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

Question

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

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

prashantrchawla · Answer

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.

Answer is E.

gracie · Answer

196-105=91
91/7=13
13+1=14 total multiples of 7
14/2=7 even multiples of 7

KrishnakumarKA1 · Answer

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).

GMATGuruNY · Answer

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.

E

ScottTargetTestPrep · Answer

If an even integer is divisible by 7, then it has to be divisible by 14 also. Therefore, we are looking for integers in the range of 100 to 200 that are divisible by 14. The number of such integers is:

(196 - 112)/14 + 1 = 7

(Note that finding the multiples of 14 rather than multiples of 7 eliminates finding the odd multiples of 7, which would have to be subtracted out, anyway.)

Answer: E

Kinshook · Answer

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

Even integers divisible by 7 are multiples of 14.

14*7 = 98
14*8 = 112
14*14 = 196

14*8,......14*14
Number of even integers divisible by 7 = 14-8 + 1 = 7

IMO E

GaurSaini · Answer

As we have to find number of even integers, let's find the number of even integers from 100 to 200, inclusive.

(200-100)/2 + 1 = 51

Out of these 51 numbers, every 7th number will be divisible by 7.

51/7 = 7

Hence, 7 numbers

pooja.sharma2909 · Answer

We can even use this approach as the numbers should be between 100 to 200 we can use 7 table so there will be 10 numbers which will be divisible by 7 from 1 till 70. Now we need for 80,90 and 100 so from 70 to 80 there is only 1 number which is divisible by 7 then again 80 to 90 we have 1 number divisible by 7, then 90 to 100 2 number so total number will 
10+1+1+2 which is 14 and now we need even number which will be 14/2= 7

Please let me know if this is correct approach?

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards