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(52 - 33) = 19, (78 - 59) = 19 and (117 - 98) = 19 LCM of 52, 78 and 117 is 468.Required least number = 468 + 19 = 487 Sum of digits of 487 = 4 + 8 + 7 = 19
CEO Joined: 15 Aug 2003 Posts: 2955
What is the least number which, when divided by 52, leaves [#permalink] 20 Sep 2003, 12:27
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Question Stats: 0% (00:00) correct 0% (00:00) wrong based on 0 sessionsHide Show timer StatisticsWhat is the least number which, when divided by 52, leaves the remainder 33, and when divided by 78, leaves 59, and when divided by 117 leaves 98 as the respective remainders? What can be said about a clock when the two hands of the clock coincide every 65 minutes? (A) It gains time (B) It loses time (C) Shows the correct time (D) Data insufficient (E) Loses and gains time alternatively --== Message from the GMAT Club Team ==-- THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION. To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Manager Joined: 21 Aug 2003 Posts: 188 Location: Bangalore
[#permalink] 21 Sep 2003, 09:48 For second question: My asnwer: B (loses time). first - under study.. -vicks
CEO Joined: 15 Aug 2003 Posts: 2955
[#permalink] 21 Sep 2003, 11:33
Vicky wrote: For second question:My asnwer: B (loses time). first - under study.. -vicks Its time you get B under study too Try again on B
Intern Joined: 12 Sep 2003 Posts: 24 Location: Peru
[#permalink] 21 Sep 2003, 15:17 2- Gains time? In 65 minutes the minute hand should move a 1+(1/12) rounds, this is five "places" from its original. The hour hand should moves five "places" and a little bit more every 65 minutes. So, if they coincide every 65 minutes the minute hand is moving faster than it should, so, it is gaining time.
Intern Joined: 16 Jul 2003 Posts: 16
[#permalink] 21 Sep 2003, 15:24 1. Answer is 449. My approach - Let number be X. So X= 52N+33=78M+59=117P+98, where M,N, P are divisors(?? I guess). We know that the smallest number which can be divided by 52, 78 and 117 is 13x2x2x3x3 = 52x9 = 468. Now, look at the remainders in each case, I can write 33 as (52-19), 59 as 78-19, and 98 as 117-19. Did you find a pattern. yes. Now rewrite the equation. X = 52(N+1) - 19 = 78(M+1) - 19 and 117(P+1) - 19. So now, the ques. boils down to find GCD of 52,78,and 117 ( which we know = 468 ) and deduct 19 from it = 449. Just to test the answer 449 / 52 = 9 + 33 remainder. 449/78 = 5 + 59 remainder, and 449/117 = 3 + 98 remainder. So Answer is 449. 2. A. It gains time. Instead coinciding every 65+5/11 mins. hands coincide every 65 mins. so gain of 5/11 every 65 mins. --== Message from the GMAT Club Team ==-- THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION. To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
[#permalink] 21 Sep 2003, 15:24 |