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When positive integer W is divided by 4233
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09 Jan 2017, 14:31
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When positive integer W is divided by 4233, the remainder is 61. What is the remainder when 2W is divided by 83? A) 11 B) 12 C) 39 D) 44 E) 61 *kudos for all correct solutions
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Re: When positive integer W is divided by 4233
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10 Jan 2017, 10:37
GMATPrepNow wrote: When positive integer W is divided by 4233, the remainder is 61. What is the remainder when 2W is divided by 83?
A) 11 B) 12 C) 39 D) 44 E) 61
IMPORTANT: If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc. For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc. So, for this question, we're told that, when positive integer W is divided by 4233, the remainder is 61. This means the possible values of W are: 61, 61 + 4233, 61 + (2)(4233), 61 + (3)(4233), 61 + (4)(4233), . . . etc. So, rather than test much bigger values of W, let's see what happens when W = 61 If W = 61, then 2W = 2(61) = 122 What is the remainder when 2W is divided by 83?83 divides into 122 one time with remainder 39 Answer: C
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Re: When positive integer W is divided by 4233
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09 Jan 2017, 15:39
When W is divided by 4233, the remainder is 61. The possible value of W = 61, 61+4233, 61+4233 (2), ..... 2W = 122, 8588, ... Example : 2W=122 is divided by 83, the remainder is 39. Answer : 39
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Re: When positive integer W is divided by 4233
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09 Jan 2017, 18:09
GMATPrepNow wrote: When positive integer W is divided by 4233, the remainder is 61. What is the remainder when 2W is divided by 83?
A) 11 B) 12 C) 39 D) 44 E) 61
*kudos for all correct solutions W=4233K + 61 2W=2*4233k + 61* 2 By applying remainder theorem 4233 is completely divided by 83 , so remainder will be 0 + 39 (122/83=39) 39. answer



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Re: When positive integer W is divided by 4233
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10 Jan 2017, 10:38
GMATPrepNow wrote: When positive integer W is divided by 4233, the remainder is 61. What is the remainder when 2W is divided by 83?
A) 11 B) 12 C) 39 D) 44 E) 61
*kudos for all correct solutions Another (much longer) solution involves another important rule regarding remainders: " If N divided by D equals Q with remainder R, then N = DQ + R" For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2 Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3 Aside: We'll also use the fact that 8466 = (83)(102)When positive integer W is divided by 4233, the remainder is 61So, we can say W = 4233Q + 61 for some integer Q. This means that... 2W = 2(4233Q + 61) = 8466Q + 122 = (83)(102)Q + 122 = (83)(102)Q + 83 + 39 = 83( 102Q + 1) + 39 In other words, 2W is 39 greater than some multiple of 83. So, when we divide 2W by 83, the remainder will be 39 Answer: C
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When positive integer W is divided by 4233
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11 Jan 2017, 04:33
1. Check if 4233 is a multiple of 83  Yes it is ==> when w is divided by 83 remainder is also 61 2. for 2w, remainder will be 61*2 = 122, which is > than 83 ==> remainder will be 12283 = 39
Ans.: C



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Re: When positive integer W is divided by 4233
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11 Jan 2017, 07:35
GMATPrepNow wrote: When positive integer W is divided by 4233, the remainder is 61. What is the remainder when 2W is divided by 83?
A) 11 B) 12 C) 39 D) 44 E) 61
*kudos for all correct solutions Least value of W = 4294 So, 2W = 8588 2W/83 = Remainder 39 Hence, remainder when 2W is divided by 83 will be (C) 39
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Re: When positive integer W is divided by 4233
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12 Jan 2017, 13:17
\(\frac{4294}{4233}\) reminds 61
twice ( 4294 )
\(\frac{8588}{83}\)reminds 39
C



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Re: When positive integer W is divided by 4233
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16 Jan 2017, 16:47
GMATPrepNow wrote: When positive integer W is divided by 4233, the remainder is 61. What is the remainder when 2W is divided by 83?
A) 11 B) 12 C) 39 D) 44 E) 61 Since W divided by 4,233 yields a remainder of 61, W could equal 4,233 + 61 = 4,294. Thus, 2W = 2 x 4,294 = 8,588. We can now divide 8,588 by 83 and we have: 8,588/83 = 103 remainder 39 Alternate Solution: W divided by 4233 produces a remainder of 61 means that W = 4233q + 61 for some integer q. Multiplying each side of the equation by 2, we obtain 2W = 8466q + 122. Note that 83 divides evenly into 8466 (because 8466 = 83 x 102) and that 122 = 83 + 39. Then, 2W = 83(102)q + 83 + 39 = 83(102q + 1) + 39. Since 83 divides evenly into 83(102q+1), the remainder is 39. Answer: C
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Re: When positive integer W is divided by 4233
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05 Aug 2019, 02:44
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Re: When positive integer W is divided by 4233
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