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What is the number of integers from 1 to 1000 (m07q14) [#permalink]
 12 Feb 2009, 23:16
What is the number of integers from 1 to 1000 (inclusive) that are not divisible by 11 nor by 35? (A) 884 (B) 890 (C) 892 (D) 910 (E) 945 Source: GMAT Club Tests - hardest GMAT questions
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Re: What is the number of integers from 1 to 1000... [#permalink]
12 Feb 2009, 23:49
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What is the number of integers from 1 to 1000 (inclusive) that are not divisible by 11 nor by 35? * 884 * 890 * 892 * 910 * 945 --------------------------------- We can go this way: Calculate the no. of terms from 1 to 1000 (inclusive) that are divisible by 11 or 35 or both. 1.) Total no. of terms divisible by 11 are 90. We can calculate this by finding the first and last terms, which are 11 & 990 respectively. Then we will find the total no. of terms by using equation Last Term = a + (n-1)d where a=11, d=11, Last Term=990. So, n=90 2.) Similarly, total no. of terms divisible by 35 are 28. Find it using the above method. 3.) To find terms divisible by both 11 & 35, find the first term. Since both have no common factors except 1, just multiply 11 & 35 to get the first common term i.e., 385. Next term is 770. So, in total, there are 2 common terms for 11 & 35. ------------------------------ Hence, the total no. of terms from 1 to 1000 (inclusive) that are divisible by 11 or 35 or both = 90 + 28 - 2 = 116 So, the correct answer = 1000 - 116 = 884, which will give us the total no. of terms that are divisible neither by 11 nor 35. So, I'll go for first option, i.e., 884Though the explanation looks a bit lengthy, it'll not take much time to solve. HTH
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Last edited by Technext on 13 Feb 2009, 03:13, edited 3 times in total.
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Re: What is the number of integers from 1 to 1000... [#permalink]
13 Feb 2009, 01:51
agree with same explanation as Technext
A
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Re: What is the number of integers from 1 to 1000... [#permalink]
13 Feb 2009, 03:56
Technext wrote: What is the number of integers from 1 to 1000 (inclusive) that are not divisible by 11 nor by 35?
* 884
* 890
* 892
* 910
* 945
---------------------------------
We can go this way:
Calculate the no. of terms from 1 to 1000 (inclusive) that are divisible by 11 or 35 or both.
1.) Total no. of terms divisible by 11 are 90. We can calculate this by finding the first and last terms, which are 11 & 990 respectively. Then we will find the total no. of terms by using equation
Last Term = a + (n-1)d where a=11, d=11, Last Term=990.
So, n=90
2.) Similarly, total no. of terms divisible by 35 are 28. Find it using the above method.
3.) To find terms divisible by both 11 & 35, find the first term. Since both have no common factors except 1, just multiply 11 & 35 to get the first common term i.e., 385. Next term is 770.
So, in total, there are 2 common terms for 11 & 35.
------------------------------
Hence, the total no. of terms from 1 to 1000 (inclusive) that are divisible by 11 or 35 or both = 90 + 28 - 2 = 116
So, the correct answer = 1000 - 116 = 884, which will give us the total no. of terms that are divisible neither by 11 nor 35.
So, I'll go for first option, i.e., 884
Though the explanation looks a bit lengthy, it'll not take much time to solve.
HTH +1 for the detailed explanation.
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Re: What is the number of integers from 1 to 1000... [#permalink]
13 Feb 2009, 15:46
OA is A.
Excellent explanation +1
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Re: What is the number of integers from 1 to 1000... [#permalink]
13 Feb 2009, 16:11
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xALIx wrote: What is the number of integers from 1 to 1000 (inclusive) that are not divisible by 11 nor by 35?
* 884
* 890
* 892
* 910
* 945 1000/11 = 90.xx divisible 11 = 90 1000/35 = 28.x Divisible by 35 = 28 We need to exclude 11*35 and 2*11*35 numbers are counted twice. Anser = 1000-(90+28-2) =1000-116=884
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Re: What is the number of integers from 1 to 1000 (m07q14) [#permalink]
06 Feb 2010, 10:18
we are subtracting 2 to avoid double counting ..( was initially breaking my head )
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Re: What is the number of integers from 1 to 1000 (m07q14) [#permalink]
31 Mar 2010, 05:31
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Numbers Divisible by 11:
(1000/11) + (1000/(11^2)) = 90+8 = 98
Numbers Divisible by 35:
1000/35 = 20
Numbers Divisible by 385 (11*35):
1000/385 = 2
Hence, Numbers Divisible by both 11 and 35 = 98+20-2 = 116
Therefore, Numbers Not Divisible = 1000-116= 884
IMO A.
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Re: What is the number of integers from 1 to 1000 (m07q14) [#permalink]
31 Mar 2010, 07:34
deepak4mba wrote: Numbers Divisible by 11:
(1000/11) + (1000/(11^2)) = 90+8 = 98
Numbers Divisible by 35:
1000/35 = 20
Numbers Divisible by 385 (11*35):
1000/385 = 2
Hence, Numbers Divisible by both 11 and 35 = 98+20-2 = 116
Therefore, Numbers Not Divisible = 1000-116= 884
IMO A. Can you explain the red color text above?
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Re: What is the number of integers from 1 to 1000 (m07q14) [#permalink]
31 Mar 2010, 08:33
deepak4mba wrote: Numbers Divisible by 11:
(1000/11) + (1000/(11^2)) = 90+8 = 98
Numbers Divisible by 35:
1000/35 = 20
Numbers Divisible by 385 (11*35):
1000/385 = 2
Hence, Numbers Divisible by both 11 and 35 = 98+20-2 = 116
Therefore, Numbers Not Divisible = 1000-116= 884
IMO A. Deepak, 1000/35 is 28 not 20.. How did you get 20? Please explain .
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Re: What is the number of integers from 1 to 1000 (m07q14) [#permalink]
04 Apr 2011, 06:11
1000/11 = 90 ( no of integers divisible by 11 and less than 1000) 1000/35 = 28 ( no of integers divisible by 11 and less than 35) No of Common factors = 1 , 11*35 =2 answer =1000-( 90+28-2 ) = 884 A Posted from my mobile device 
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Re: What is the number of integers from 1 to 1000 (m07q14) [#permalink]
04 Apr 2011, 10:50
good explanation technext +1
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Re: What is the number of integers from 1 to 1000 (m07q14) [#permalink]
04 Apr 2011, 18:10
So total multiples of 35 in 1000 = Quotient of 1000/35 = 28 For 11, total multiples = 1000/11 = 90 But there are common multiples as 385,770 which should be counted only once Because - 35 and 11 LCM = 7 * 5 * 11 = 35 * 11 = 185 so 385 * 2 = 770 So total = 90 + 28 - 2 = 90 + 26 = 116 Hence not divisible = 1000 - 116 = 884 Answer - A
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Re: What is the number of integers from 1 to 1000 (m07q14) [#permalink]
07 Apr 2011, 11:12
no.s div by 11 =90
no.s div by 35 =28
rem = 1000-(90+28) = 882
but 2 no.s div by both 11 and 35
hence, my ans: 882+2=884 i.e., A
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Re: What is the number of integers from 1 to 1000 (m07q14) [#permalink]
08 Apr 2011, 13:11
I did careless mistake and got B but on checking the calculation again it shud be A 
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Re: What is the number of integers from 1 to 1000 (m07q14) [#permalink]
06 Apr 2012, 20:25
xALIx wrote: What is the number of integers from 1 to 1000 (inclusive) that are not divisible by 11 nor by 35? (A) 884 (B) 890 (C) 892 (D) 910 (E) 945 Source: GMAT Club Tests - hardest GMAT questions My answer is 890, i think i have not calculated the common terms divisible by both 11 & 35... so might be lesser....
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Re: What is the number of integers from 1 to 1000 (m07q14) [#permalink]
07 Apr 2012, 03:03
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Re: What is the number of integers from 1 to 1000 (m07q14) [#permalink]
09 Apr 2012, 22:19
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Hello,
Calculate the no. of terms from 1 to 1000 (inclusive) that are divisible by 11 or 35 or both.
1. No of terms divisible by 11 -> 1000/11 = 90
2. No of terms divisible by 35 -> 1000/35 = 28
3. No of terms divisible by 11 and 35 -> 1000/(11*35) = 2
Answer = 1000- (90+28-2) = 884.
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Re: What is the number of integers from 1 to 1000 (m07q14) [#permalink]
11 Apr 2012, 08:31
Hi,
How can you rephrase the question in problem solving method and also in Data sufficiency method.
Thanks in advance.
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Re: What is the number of integers from 1 to 1000 (m07q14) [#permalink]
11 Apr 2012, 08:45
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Re: What is the number of integers from 1 to 1000 (m07q14)
[#permalink]
11 Apr 2012, 08:45
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