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# In a group of 3 girls and 2 boys, the average height is

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In a group of 3 girls and 2 boys, the average height is  [#permalink]

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12 Apr 2018, 12:26
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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

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12 Apr 2018, 12:43
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D.

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.

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12 Apr 2018, 13:02
souvik101990 wrote:

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

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.

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Re: In a group of 3 girls and 2 boys, the average height is  [#permalink]

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12 Apr 2018, 13:45
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urvashis09 wrote:
D.

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.

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urvashis09 Seems I made a mistake. This looks gud to me, thx for the explanation. Congrats. +1.
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12 Apr 2018, 15:09

Given:
G1+G2+G3+B(Tall)+B(Short)= 600
B(Tall)= 120 that means G1+G2+G3+B(S)= 460

What we have to find is (G1+G2+G3)/3< 117 (Yes or No)

Statement A
B(S)= 130
This gives us the age of both boys and we can find the sum of the ages of all the three girls. We will divide the sum by 3 and that will give us the average height of the girls. Hence sufficient for us to answer the question

Statement 2
Shortest members of the group are the two girls and they both have the same height which is 110
G1 (shortest) + G2(other shortest) + G3 + B(Tallest) + B(Short)= 600

110+110+ G3+140+ B(S)=600

G3+B(S)= 240
we know that each G3 & B(S) have a height above 110. Therefore we can take two cases.
Case-I= G(3) has a height of 129 and B(S) has a height of 111
(G1+G2+G3)/3= (110+110+129)/3 = 116.3.. which is less than 117

Case-I= G(3) has a height of 111 and B(S) has a height of 129
(G1+G2+G3)/3= (110+110+111)/3 = 110.3.. which is also less than 117

Hence statement two is sufficient to answer the question. Therefore the answer is D (each statement alone is sufficient)
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Re: In a group of 3 girls and 2 boys, the average height is  [#permalink]

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12 Apr 2018, 22:12
1
Sum of heights = 120*5 = 600
3G + 2B = 600
Height of tallest boy = 140

1) 3G+B+140=600
3G + 130 +140=600
3G = 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.

G + B = 240.

It's given that the shortest height is 110
therefore girl's height can be either 111 or 129

Taking both value into consideration
3rd Girl's height lies between 110 and 117

Therefore Sufficient

Ans. D
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Re: In a group of 3 girls and 2 boys, the average height is  [#permalink]

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14 Apr 2018, 05:46
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urvashis09 - Nailled it. Feel free to PM me to get your GMAT Club Tests subscription!
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Re: In a group of 3 girls and 2 boys, the average height is  [#permalink]

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22 Jun 2018, 13:05
How can the maximum of the girl's height be 129? Nobody has explained this. Wouldn't the maximum be 139? If so, that would make A the right answer.
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In a group of 3 girls and 2 boys, the average height is  [#permalink]

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22 Jun 2018, 13:17
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ulanky wrote:
How can the maximum of the girl's height be 129? Nobody has explained this. Wouldn't the maximum be 139? If so, that would make A the right answer.

The sum of the heights is 240. If you take one value to be 139, the other becomes 101, which is not possible since the lowest value given is 110. Hence, if you have 111, the other value becomes 129. Obviously, as 110 is the shortest height, the value of either remaining heights cannot go lower than this. Hence, from 240, lowest value can be 111 and highest can be 129. Hope it helps.
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Re: In a group of 3 girls and 2 boys, the average height is  [#permalink]

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22 Jun 2018, 16:45
urvashis09 wrote:
ulanky wrote:
How can the maximum of the girl's height be 129? Nobody has explained this. Wouldn't the maximum be 139? If so, that would make A the right answer.

The sum of the heights is 240. If you take one value to be 139, the other becomes 101, which is not possible since the lowest value given is 110. Hence, if you have 111, the other value becomes 129. Obviously, as 110 is the shortest height, the value of either remaining heights cannot go lower than this. Hence, from 240, lowest value can be 111 and highest can be 129. Hope it helps.

Ah. That makes sense. Thank you.
Re: In a group of 3 girls and 2 boys, the average height is &nbs [#permalink] 22 Jun 2018, 16:45
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