3 girls and 2 boys, the average height is 120 centimeters. If the tallest boy is 140 centimeters, is the average height of the girls less than 117 centimeters?
(1) The height of the other boy is 130 centimeters.
(2) The shortest members of the group are two girls who are each 110
12 Apr 2018, 13:43
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Sum of heights of 3 girls and 2 boys = 120*5 = 600.
1) Sum of heights of boys = 130+140 = 270
Therefore, sum of heights of girls = 600-270 = 330
Hence, average height of girls = 330/3 = 110
Sufficient.
2) Sum of heights of the two girls and tallest boy = 110*2 + 140 = 220+140 = 360.
Therefore, sum of heights of the remaining one girl and one boy = 240.
It's given that the shortest height is 110 and the tallest height is 140.
Hence, maximum height that the remaining girl can have is 129 and the minimum height she can have is 111. Calculating for both values, average height of girls say x, 110<x<116. Sufficient.
Sent from my iPhone using GMAT Club Forum
Sum of heights of 3 girls and 2 boys = 120*5 = 600.
1) Sum of heights of boys = 130+140 = 270
Therefore, sum of heights of girls = 600-270 = 330
Hence, average height of girls = 330/3 = 110
Sufficient.
2) Sum of heights of the two girls and tallest boy = 110*2 + 140 = 220+140 = 360.
Therefore, sum of heights of the remaining one girl and one boy = 240.
It's given that the shortest height is 110 and the tallest height is 140.
Hence, maximum height that the remaining girl can have is 129 and the minimum height she can have is 111. Calculating for both values, average height of girls say x, 110<x<116. Sufficient.
Sent from my iPhone using GMAT Club Forum
12 Apr 2018, 14:02
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souvik101990
Sum=G1+G2+G3+B1+B2 heights.
Sum/5=120 cm -> Sum=600 cm -> G1+G2+G3+B1+B2=600 cm tallest boy say B1 is 140 then G1+G2+G3+B2=600 cm - B1 -> G1+G2+G3+B2=600 cm - 140=460
We are asked to find if (G1+G2+G3)/3<117. If we know the value of B2 then sum of heights of all girls will be known.
1) B2=130. From this we can get G1+G2+G3 and calculate (G1+G2+G3)/3. Sufficient.
2) We have G1+G2+G3+B2=560. Say G1 and G2 are the shortest member with 110 cm of height. Then the equation becomes 110+110+G3+B2=460 -> B2+G3=460-220=240. We still don't know B2 or G3 but G3 can be between (least) 110 & 140 (max) .i.e. 110<G3<140. If G3=111 then (G1+G2+G3)/3>110<117 Yes. If G3=139 then (G1+G2+G3)/3>117 No. hence, (G1+G2+G3)/3 cannot be determined to be <117. Not Sufficient.
Answer (A).
