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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## When positive integer x is divided by 20, the remainder is 8 tagged by: BTGmoderatorLU ##### This topic has 4 expert replies and 1 member reply ### Top Member ## When positive integer x is divided by 20, the remainder is 8 When positive integer x is divided by 20, the remainder is 8. What is the remainder when x is divided by 5? A. 1 B. 3 C. 5 D. 8 E. Cannot be determined The OA is B. I get the solution to this PS question as follow, When x is divided by 20 the remainder is 8. Therefore x is of form 20k + 8, where k is an integer. When x is divided by 5, the component 5(4k + 1) is divided by 5. Hence, remainder when x is divided by 5 = remainder(3/5) = 3. Option B. Experts, any suggestion? Thanks in advance. ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12838 messages Followed by: 1247 members Upvotes: 5254 GMAT Score: 770 LUANDATO wrote: When positive integer x is divided by 20, the remainder is 8. What is the remainder when x is divided by 5? A. 1 B. 3 C. 5 D. 8 E. Cannot be determined There's a nice rule that say, "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 In this case, we aren't told how many times 20 divides into x, but this isn't a problem. Let's just say that 20 divides into x k times. In other words, x divided by 20 equals k with remainder 8 Applying the above rule, we can then say: x = 20k + 8 for some positive integer k What is the remainder when x is divided by 5? We know that: x = 20k + 8 Rewrite as: x = 20k + 5 + 3 And the factor to get: x = 5(4k + 1) + 3 So, we can see that x is 3 greater than some multiple of 5 This tells us that, if we divide x by 5, the remainder will be 3 Answer: B Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use our video course along with Sign up for our free Question of the Day emails And check out all of our free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 122 members Upvotes: 1153 GMAT Score: 770 LUANDATO wrote: When positive integer x is divided by 20, the remainder is 8. What is the remainder when x is divided by 5? A. 1 B. 3 C. 5 D. 8 E. Cannot be determined The OA is B. I get the solution to this PS question as follow, When x is divided by 20 the remainder is 8. Therefore x is of form 20k + 8, where k is an integer. When x is divided by 5, the component 5(4k + 1) is divided by 5. Hence, remainder when x is divided by 5 = remainder(3/5) = 3. Option B. Experts, any suggestion? Thanks in advance. Note that in these types of questions, x can always equal the remainder. (8/20 is the same thing as 0 + 8/20.) You can see this if you take Brent's equation and plug 0 into the Q. If x = 8, then 8/5 = 1 + 3/5, giving us a remainder of 3. The answer is B _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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Hi LUANDATO,

DavidG brings up a good point - when TESTing VALUES in these types of questions, the easiest value for X is almost always the remainder itself. That having been said, you don't have to use that value to get the correct answer. If we use X = 28, then 28/20 = 1 r 8.... and the answer to the question is 28/5 = 5 r 3 --> so the answer is still 3.

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LUANDATO wrote:
When positive integer x is divided by 20, the remainder is 8. What is the remainder when x is divided by 5?

A. 1
B. 3
C. 5
D. 8
E. Cannot be determined
We can create the equation:

x/20 = Q + 8/20

x = 20Q + 8

When 20Q + 8 is divided by 5 we have:

(20Q + 8)/5 = 4Q + 8/5

Since 8/5 = 1 3/5, the remainder is 3.

Alternate Solution:

Since we have a remainder of 8 when x is divided by 20, x could equal 28. When we divide 28 by 5, the quotient is 5 with a remainder of 3.

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$$\frac{x}{20}=Q+\frac{8}{20}$$
$$x=20Q+8$$
$$when\ x\ is\ divided\ by\ 5\ i.e\ \frac{x}{5}=???$$
$$substituting\ 20Q+8=x$$
$$we\ have,\ \frac{\left(20Q+8\right)}{5}=4Q+\frac{8}{5}$$
$$=4Q+1\frac{3}{5}$$
$$Hence,\ the\ remainder\ is\ 3.\ Option\ B$$

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