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The median height of the 5 children

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by BTGmoderatorDC » Sat Nov 18, 2017 3:28 am
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.

Isn't statement 1 sufficient?

OA B
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Source: — Data Sufficiency |

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by [email protected] » Sat Nov 18, 2017 11:07 am
Hi lheiannie07,

We're told that the MEDIAN height of the 5 children in a family is 118 cm. We're asked for the number of children in that family are taller than 128cm. To start, since there are 5 children, the MEDIAN height will be the 3rd child (when the children are ordered from shortest to tallest). With a median of 118cm, there can be no more than 2 children who are taller than 128cm (so the answer to the question can only be 0, 1 or 2).

1) The average height of the children in family A is 120cm.

With an AVERAGE height of 120cm, the TOTAL height of all 5 children is (5)(120) = 600cm. We know that the median height is 118cm, but there are several possibilities.
IF... the children's heights are (in cm) are...
117, 117, 118, 124, 124 then the answer to the question is 0
111, 111, 118, 130, 130 then the answer to the question is 2
Fact 1 is INSUFFICIENT

2) The second highest child in family A is 130cm.

We already know that the median height is 118cm. Fact 2 tells us that the second-tallest child is 130cm, thus the tallest child must be AT LEAST 130cm. Therefore, we know that 2 of the children ARE taller than 128cm and there are no other options.
Fact 2 is SUFFICIENT

Final Answer: B

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
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by BTGmoderatorDC » Wed Jan 10, 2018 9:45 pm
[email protected] wrote:Hi lheiannie07,

We're told that the MEDIAN height of the 5 children in a family is 118 cm. We're asked for the number of children in that family are taller than 128cm. To start, since there are 5 children, the MEDIAN height will be the 3rd child (when the children are ordered from shortest to tallest). With a median of 118cm, there can be no more than 2 children who are taller than 128cm (so the answer to the question can only be 0, 1 or 2).

1) The average height of the children in family A is 120cm.

With an AVERAGE height of 120cm, the TOTAL height of all 5 children is (5)(120) = 600cm. We know that the median height is 118cm, but there are several possibilities.
IF... the children's heights are (in cm) are...
117, 117, 118, 124, 124 then the answer to the question is 0
111, 111, 118, 130, 130 then the answer to the question is 2
Fact 1 is INSUFFICIENT

2) The second highest child in family A is 130cm.

We already know that the median height is 118cm. Fact 2 tells us that the second-tallest child is 130cm, thus the tallest child must be AT LEAST 130cm. Therefore, we know that 2 of the children ARE taller than 128cm and there are no other options.
Fact 2 is SUFFICIENT

Final Answer: B

GMAT assassins aren't born, they're made,
Rich
Thanks a lot!
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