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# How many integers between 50 and 100, inclusive, are divisible by 2 o

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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How many integers between 50 and 100, inclusive, are divisible by 2 o  [#permalink]

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07 Jun 2018, 01:43
1
1
00:00

Difficulty:

55% (hard)

Question Stats:

62% (01:58) correct 38% (01:33) wrong based on 82 sessions

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[GMAT math practice question]

How many integers between 50 and 100, inclusive, are divisible by 2 or 3?

A. 35
B. 37
C. 42
D. 47
E. 52

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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Manager Joined: 28 Nov 2017 Posts: 145 Location: Uzbekistan Re: How many integers between 50 and 100, inclusive, are divisible by 2 o [#permalink] ### Show Tags 07 Jun 2018, 01:59 1 1 MathRevolution wrote: [GMAT math practice question] How many integers between 50 and 100, inclusive, are divisible by 2 or 3? A. 35 B. 37 C. 42 D. 47 E. 52 First integer divisible by $$2$$ on the list is $$50$$ and last is $$100$$. Divide them by $$2$$: $$25$$ and $$50$$ respectively. So, there are $$50-25+1=26$$ integers that are divisible by $$2$$. First integer divisible by 3 on the list is 51 and last is 99. Divide them by $$3$$: $$17$$ and $$33$$ respectively. So, there are $$33-17+1=17$$ integers that are divisible by $$3$$. Pay attention that some integers are divisible by both $$2$$ and $$3$$. So, they are divisible by $$6$$. We have to exclude this overlap. Thus, first integer divisible by 6 on the list is 54 and last is 96. Divide them by $$6$$: $$9$$ and $$16$$ respectively. So, there are $$16-9+1=8$$ integers that are divisible by $$6$$. $$26-8=18$$ integers are divisible by $$2$$, but not by $$3$$. $$17-8=9$$ integers are divisible by $$3$$, but not by $$2$$. $$8$$ integers are divisible by both $$2$$ and $$3$$. Thus, overall $$18+9+8=35$$ integers are divisible by $$2$$ or $$3$$. It took about two minutes to solve the question. Answer: A _________________ Kindest Regards! Tulkin. Director Status: Learning stage Joined: 01 Oct 2017 Posts: 931 WE: Supply Chain Management (Energy and Utilities) Re: How many integers between 50 and 100, inclusive, are divisible by 2 o [#permalink] ### Show Tags 07 Jun 2018, 02:10 1 MathRevolution wrote: [GMAT math practice question] How many integers between 50 and 100, inclusive, are divisible by 2 or 3? A. 35 B. 37 C. 42 D. 47 E. 52 Question stem:- Required no of integers(divisible by 2 or 3)=No of integers divisible by 2+ No of integers divisible by 3- No of integers divisible by both(2 and 3) [( A or B= A+B-A and B)] Now, No of integers divisible by 2= $$\frac{(100-50)}{2}$$+1=26 No of integers divisible by 3=$$\frac{(99-51)}{3}$$+1=17 No of integers divisible by both(2 and 3) or No of integers divisible 6= $$\frac{(96-54)}{6}$$+1=8 Therefore, Required no of integers(divisible by 2 or 3)=26+17-8=35 So, Answer option(A). _________________ Regards, PKN Rise above the storm, you will find the sunshine Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 4278 Location: United States (CA) Re: How many integers between 50 and 100, inclusive, are divisible by 2 o [#permalink] ### Show Tags 08 Jun 2018, 10:22 MathRevolution wrote: [GMAT math practice question] How many integers between 50 and 100, inclusive, are divisible by 2 or 3? A. 35 B. 37 C. 42 D. 47 E. 52 For this problem, we must recall that to calculate the number of integers in a range of values that are divisible by a certain number n, we use the formula: (largest multiple - smallest multiple)/n + 1. For example, to calculate the number of integers between 10 and 29 that are divisible by 3, we see that 27 is the largest multiple of 3 in that range of numbers, and 12 is the smallest multiple of 3. Thus, we have (27 - 12)/3 + 1 = 15/3 + 1 = 6. The number of integers from 50 to 100, inclusive, that are divisible by 2 is: (100 - 50)/2 + 1 = 26 The number of integers from 50 to 100, inclusive, that are divisible by 3 is: (99 - 51)/3 + 1 = 17 Now we need to subtract the overlap, that is, we have to subtract the number of multiples of 6 because multiples of 6 were counted as both multiples of 2 and multiples of 3. The number of integers from 50 to 100, inclusive, that are divisible by 6 is: (96 - 54)/6 + 1 = 8 Thus, the number integers between 50 and 100, inclusive, that are divisible by 2 or 3 is 26 + 17 - 8 = 35. Answer: A _________________ Scott Woodbury-Stewart Founder and CEO GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6625 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: How many integers between 50 and 100, inclusive, are divisible by 2 o [#permalink] ### Show Tags 10 Jun 2018, 17:34 => Let A be the set of integers between 50 and 100 that are divisible by 2. Let B be the set of integers between 50 and 100 that are divisible by 3. Let C be the set of integers between 50 and 100 that are divisible by both 2 and 3. This is the same as the set of integers between 50 and 100 that are divisible by 6. Then $$A = { 50, 52, …, 100 }$$ $$B = { 51, 54, …, 96, 99 }$$ $$C = { 54, 60, …, 96 }$$ The number of elements of the set A is $$|A| = \frac{( 100 – 50 )}{2 + 1} = 26.$$ The number of elements of the set B is $$|B| = \frac{( 99 – 51 )}{3 + 1} = 17.$$ The number of elements of the set C is $$|C| = \frac{( 96 – 54 )}{6 + 1} = 8.$$ Using a Venn diagram, we can see that we need to find $$|A| + |B| - |C|$$ as the integers in the intersection of sets A and B are counted twice. Attachment: 6.11.png [ 5.62 KiB | Viewed 952 times ] $$|A| + |B| - |C| = 26 + 17 – 8 = 35.$$ Therefore, the answer is A. Answer : A _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Re: How many integers between 50 and 100, inclusive, are divisible by 2 o &nbs [#permalink] 10 Jun 2018, 17:34
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