BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

The four members of a jazz quartet all play in different

Expert replies
by M7MBA » Sun Nov 24, 2019 1:29 pm
The four members of a jazz quartet all play in different rhythms. The pianist plays in 9/8 time, meaning that his downbeats occur every 9/8 of a measure of time. Meanwhile, the saxophonist plays in 7/4 time, the harpist in 5/8 time, and the drummer in plain old 4/4 time (all with respect to the same measure of time as the pianist). If all four musicians start a song together on the same downbeat, how many measures later will all their downbeats occur simultaneously?

(A) 315
(B) 630
(C) 1,260
(D) 2,520
(E) 5,040

[spoiler]OA=A[/spoiler]

Source: Manhattan GMAT
Join the discussion
Source: — Problem Solving |

by Scott@TargetTestPrep » Thu Nov 28, 2019 4:22 pm
M7MBA wrote:The four members of a jazz quartet all play in different rhythms. The pianist plays in 9/8 time, meaning that his downbeats occur every 9/8 of a measure of time. Meanwhile, the saxophonist plays in 7/4 time, the harpist in 5/8 time, and the drummer in plain old 4/4 time (all with respect to the same measure of time as the pianist). If all four musicians start a song together on the same downbeat, how many measures later will all their downbeats occur simultaneously?

(A) 315
(B) 630
(C) 1,260
(D) 2,520
(E) 5,040

[spoiler]OA=A[/spoiler]

Source: Manhattan GMAT
In this type of problems, we need to find the LCM of the numbers given. However, we see that they (except the last one) are not whole numbers. So first we can multiply each number by 8 to obtain 9, 14, 5 and 8, respectively. Next we find the LCM of these 4 whole numbers:

9 = 3^2

14 = 2 x 7

5 = 5

8 = 2^3

Therefore, the LCM is 2^3 x 3^2 x 5 x 7 = 2,520. However, since we multiplied each number by 8 earlier, as a result, we need to divide the LCM by 8 to obtain the correct answer of 2,520/8 = 315.

Answer: A

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Join the discussion