If 100

Question

If 100 \leq x \leq 200 , then how many Integer values of x are even multiples of at least one of the numbers 7 and 9? A) 15 B) 14 C) 13 D) 12 E) 11 https://www.GMATinsight.com

amanvermagmat · Accepted Answer

Even multiples of 7 = those which are divisible by both 2 and 7 = those which are divisible by 14 in the range 100 to 200 inclusive
Even multiples of 9 = those which are divisible by both 2 and 9 = those which are divisible by 18 in the range 100 to 200 inclusive

So basically we have to find the numbers of integers from 100 to 200 inclusive which are divisible by at least one of 14 or 18

Multiples of 14 = 112, 126, 140, .... 196 = 7 multiples
Multiples of 18 = 108, 126, 144, .... 198 = 6 multiples

Multiples of both 14 and 18 = Multiples of 126 in the range 100 to 200 inclusive = 1 only (which is 126)

So total numbers in range 100 to 200 inclusive which are divisible by either 14 or 18 or both = 7 + 6 - 1 = 12

Hence  D answer

JS1290 · Answer

Not sure if my way is correct, but this is how I approached this problem. Between 100 to 200, we can count how many multiples of 7 and 9 there are.

# of multiples of 7 between 100 to 200: 105 to 196- ((196-105)/7)+1)= 14 multiples total
# of multiples of 9 between 100 to 200: 108 to 198- ((198-108)/9)+1)= 11 multiples total

Now, we can count the even multiples. 14 has 7 even multiples and 11 and 5 even multiples. S0, 7+5= 12, Hence, D.

Please let me know if my way is correct. 
Thanks!

NanaA · Answer

The only intuitive way that came to me was to do the times table for 7 & 9 . Starting with 9*1 & 7*1 , then stopping before I hit 100 . Seven has 7 even multiples and nine has 5 even multiples. Since the range was 100 and 200, I knew the number even multiples under 100 would be consistent in the range of 100-200. There is probably some easier equation ,but I try to solve the questions intuitively since I typically cant remember equations I have not practiced in years.

pushpitkc · Answer

Between 100 and 200, 
7 has multiples  starting 105(15*7) and ending 196(28*7) 
Of these multiples, there are  7 even multiples  and 7 odd multiples
9 has multiples  starting 108(12*9) and ending 198(22*9) 
Of these multiples, there are  6 even multiples  and 5 odd multiples

7*9 or 63 has 2 multiples, 126 and 189( one of which is even )

Since we are asked how many integer values of x are even multiples of atleast 7 or 9, 
we will have  7+6(13)  even multiples of which 
 126 (a number which repeats in both the lists 18*7 and 14*9) 
has to be reduced once, making a grand total of 12 even multiples(Option D)

GMATinsight · Answer

The highlighted part seems incorrect. The number of multiple if every range of 100 consecutive numbers is not the same. e.g. there are 5 even multiples of 9 from 1 to 100 but there are 6 even multiples of 9 from 100 to 200 Word of Caution: Intuition doesn't pay well in GMAT

chetan2u · Answer

Hi ,
You are getting the correct answer but the method may not be entirely correct.
11 multiples does not mean 5 even, it can mean 6 even multiple..
 It will depend on the first multiple in that set 
Here it's 108 which is even, so 11 will have more even multiples so 6 even and 5 odd..

Total becomes 7+6=13.. but there may be repetition so check for it by taking LCM..
LCM of 7,9 is 63.... There is one even multiple of 63 in the range.. 63*2 as 63*4 will go out of range..
Ans 13-1=12

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.

If 100<= x <=200, then how many Integer values of x are even multiples

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