Prep question:
When the positiv integer n i is divided by 25, the remainder is 13. What is the valu of n?
(1) n < 100
(2) When n is divided by 20, the remainder is 3
Has anyone a clue how to solve this?
While Jai123oct got the answer right, I feel the explanation may be a bit misleading. He doesn't give you a step-by-step, especially as it is a DS problem. Let's see if I can do better,
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Remainder problems have a formula that makes it somewhat easy to find 'n' among the answer choices. The formula is this: If n is divisible by 25 with a remainder of 13, then that quotient must be an integer (a quotient is what you get when you divide two integers). Thus n/25= (some number k) with a remainder of 13. If you multiply both sides by 25, you get n= 25k (+13, the remainder). K must be some number that when multiplied with 25 produces a multiple of 25. This multiple added to 13 will equal n. Now when it comes to remainder questions, always consider 0 when listing multiples of the divisor. E.g. in this question, when we list possible multiples of 25, start with 0 e.g. 25x0= 0, plus 13= 13 so n could be 13. Then you consider the next integer, 25x1=25, plus 13 and you get 38. So n could be 38. The next integer for k is 2- 25x2=50, plus 13 is 63. So n could be 63 and so on and so forth. Now that we've listed all the possible integers for n, we're ready to view the statements.
Note, for DS questions, ALWAYS be sure to read the statements SEPARATELY. Now that we have a formula for finding n (by guessing k), we are ready to look for clues to point us in the right direction. Let's start with statement 2: When n is divided by 20 the remainder is 3. This leaves us a very broad margin to guess from as n could be 63 or 103 or 503 or 603... and so on, so Statement 2 is not sufficient.
Now we take Statement 1: n <100. Since we've made a list of the integers n could be, n could be 13, or 38 or 63 or 88 (when k is 3), this doesn't give us one definite answer. So statement 1 is insufficient.
Now we combine the statements: we know from S2 that n is a multiple of 20, with a remainder of 3, and from S1 we know that n is less than 100. If we take a look at our list, only 63 falls into that bracket (20 divides 88 but with a remainder of 8, so it's out). So
C is the answer, both statements are needed to solve the question.
Always remember to include 0 as a possible integer for your divisor for it to give you the remainder i.e. 25x0= 0, +13= 13.
Hope this helps!
