If in a certain sequence of consecutive multiples of 50, the median is 625, and the greatest term is 950, how many terms that are smaller than 625 are there in the sequence?
A. 6
B. 7
C. 8
D. 12
E. 13
Given Answer - Option B
Based on an approach I used, I arrived at a wrong answer. I am not sure what specifically was wrong in my approach. Please help..!
Thanks
Bullzi
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Terms smaller than the Median
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The median of 625 is not itself a multiple of 50.Bullzi wrote:If in a certain sequence of consecutive multiples of 50, the median is 625, and the greatest term is 950, how many terms that are smaller than 625 are there in the sequence?
A. 6
B. 7
C. 8
D. 13
E. 13
Implication:
This median must be HALFWAY between two multiples of 50.
Thus, the two middle terms in the sequence must be 600 and 650, with result that the median of 625 is halfway between them.
Since the greatest term is 950, the latter half of the sequence is as follows:
600, 650, 700, 750, 800, 850, 900, 950.
As illustrated by the values in red, the latter half of the sequence has 7 terms ABOVE the median of 625.
Thus, the first half of the sequence must have 7 terms BELOW the median of 625.
The correct answer is B.
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Thanks Mitch!
Ahh, now that you've explained the approach, the answer makes sense. I had somehow missed recognizing the key element in the question and tried listing out multiples from 50 till 600 which was obviously incorrect
Thanks
Bullzi
Ahh, now that you've explained the approach, the answer makes sense. I had somehow missed recognizing the key element in the question and tried listing out multiples from 50 till 600 which was obviously incorrect
Thanks
Bullzi
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Hi Bullzi,
When dealing with large sequences of numbers, it often helps to find a logical 'starting point' so that you can 'map out' the overall sequence. It's important to note that the 'starting point' might not be the first term in the sequence....
Since we're dealing with CONSECUTIVE multiples of 50, and the MEDIAN is 625...we can 'map out' 2 of the terms in the sequence. Since 625 is NOT a multiple of 50, it must be the AVERAGE of the two 'middle terms'....so we need two consecutive multiples of 50 that average to 625.....those would be...
600 and 650
600 is below the median; 650 is above it. From here, we can map 'up' to 950, count those total terms and then map 'down' in the other direction (which would be the same number of terms). Since the question just asks for the number of terms, we don't have to physically write them all out.
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
When dealing with large sequences of numbers, it often helps to find a logical 'starting point' so that you can 'map out' the overall sequence. It's important to note that the 'starting point' might not be the first term in the sequence....
Since we're dealing with CONSECUTIVE multiples of 50, and the MEDIAN is 625...we can 'map out' 2 of the terms in the sequence. Since 625 is NOT a multiple of 50, it must be the AVERAGE of the two 'middle terms'....so we need two consecutive multiples of 50 that average to 625.....those would be...
600 and 650
600 is below the median; 650 is above it. From here, we can map 'up' to 950, count those total terms and then map 'down' in the other direction (which would be the same number of terms). Since the question just asks for the number of terms, we don't have to physically write them all out.
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
