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# How many even multiples of 35 are there between 349 and 701?

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How many even multiples of 35 are there between 349 and 701? [#permalink]

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27 Jun 2015, 03:56
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How many even multiples of 35 are there between 349 and 701?

A. 5
B. 6
C. 9
D. 10
E. 11
[Reveal] Spoiler: OA

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Re: How many even multiples of 35 are there between 349 and 701? [#permalink]

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27 Jun 2015, 05:45
reto wrote:
How many even multiples of 35 are there between 349 and 701?

A. 5
B. 6
C. 9
D. 10
E. 11

The given problem is in Arithmetic Progression.

Last Term = First Term + (N-1) Common Difference

First term = 350
Last Term = 700
Common Difference (D) = 35

From above formula N=11

350 is an even multiple and every 2nd multiple from 350 onward will be an even multiple.
Therefore number of even multiples is 6

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Re: How many even multiples of 35 are there between 349 and 701? [#permalink]

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25 Aug 2017, 22:37
Bunuel, I did not understand this question.
Can you help me with an explanation to this?
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Re: How many even multiples of 35 are there between 349 and 701? [#permalink]

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25 Aug 2017, 23:29
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amitpandey25 wrote:
Bunuel, I did not understand this question.
Can you help me with an explanation to this?

Hi amitpandey25

any even multiple of $$35$$ will be of the form $$35*2k = 70k$$. Hence the first even multiple of $$35$$ will be $$70$$ ($$k=1$$)

In the given series the first multiple of $$70$$ is $$350$$ and the last multiple of $$70$$ is $$700$$. Hence we can use the AP formula to calculate total numbers
therefore, $$700 = 350 + (n-1)*70$$

or $$n = 6$$

Option B
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How many even multiples of 35 are there between 349 and 701? [#permalink]

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26 Aug 2017, 15:07
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reto wrote:
How many even multiples of 35 are there between 349 and 701?

A. 5
B. 6
C. 9
D. 10
E. 11

I found number of terms with $$\frac{Last - first}{increment}$$ + 1, where n = 11 and the number of even multiples should outnumber the odd multiples by one: $$n_{even}$$ = 6

But if you were stuck, the numbers here are few enough that you could list them.

We need EVEN multiples of 35 between 349 and 701.

The first one after 349 (that number is a big fat hint), is 350

350 + 35 = 385, but that's odd

385 + 35 = 420

That works. To get to the next even multiple after 350, you had to add 70.

Adding 35 to an even multiple yields odd (350 + 35). Adding 70 to an even multiple yields even (350 + 70). So just add 70 to the first multiple, keep adding 70, and stop when you're at < 701. Thus:

350
420
490
560
630
700

Done. There are 6 even multiples of 35 between 349 and 701.

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How many even multiples of 35 are there between 349 and 701? [#permalink]

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15 Sep 2017, 12:31
Notice that in the given set of numbers 349 and 701, the first/lowest of the even multiples of 35 can only start from 350, which is 35 * 10. Subsequently, notice that the last even multiple of 35 in the set that is closest to 701 is 700 which is 350 * 2 which is basically 35 * 20. Therefore, there are a total of 10+1 terms (inclusive set) that are all multiples of 35 that fall between 349 and 701. Of these we only need to find the number of even multiples thus 10/2 +1 = 5+1 = 6 answer option B.

Also interesting to note is that because the terms are even multiples of 35, after the first term in the set the numbers increase successively by 35*2, maintaining a difference of 70.
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How many even multiples of 35 are there between 349 and 701?   [#permalink] 15 Sep 2017, 12:31
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