There are 25 arithmetic means between a and b such that the common difference is 4 and the sum of th means is 1375. find the value of a and b.
1) a-4,b-34
2) a-5,b-78
3) a-3,b-107,
4) a-7,b-113
5) none of above
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Unfortunately, the questions you are posting are either difficult to interpret, or they use terminology that is out of scope for the GMAT (or both). What is the source of this question?Imsukhi wrote:There are 25 arithmetic means between a and b such that the common difference is 4 and the sum of th means is 1375. find the value of a and b.
1) a-4,b-34
2) a-5,b-78
3) a-3,b-107,
4) a-7,b-113
5) none of above
"25 arithmetic means between a and b" Do you mean 25 terms between a and b (as in a sequence)?
"common difference": Not an expression that GMAT test-takers need to know.
I think this question involves a sequence in which every term is 4 greater than the term before it (e.g., 5, 9, 13, 17, ...). There are 27 terms in the sequence. The sequence begins with a and ends with b. The 25 terms in between a and b add to 1375. What is the value of a and b?
Is this interpretation correct?
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send2dar
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For every 3 terms, the middle term is the arithmetic mean (in the arithmetic progression), in a series of N numbers (including a and b), there would be (N - 2) arithmetic means between a and b.
So, b should be a + 104 (as the common difference between two consecutive terms is 4 and b is 26th term after a, the difference between a and b should be 4 * 26 = 104).
In that case only option D is right (a = 3, b = 107).
Further, sums of these 25 terms would be 3*25 + 4*(25*26)/2 = 1375, this check confirms the answer...
I agree with Brent that these types of questions wont be part of GMAT in the language given... however if the question is worded differently, it can be a good candidate for inclusion to Quant section.
Cheers!
So, b should be a + 104 (as the common difference between two consecutive terms is 4 and b is 26th term after a, the difference between a and b should be 4 * 26 = 104).
In that case only option D is right (a = 3, b = 107).
Further, sums of these 25 terms would be 3*25 + 4*(25*26)/2 = 1375, this check confirms the answer...
I agree with Brent that these types of questions wont be part of GMAT in the language given... however if the question is worded differently, it can be a good candidate for inclusion to Quant section.
Cheers!
Thanks
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