Events & Promotions
|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Apr 2601:30 AM EDT
-02:30 AM EDT
Learn how Keshav, a Chartered Accountant, scored an impressive 705 on GMAT in just 30 days with GMATWhiz's expert guidance. In this video, he shares preparation tips and strategies that worked for him, including the mock, time management, and more.
Apr 2610:00 AM EDT
-11:00 AM EDT
The Target Test Prep course represents a quantum leap forward in GMAT preparation, a radical reinterpretation of the way that students should study. Try before you buy with a 5-day, full-access trial of the course for FREE!
Apr 2512:30 AM EDT
-01:30 AM EDT
At one point, she believed GMAT wasn’t for her. After scoring 595, self-doubt crept in and she questioned her potential. But instead of quitting, she made the right strategic changes. The result? A remarkable comeback to 695. Check out how Saakshi did it.
Apr 2711:00 AM EDT
-12:00 PM EDT
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
May 0111:00 AM PDT
-12:00 PM PDT
Free- full-length test + 15 concept videos + 150+ short videos + study plan!
10 May 2019, 00:45
Kudos
Bookmarks
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
43% (02:34) correct
57%
(02:40)
wrong
based on 94
sessions
History
Date
Time
Result
Not Attempted Yet
There are 10 horses, named Horse 1, Horse 2, ..., Horse 10. They get their names from how many minutes it takes them to run one lap around a circular race track: Horse k runs one lap in exactly k minutes. At time 0 all the horses are together at the starting point on the track. The horses start running in the same direction, and they keep running around the circular track at their constant speeds. The least time S > 0, in minutes, at which all 10 horses will again simultaneously be at the starting point is S = 2520. Let T > 0 be the least time, in minutes, such that at least 5 of the horses are again at the starting point. What is the sum of the digits of T?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
10 May 2019, 01:35
Kudos
Bookmarks
Bunuel
Here is my approach. ?
Time taken by all the 10 horses for 1 lap are the following:
- • Horse 1: 1 min
• Horse 2: 2 min = 2^1
• Horse 3: 3 min = 3^1
• Horse 4: 4 min = 2^2
• Horse 5: 5 min = 5^1
• Horse 6: 6 min = 2^1 * 3^1
• Horse 7: 7 min = 7^1
• Horse 8: 8 min = 2^3
• Horse 9: 9 min = 3^2
• Horse 10: 10 min = 2^1 * 5^1
Each of these horses will reach the starting point after exactly these many minutes written above.
- • Now a common time at which all the 10 would meet is nothing but the a common multiple of all the number.
- o That would give us the a number at which all the horses will be present at the starting point.
- The lowest multiple is the LCM of (1,2,3,4,5,6,7,8,9,10) = 2^3 * 3^2 * 5*7 = 2520
And that is what is given in the question too.
Now, if we want to find the least time T, for at least 5 horses meeting at the starting point, then we need to consider 5 horses out of those ten, for which we will get the least value of the LCM.
So, we can choose:
- • Horse 1: 1 min
• Horse 2: 2 min = 2^1
• Horse 3: 3 min = 3^1
• Horse 4: 4 min = 2^2
Now, if take horse 5, then in that case:
- • Horse 5: 5 min = 5^1
However, a better alternate would be to take:
- • Horse 6: 6 min = 2^1 * 3^1
Since we are asked sum of digits that will be 3. (Option B)
03 Mar 2025, 16:21
Kudos
Bookmarks
You need to know the time at which atleast 5 horses are at the starting line, now Horse 1 takes 1 min for a lap, so it will be at the starting position every minute.
Along with H1,
at 2 mins, there will be only H2
at 3 mins => H3
at 4 => H2 and H4
..and so on
Realize that the factors of the minutes you choose should at least be 5 or more, because the no. of factors of minutes are nothing but no. of horses
Now, for 5 factors least no. is \(2^4 = 16\) minutes and for 6 factors least no. is \(2^2 * 3 = 12\) minutes
You need to find the least time T, therefore T = 12; H1, H2, H3, H4, and H6 will be at starting line.
Sum of digits of T = 1 + 2 = 3
Answer B.
Along with H1,
at 2 mins, there will be only H2
at 3 mins => H3
at 4 => H2 and H4
..and so on
Realize that the factors of the minutes you choose should at least be 5 or more, because the no. of factors of minutes are nothing but no. of horses
Now, for 5 factors least no. is \(2^4 = 16\) minutes and for 6 factors least no. is \(2^2 * 3 = 12\) minutes
You need to find the least time T, therefore T = 12; H1, H2, H3, H4, and H6 will be at starting line.
Sum of digits of T = 1 + 2 = 3
Answer B.
