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16 Sep 2014, 00:43
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The average (arithmetic mean) height of a group of 4 people is 175 cm. If after adding 2 more people to the group, the average (arithmetic mean) height increases, which of the following cannot be the heights of the two new members?
A. 179 cm and 172 cm
B. 181 cm and 169 cm
C. 173 cm and 178 cm
D. 176 cm and 176 cm
E. 174 cm and 177 cm
A. 179 cm and 172 cm
B. 181 cm and 169 cm
C. 173 cm and 178 cm
D. 176 cm and 176 cm
E. 174 cm and 177 cm
16 Sep 2014, 00:43
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Official Solution:
The average (arithmetic mean) height of a group of 4 people is 175 cm. If after adding 2 more people to the group, the average (arithmetic mean) height increases, which of the following cannot be the heights of the two new members?
A. 179 cm and 172 cm
B. 181 cm and 169 cm
C. 173 cm and 178 cm
D. 176 cm and 176 cm
E. 174 cm and 177 cm
For the average to increase, the combined average height of the two new members should be greater than the old average of 175 cm. Thus, their total height should exceed \(2*175 = 350\) cm. Only the heights from option B total exactly 350 cm. All other pairs surpass 350 cm. Therefore, the heights from option B cannot be those of the two new members.
Answer: B
The average (arithmetic mean) height of a group of 4 people is 175 cm. If after adding 2 more people to the group, the average (arithmetic mean) height increases, which of the following cannot be the heights of the two new members?
A. 179 cm and 172 cm
B. 181 cm and 169 cm
C. 173 cm and 178 cm
D. 176 cm and 176 cm
E. 174 cm and 177 cm
For the average to increase, the combined average height of the two new members should be greater than the old average of 175 cm. Thus, their total height should exceed \(2*175 = 350\) cm. Only the heights from option B total exactly 350 cm. All other pairs surpass 350 cm. Therefore, the heights from option B cannot be those of the two new members.
Answer: B
12 Sep 2017, 09:47
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Hello all,
Another approach to get to the answer is by using the differential method. Here, we basically see by "How much above the average is the items added. This gives us the answer quickly. Less Math, faster answers
Here's the Differential values from the average for the options
A. 179 and 172 : Differential from the current average of 175 = +4-3 = +1 => The average will be more than 175
B. 181 and 169 : Differential from the current average of 175 = +6-6 = 0 => The average will remain unchanged (Note you can stop here and pick the answer)
C. 173 and 178 : Differential from the current average of 175 = -2+3 = +1 => The average will be more than 175
D. 176 and 176 : Differential from the current average of 175 = +1+1 = +2 => The average will be more than 175
E. 174 and 177 : Differential from the current average of 175 = -1+2 = +1 => The average will be more than 175
Clearly, the required answer is B
Hope this helps!
Another approach to get to the answer is by using the differential method. Here, we basically see by "How much above the average is the items added. This gives us the answer quickly. Less Math, faster answers
Here's the Differential values from the average for the options
A. 179 and 172 : Differential from the current average of 175 = +4-3 = +1 => The average will be more than 175
B. 181 and 169 : Differential from the current average of 175 = +6-6 = 0 => The average will remain unchanged (Note you can stop here and pick the answer)
C. 173 and 178 : Differential from the current average of 175 = -2+3 = +1 => The average will be more than 175
D. 176 and 176 : Differential from the current average of 175 = +1+1 = +2 => The average will be more than 175
E. 174 and 177 : Differential from the current average of 175 = -1+2 = +1 => The average will be more than 175
Clearly, the required answer is B
Hope this helps!
