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# How many even integers between 100 and 200, inclusive, are divisible

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Math Expert
Joined: 02 Sep 2009
Posts: 50004
How many even integers between 100 and 200, inclusive, are divisible  [#permalink]

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25 Dec 2016, 02:30
1
7
00:00

Difficulty:

55% (hard)

Question Stats:

58% (01:43) correct 42% (01:38) wrong based on 128 sessions

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How many even integers between 100 and 200, inclusive, are divisible by 7?

A. 20
B. 18
C. 16
D. 14
E. 7

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Joined: 02 Nov 2013
Posts: 87
Location: India
Re: How many even integers between 100 and 200, inclusive, are divisible  [#permalink]

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25 Dec 2016, 03:39
The number is divisible by 7 when removing last digit off the number, double it and subtract the doubled number from the remaining number. If the result is evenly divisible by 7 (e.g. 14, 7, 0, -7, etc.), then the number is divisible by seven. However we do not need to calculate with this method..
Here we need to calculate the even integers which are divisible by 7. As 7 is odd integer any even number will not be completely divisible by 7. Hence to divide it completely multiply it by 2... i.e. 14.
Now see how many number are divisible by 14. Total numbers are 7.

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How many even integers between 100 and 200, inclusive, are divisible  [#permalink]

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25 Dec 2016, 13:37
1
Bunuel wrote:
How many even integers between 100 and 200, inclusive, are divisible by 7?

A. 20
B. 18
C. 16
D. 14
E. 7

196-105=91
91/7=13
13+1=14 total multiples of 7
14/2=7 even multiples of 7
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Re: How many even integers between 100 and 200, inclusive, are divisible  [#permalink]

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01 Aug 2018, 02:36
Hi,

This question no need to do any calculations, we can just solve this by elimination the options.

If you know the seven tables(multiples), then it is pretty straight forward, in a hundred there are 14 multiples (7 * 14 = 98) and since the question asking for even multiples it has to be less than 14
multiples (In-fact 7 even multiples because half even and half odd). So the only answer choice has to be 7.

Also, first three digit number divisible by 7 is 105(7*15) and the last number (less than 200) is 196(28*7).

If you are looking for a standard approach, then,

To find the number of elements(if they are evenly spaced), use the below expression,

(L – A )/D + 1 = to count the number of elements

L is the last element, A is the first element and D is the common difference.

So, (196 – 105)/ 7 + 1 = 14.

Since only even numbers , so divide the above count by 2. So the answer is E(7).
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Re: How many even integers between 100 and 200, inclusive, are divisible  [#permalink]

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01 Aug 2018, 05:20
Bunuel wrote:
How many even integers between 100 and 200, inclusive, are divisible by 7?

A. 20
B. 18
C. 16
D. 14
E. 7

An even integer divisible by 7 is a multiple of 14.
Neither endpoint of the given range -- 100, 200 -- is a multiple of 14.
For this reason, the multiples of 14 between 100 and 200, inclusive, can be counted simply by dividing 14 into the difference between the two endpoints:
$$\frac{(200-100)}{14} = \frac{100}{14} = \frac{50}{7} = 7 \frac{1}{7}$$
Since 14 divides into the difference 7 times, there are 7 multiples of 14 between 100 and 200, inclusive.

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Re: How many even integers between 100 and 200, inclusive, are divisible &nbs [#permalink] 01 Aug 2018, 05:20
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