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18 Aug 2009, 05:39
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B
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Difficulty:
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Question Stats:
50% (02:35) correct
50%
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wrong
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When n is divided by 5 the remainder is 2. When n is divided by 7 the remainder is 1. If n is less than 800 , how many values of n are possible?
A. 22
B. 23
C. 24
D. 25
E. 26
A. 22
B. 23
C. 24
D. 25
E. 26
27 Feb 2012, 14:24
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yezz
First of all it should be mentioned in the stem that \(n\) is a positive integer: every GMAT divisibility question will tell you in advance that any unknowns represent positive integers.
Given:
\(n=5p+2\), so \(n\) can be: 2, 7, 12, 17, 22, 27, ...
\(n=7q+1\), so \(n\) can be: 1, 8, 15, 22, 29, ...
General formula for \(n\) based on above two statements will be: \(n=35k+22\) (the divisor should be the least common multiple of above two divisors 5 and 7, so 35 and the remainder should be the first common integer in above two patterns, hence 22).
Next, given that \(35k+22<800\) --> \(k<22.something\) --> so \(k\), can take 23 values from 0 to 22, inclusive, which means that \(n\) also can take 23 values (the least value of \(n\) will be 22 for \(k=0\)).
Answer: B.
For more about this concept see:
manhattan-remainder-problem-93752.html#p721341
when-positive-integer-n-is-divided-by-5-the-remainder-is-90442.html#p722552
when-the-positive-integer-a-is-divided-by-5-and-125591.html#p1028654
Hope it helps.
18 Aug 2009, 07:14
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mirzohidjon
well we start with 22. Now we need to find the next number that ends in 2 or 7 to satisfy 5's criteria. Since 22 already has remainder of 1 for 7 all we need to do is add 7 to it to find the next number ends in 2 or 7. After finding that number (57) we see the gap is 35. it will keep being 35 since the remainder will keep switching like before until the next N is found. since we know the "gap" is 35 then we multiply by 22( the lowest possible answer) to get 770. Since we know the value starts at 22 and 792 is only a few behind 800 so we stop there. You could also see it as : 22 + 35*x = 800 and find the value that way but I was lazy and used the answer choices (plus it is pretty easy to do 35*22 on the fly). It is probably no coincidence that the gap is 5 X 7 (both values in question are in it) but the number property escapes me so i dont want to feed you the wrong info. But even without it you can get to the 2nd value pretty quick and notice the pattern (can add another 35 to it to double check i guess...).
