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02 May 2021, 01:45
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B
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80% (01:34) correct
20%
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wrong
based on 99
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The median height of the 5 children in family A is 118 cm. How many children in family A are taller than 128cm?
(1) The average height of the children in family A is 120cm.
(2) The second highest child in family A is 130cm.
(1) The average height of the children in family A is 120cm.
(2) The second highest child in family A is 130cm.
09 May 2021, 03:00
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Bunuel
The median height of the 5 children in family A is 118 cm. How many children in family A are taller than 128cm?
The median of a set with odd (5) number of elements is the middle term, so we have that the heights in ascending order are {a, b, 118, c, d} (\(a\leq{b}\leq{118}\leq{c}\leq{d}\))
(1) The average height of the children in family A is 120cm --> the sum of the heights is 120*5=600 cm:
If the heights are {10, 12, 118, 130, 130}, then 2 children are taller than 128 cm.
If the heights are {118, 118, 118, 122, 124}, then no child is taller than 128 cm.
Not sufficient.
(2) The second highest child in family A is 130cm --> c=130 --> \(a\leq{b}\leq{118}\leq{130}\leq{d}\) --> 2 children, c and d, are taller than 128cm. Sufficient.
Answer: B.
General Discussion
02 May 2021, 02:00
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The question tells us that the 3rd highest child is 118cm tall and that two children will be shorter than that and 2 will be taller. This means that there can either be no child, one child or two children taller than 128 cm
1) statement 1 tells us that the avergae is 120cm. Let's consider a case: the heights of the 5 children are 118, 118, 118, 122, 124
Here the average is 120 and the median is 118 - no child is above 128cm
Another case: the heights of the 5 children are 111, 118, 118, 122, 131
Here the average is 120 and the median is 118 - one child is over 128cm
Similarly there can be another case where we get that 2 children are over 128cm. As this option does not give any definate answer.
1) NOT SUFFICIENT
2) from the question we got to know that there can be 0,1 or 2 children above 128cm. This statement tells us that the height of the second highest child is 130cm which is above 128cm. Also, the height of the highest child has to be greater than 130cm which tells us that there are 2 children above 128cm.
This statement gives a definate answer and is SUFFICIENT
So the answer should be B) statement 2 alone is sufficient to answer the question
Posted from my mobile device
1) statement 1 tells us that the avergae is 120cm. Let's consider a case: the heights of the 5 children are 118, 118, 118, 122, 124
Here the average is 120 and the median is 118 - no child is above 128cm
Another case: the heights of the 5 children are 111, 118, 118, 122, 131
Here the average is 120 and the median is 118 - one child is over 128cm
Similarly there can be another case where we get that 2 children are over 128cm. As this option does not give any definate answer.
1) NOT SUFFICIENT
2) from the question we got to know that there can be 0,1 or 2 children above 128cm. This statement tells us that the height of the second highest child is 130cm which is above 128cm. Also, the height of the highest child has to be greater than 130cm which tells us that there are 2 children above 128cm.
This statement gives a definate answer and is SUFFICIENT
So the answer should be B) statement 2 alone is sufficient to answer the question
Posted from my mobile device
