A certain marching band has fewer than 50 members. During performances

Question

A certain marching band has fewer than 50 members. During performances, the members march in different formations. When they march in Formation A, each row has 5 members, except the last row, which has 3 members. When they march in Formation B, each row has 6 members, except the last row, which has 5 members. If they march in Formation C, each row has 7 members, except the last row. How many band members are in the last row in Formation C?

A) 1
B) 2
C) 3
D) 4
E) 6

A) 1
B) 2
C) 3
D) 4
E) 6

gmatophobia · Accepted Answer

Let the number of members in the band = n

When they march in Formation A, each row has 5 members, except the last row, which has 3 members.

n = 5x_1 + 3

x_1  → Number of rows that have 5 members

When they march in Formation B, each row has 6 members, except the last row, which has 5 members.

n = 6x_2 + 5

x_2  → Number of rows that have 6 members

Combining both of the information, we can combine

n = 	ext{LCM}(6,5)x + 	ext{first common term}

n = 5x_1 + 3  ⇒ 3, 8, 13, 18, 23, ....

n = 6x_2 + 5  ⇒ 5, 11, 17, 23, ....

Therefore

n = 	ext{LCM}(6,5)x + 23

As the number of members is fewer than 50, the number of members in the marching band = 23

Question :   If they march in Formation C, each row has 7 members, except the last row. How many band members are in the last row in Formation C?

Inference: The question requires us to find the remainder when the number of members in the marching band, i.e. 23, is divisible by 7.

23 = 7 * 3 + 2

Remainder =  2

Option B

tdrowberry · Answer

Sorry, but this is a problem I just do not understand. How could we be sure the lowest combo of the two formulas would be the correct one that seven would also be apart of? Why is there an LCM if we don't use it?

chetan2u · Answer

1) Why would the combo suit the third formation too?
 Finally the number of people are the same in all three formations, they are same set of people. Since you know only possibility of number people is 23, you can place 23 in rows of 7 to get remainder.

2) Why LCM?
 LCM would help you get the next numbers. Here we know that number of people is less than 50 and there is only one possibility. But say the number was between 50 and 100. Then next would be 30+23 and 30+30+23 or 53 and 83. So here you would have two possibilities and if you put them in rows of 6.. 
53 is 7*7+4, so 4 people in last row. 
83 is 7*11+6, so 6 people in last row. 
Two answers here, but we had our single solution when it was less than 50.

Archit3110 · Answer

let rows in A be x 5x+3
and rows in B be y 6y+5
5x+3 = 6y+5
2=5x-6y
possible when x is 4 and y is 3
we get total as 23
so in formation C we will have 3 rows of 7 each and 2 in last 
option B

Souvik7 · Answer

Let 
#of people in the band = n
#of rows in formation A = x
#of rows in formations B = y

Then, A) n = 5x + 3
 B) n = 6y+ 5
Or, 5x + 3 = 6y + 5
Now no. Of rows must be an interger so ,
5x = 6y+ 2 
X = (6y + 2) / 5

For y = 3 ; x will be integer i.e X= 4

#of people in the band will be n = 5.4 + 3 = 23

Now from the options, only 2 satisfies 
23 = 7.3 + 2

Ans : 2

Posted from my mobile device

Jake7Wimmer · Answer

First Column 
Formation A -> Write out multiples of 5 under 50. 
Formation B -> Write out multiples of 6 under 50. 
Formation C -> Write out multiples of 7 under 50.

Second Column 
Formation A -> Add 3 to every multiple of 5 
Formation B -> Add 5 to every multiple of 6

Formation A -> 20 + 3 = 23 
Formation B -> 18 + 5 = 23 
This is the only common number, thus there are 23 people in the band.

Formation C -> 7 people per row means 21 + ___ -> this number must be 2.

Option B

GMATCoachBen · Answer

@ gmatophobia  A student saw this on Focus Exam #3, could you please tag it as source GMAT Prep (Focus)?

Bunuel · Answer

The question has already been tagged as GMAT Prep Focus. Thank you!

GMATCoachBen · Answer

Yes, I'm seeing it now, for some reason it was showing a blank earlier: https://gmatclub.com/forum/download/file.php?id=82373 GMAT-Club-Forum-e9u55123.png

Pr4n · Answer

If anyone is struggling with this question, i highly recommend to go through Aditya Kumar Remainder concept session on YT. If i hadn't seen it before this question came i would have taken too long.

I won't post the explaination as Aditya has done a brilliant job and you will instantly see what's going on in this question once you see the video.

A certain marching band has fewer than 50 members. During performances

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A certain marching band has fewer than 50 members. During performances

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