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Bunuel
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A local club with x members has between 32 and 101 members. The member 10 Dec 2016, 06:17
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55% (hard)

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68% (02:56) correct 32% (02:58) wrong based on 214 sessions

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A local club with x members has between 32 and 101 members. The members of the club can be separated into groups of which all but the one group, which will have 3 members, will have 4 members. The members can also be separated into groups so that all groups but one group, which will have 1 member, will have 5 members. Which of the following could be the value of 3x?

A. 263
B. 213
C. 123
D. 83
E. 49
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B
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atshy21saraf
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A local club with x members has between 32 and 101 members. The member 10 Dec 2016, 09:46
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Bunuel
A local club with x members has between 32 and 101 members. The members of the club can be separated into groups of which all but the one group, which will have 3 members, will have 4 members. The members can also be separated into groups so that all groups but one group, which will have 1 member, will have 5 members. Which of the following could be the value of 3x?

A. 263
B. 213
C. 123
D. 83
E. 49
Show more


Given that
x= integer
x=4n+3
and
x=5m+1

The value of 3x is asked, so after dividing our answer by 3 it should give the value of integer x:

A. 263 is not divisible by 3
B. 213/3= 71 [and 71 is of the form 4n+3 and also of the form 5m+1]
C. 123/3= 41 [but 41 does not satisfy 4n+3]
D. 83/3= non-integer
E. 9/3= non-integer

The only option satisfying the given constraints is B

Correct me if I am wrong. What's OA?
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A local club with x members has between 32 and 101 members. The member 10 Dec 2016, 12:57
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Bunuel
A local club with x members has between 32 and 101 members. The members of the club can be separated into groups of which all but the one group, which will have 3 members, will have 4 members. The members can also be separated into groups so that all groups but one group, which will have 1 member, will have 5 members. Which of the following could be the value of 3x?

A. 263
B. 213
C. 123
D. 83
E. 49
Show more

\(X=4a+3\)
\(X=5b+1\)

\(X=20n+11\)

\(3X = 60n+33\)

And we have following AP

\(33, 93, 153, 213, 273 ...\)

Only option that coinsides with AP is B
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georgekaterji
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A local club with x members has between 32 and 101 members. The member 13 Dec 2016, 08:33
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vitaliyGMAT
Bunuel
A local club with x members has between 32 and 101 members. The members of the club can be separated into groups of which all but the one group, which will have 3 members, will have 4 members. The members can also be separated into groups so that all groups but one group, which will have 1 member, will have 5 members. Which of the following could be the value of 3x?

A. 263
B. 213
C. 123
D. 83
E. 49

\(X=4a+3\)
\(X=5b+1\)

\(X=20n+11\)

\(3X = 60n+33\)

And we have following AP

\(33, 93, 153, 213, 273 ...\)

Only option that coinsides with AP is B
Show more


How did u get x=20n +11?? please
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A local club with x members has between 32 and 101 members. The member 13 Dec 2016, 08:46
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georgekaterji
vitaliyGMAT
Bunuel
A local club with x members has between 32 and 101 members. The members of the club can be separated into groups of which all but the one group, which will have 3 members, will have 4 members. The members can also be separated into groups so that all groups but one group, which will have 1 member, will have 5 members. Which of the following could be the value of 3x?

A. 263
B. 213
C. 123
D. 83
E. 49

\(X=4a+3\)
\(X=5b+1\)

\(X=20n+11\)

\(3X = 60n+33\)

And we have following AP

\(33, 93, 153, 213, 273 ...\)

Only option that coinsides with AP is B


How did u get x=20n +11?? please
Show more

We need to solve following equation and get integer values:

4a + 3 = 5b + 1
5b = 4a + 2

If we put a=2 we got integer value of b=2

Now put one of them into equations to get our remainder:

4*2 + 3 = 11

Our number is in the form:

N = LCM (4,5)*x + 11 where x is a variable.

N = 20x + 11

Hope it helps.
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A local club with x members has between 32 and 101 members. The member 13 Dec 2016, 08:55
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\(X=4a+3\)
\(X=5b+1\)

\(X=20n+11\)

\(3X = 60n+33\)

And we have following AP

\(33, 93, 153, 213, 273 ...\)

Only option that coinsides with AP is B[/quote]


How did u get x=20n +11?? please[/quote]

We need to solve following equation and get integer values:

4a + 3 = 5b + 1
5b = 4a + 2

If we put a=2 we got integer value of b=2

Now put one of them into equations to get our remainder:

4*2 + 3 = 11

Our number is in the form:

N = LCM (4,5)*x + 11 where x is a variable.

N = 20x + 11

Hope it helps.[/quote]


if I take a=7 then I get b=6, how do I continue from here?

Can u please explain the theory? I mean, in general, if the remainder of r when divided by 3 is 2, and remainder of r when divided by 5 is 3. Then, theoretically, how do I get the remainder when r is divided by 15?
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A local club with x members has between 32 and 101 members. The member Updated on: 13 Nov 2018, 00:16
Originally posted by gracie on 13 Dec 2016, 14:29.
Last edited by gracie on 13 Nov 2018, 00:16, edited 1 time in total.
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Bunuel
A local club with x members has between 32 and 101 members. The members of the club can be separated into groups of which all but the one group, which will have 3 members, will have 4 members. The members can also be separated into groups so that all groups but one group, which will have 1 member, will have 5 members. Which of the following could be the value of 3x?

A. 263
B. 213
C. 123
D. 83
E. 49
Show more

from answer choices, assume x has ones digit of 1
let y=tens unit of x
so x=10y+1
and 3x=3(10y+1)=30y+3
plugging in answers, 30y+3=213 works
y=7
10y+1=71=x
3*71=213
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A local club with x members has between 32 and 101 members. The member 24 Nov 2025, 04:54
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