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Two amateur wrestling squads—Squad A and Squad B—competed against each other. Each squad had the same (nonzero) number of its members who were contestants. In the competition, each contestant in Squads A and B wrestled against exactly one contestant in the other squad, and no non-contestant member of either squad wrestled. Let x be the proportion of Squad A's members who were contestants in the competition and let y be the proportion of Squad B’s members who were contestants in the competition. In terms of x and y only, what is the proportion of the total number of members in the two squads who were contestants in the competition?
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
64% (03:17) correct
36%
(03:29)
wrong
based on 1766
sessions
History
Date
Time
Result
Not Attempted Yet
Which one of the following procedures, when applied to the last mathematical expression in the Concise Solution tab, gives a mathematical expression that answers the question asked in the Problem Statement tab?
| Multiply both the numerator and denominator by a. | |
| Multiply both the numerator and denominator by y. | |
| Divide both the numerator and denominator by a. | |
| Subtract a and then divide the result \(a + \frac{x}{y}a\). | |
| Divide by \(a + \frac{x}{y}a\). and then subtract a from the result. |
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:
40% (02:10) correct
60%
(02:17)
wrong
based on 1791
sessions
History
Date
Time
Result
Not Attempted Yet
A given number is a possible value of a’ if, for each value of x in the Table tab, there is a value of a that is compatible with that value of x and the other information provided. For each of the following numbers, select Yes if, given this condition, it is a possible value of a' Otherwise select No.
| Yes | No | |
| 9 | ||
| 10 | ||
| 12 |
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
74% (01:05) correct
26%
(01:06)
wrong
based on 1650
sessions
History
Date
Time
Result
Not Attempted Yet
Assume the information provided is true. For each of the following mathematical statements, select Yes if, according to the information provided, the statement is true for the possible values of x and y. Otherwise select No.
| Yes | No | |
| \(a' = yb\) | ||
| \(a' = b'\) | ||
| \(a + b < xa + yb\) |
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Question 1
Which one of the following procedures, when applied to the last mathematical expression in the Concise Solution tab, gives a mathematical expression that answers the question asked in the Problem Statement tab?
The equation being talked about is \(\frac{2xa}{a+\frac{x}{y}*a}\)
we want this expression in terms of only x and y. We have an extra in both numerator and denominator => \(\frac{2xa}{a(1+\frac{x}{y})}\)
So, divide numerator and denominator by a to get \(\frac{2x}{1+\frac{x}{y}}\)
Question 2.
A given number is a possible value of [i]a’ if, for each value of x in the Table tab, there is a value of a that is compatible with that value of x and the other information provided. For each of the following numbers, select Yes if, given this condition, it is a possible value of a' Otherwise select No.[/i]
Now x has values 1/3, 1/4 etc, and xa has to be integer as xa is the number of contestants. Thus a has to be a multiple of LCM of denominators of values of x. Thus 12 or multiples of 12.
Hence 9 and 10 are not valid while 12 is.
Question 3.
Assume the information provided is true. For each of the following mathematical statements, select [i]Yes if, according to the information provided, the statement is true for the possible values of x and y. Otherwise select No.[/i]
a'=b'=xa=yb.
Thus, a'=yb is true.
a'=b' is also true.
However, \(a + b < xa + yb\) is not true as xa<a and yb<b, resulting in a+b>xa+yb
_________________
Which one of the following procedures, when applied to the last mathematical expression in the Concise Solution tab, gives a mathematical expression that answers the question asked in the Problem Statement tab?
The equation being talked about is \(\frac{2xa}{a+\frac{x}{y}*a}\)
we want this expression in terms of only x and y. We have an extra in both numerator and denominator => \(\frac{2xa}{a(1+\frac{x}{y})}\)
So, divide numerator and denominator by a to get \(\frac{2x}{1+\frac{x}{y}}\)
Question 2.
A given number is a possible value of [i]a’ if, for each value of x in the Table tab, there is a value of a that is compatible with that value of x and the other information provided. For each of the following numbers, select Yes if, given this condition, it is a possible value of a' Otherwise select No.[/i]
Now x has values 1/3, 1/4 etc, and xa has to be integer as xa is the number of contestants. Thus a has to be a multiple of LCM of denominators of values of x. Thus 12 or multiples of 12.
Hence 9 and 10 are not valid while 12 is.
Question 3.
Assume the information provided is true. For each of the following mathematical statements, select [i]Yes if, according to the information provided, the statement is true for the possible values of x and y. Otherwise select No.[/i]
a'=b'=xa=yb.
Thus, a'=yb is true.
a'=b' is also true.
However, \(a + b < xa + yb\) is not true as xa<a and yb<b, resulting in a+b>xa+yb
_________________
Dhruv0911
The video solution of this question is given here:
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General Discussion
Posts: 57
Updated on: 19 Jul 2024, 01:00
Originally posted by illegallyblonde on 08 Jun 2024, 22:58.
Last edited by illegallyblonde on 19 Jul 2024, 01:00, edited 1 time in total.
Last edited by illegallyblonde on 19 Jul 2024, 01:00, edited 1 time in total.
Quote:
chetan2u Aren't we talking about a' and not a?
Since a' = xa and we have to select a value for a', it could be anything, right?
1/4 . a = 9 where a = 36, 1/3 . a = 10 where a = 30, etc.
Have I misinterpreted the question? Please let me know. Thanks!
arkaja11
Joined: 22 Nov 2023
Last visit: 22 Aug 2025
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Schools: ISB '27 (A) INSEAD '26 Tuck '27
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WE:Consulting (Pharmaceuticals and Biotech)
Products:
Schools: ISB '27 (A) INSEAD '26 Tuck '27
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Posts: 39
ellewoods2
I think you're correct. But let's take a' = 9 , for all values of x, it won't return an integer a. Similarly for a'=10.
So, the answer will still be 12.
chetan2u
Wouldnt it be numerators?
Since a'=x*a
=> a= a'*1/x
e.g.: a = 9*3/2 (not possible)
Since a has to be an integer, it would be the reciprocal of x and hence the LCM of the numrator?
illegallyblonde
\(x=\frac{1}{4},\frac{1}{3},\frac{1}{2},\frac{2}{3},\frac{3}{4}\)
\(a=\frac{a'}{x}\)
\(a' =9\) would fail if the numerator of x were an even number, such as \(x=\frac{2}{3}\) and \(a=\frac{9}{\frac{2}{3}}\)
\(a' =10\) would fail if the numerator of x were an odd number greater than 1, such as \(x=\frac{3}{4}\) and \(a=\frac{10}{\frac{3}{4}}\)
only \(a' =12\) can deal with all those possible x listed above.
the numerator of x matters, not the denominator. if three options are 6, 10, and 12, the answer will be 6 and 12.
In MSR, do we take the info in each tab as always true? I noticed in your video explanation that you were checking if the math in the concise solution was legit.
I am assuming MSR tabs are always true, as in 3rd question it is asking us to validate whether a' = b' (which can only be true if xa = yb)
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I am assuming MSR tabs are always true, as in 3rd question it is asking us to validate whether a' = b' (which can only be true if xa = yb)
KarishmaB
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anshhh2705
Joined: 08 Jun 2025
Last visit: 10 Sep 2026
Posts: 20
Location: India
Concentration: General Management, Marketing
Schools: ISB HEC MiM '27 MiM '27 INSEAD MiM '27 ESSEC MiM '27
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Posts: 20
For 3.
It's given in the table section that: a' = b' = xa = yb. (YES)
This means that a' = yb is correct, and because b' = yb, a' = b' is also correct. (YES)
However, the statement a + b < xa + yb is incorrect, as we can see, xa < an and yb < b, which actually leads to a + b > xa + yb. (NO)
It's given in the table section that: a' = b' = xa = yb. (YES)
This means that a' = yb is correct, and because b' = yb, a' = b' is also correct. (YES)
However, the statement a + b < xa + yb is incorrect, as we can see, xa < an and yb < b, which actually leads to a + b > xa + yb. (NO)
Dhruv0911
Posts: 4
but isn't it asking for possible values and it can be true for some of them
nisen20
Parvin93
Check the question:
A given number is a possible value of a’ if, for each value of x in the Table tab, there is a value of a that is compatible with that value of x and the other information provided. For each of the following numbers, select Yes if, given this condition, it is a possible value of a' Otherwise select No.
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