24 questions, 2 of them short answer (type the number, as in IPMAT Indore). Each is marked with the exam level it suits. Answer, then open the step-by-step solution.
A team of 4 is to be chosen from 6 students, P, Q, R, S, T and U, under these conditions:
1. Exactly one of S and P is selected.
2. R is selected only if P is not selected.
3. Exactly one of P and U is selected.
Which student cannot be in any possible team?
The possible teams are: QRSU, QSTU, RSTU.
P is in none of them.
A team of 3 is to be chosen from 6 students, P, Q, R, S, T and U, under these conditions:
1. Exactly one of P and S is selected.
2. If Q is selected, T must also be selected.
3. Exactly one of S and U is selected.
4. If R is selected, Q must also be selected.
Which student cannot be in any possible team?
The possible teams are: PTU, QST.
R is in none of them.
A team of 3 is to be chosen from 6 students, P, Q, R, S, T and U, under these conditions:
1. Exactly one of T and Q is selected.
2. Exactly one of S and U is selected.
3. T is selected only if P is not selected.
Which of the following could be the team?
QRU meets every condition.
PQR breaks condition 2.
RSU breaks condition 1, 2.
PRT breaks condition 2, 3.
A team of 3 is to be chosen from 6 students, P, Q, R, S, T and U, under these conditions:
1. If S is selected, U must also be selected.
2. If P is selected, R must also be selected.
3. U is selected only if P is not selected.
How many different teams are possible?
Check every group of 3: 20 groups in all.
The groups that meet every condition are: PQR, PRT, QRT, QRU, QSU, QTU, RSU, RTU, STU.
So 9 teams are possible.
A team of 4 is to be chosen from 6 students, P, Q, R, S, T and U, under these conditions:
1. If T is selected, U must also be selected.
2. T and S cannot both be selected.
3. T and R cannot both be selected.
How many different teams are possible?
Check every group of 4: 15 groups in all.
The groups that meet every condition are: PQRS, PQRU, PQSU, PQTU, PRSU, QRSU.
So 6 teams are possible.
A team of 4 is to be chosen from 6 students, P, Q, R, S, T and U, under these conditions:
1. Exactly one of R and P is selected.
2. At least one of S and T is selected.
3. S is selected only if P is not selected.
4. At least one of R and S is selected.
Which student cannot be in any possible team?
The possible teams are: QRST, QRSU, QRTU, RSTU.
P is in none of them.
A team of 3 is to be chosen from 7 students, P, Q, R, S, T, U and V, under these conditions:
1. Exactly one of S and V is selected.
2. S and P cannot both be selected.
3. P is selected only if V is not selected.
How many different teams are possible?
Check every group of 3: 35 groups in all.
The groups that meet every condition are: QRS, QRV, QST, QSU, QTV, QUV, RST, RSU, RTV, RUV, STU, TUV.
So 12 teams are possible.
A team of 3 is to be chosen from 6 students, P, Q, R, S, T and U, under these conditions:
1. R is selected only if P is not selected.
2. If U is selected, R must also be selected.
3. S and R cannot both be selected.
Which of the following could be the team?
RTU meets every condition.
PQU breaks condition 2.
QSU breaks condition 2.
QRS breaks condition 3.
A team of 4 is to be chosen from 6 students, P, Q, R, S, T and U, under these conditions:
1. If T is selected, S must also be selected.
2. P and Q cannot both be selected.
3. If R is selected, P must also be selected.
4. Q is selected only if S is not selected.
How many different teams are possible?
Check every group of 4: 15 groups in all.
The groups that meet every condition are: PRST, PRSU, PSTU.
So 3 teams are possible.
A team of 4 is to be chosen from 7 students, P, Q, R, S, T, U and V, under these conditions:
1. At least one of S and R is selected.
2. Exactly one of T and V is selected.
3. Exactly one of S and P is selected.
4. R and Q cannot both be selected.
Which student must be in every possible team?
The possible teams are: PRTU, PRUV, QSTU, QSUV, RSTU, RSUV.
U is in all of them.
A team of 3 is to be chosen from 8 students, P, Q, R, S, T, U, V and W, under these conditions:
1. Exactly one of T and V is selected.
2. If Q is selected, W must also be selected.
3. R and P cannot both be selected.
4. If W is selected, S must also be selected.
How many different teams are possible?
Check every group of 3: 56 groups in all.
The groups that meet every condition are: PST, PSV, PTU, PUV, RST, RSV, RTU, RUV, STU, STW, SUV, SVW.
So 12 teams are possible.
A team of 4 is to be chosen from 7 students, P, Q, R, S, T, U and V, under these conditions:
1. U and T cannot both be selected.
2. Exactly one of Q and R is selected.
3. P is selected only if R is not selected.
4. P and Q cannot both be selected.
Which student cannot be in any possible team?
The possible teams are: QSTV, QSUV, RSTV, RSUV.
P is in none of them.
A team of 4 is to be chosen from 7 students, P, Q, R, S, T, U and V, under these conditions:
1. Exactly one of P and V is selected.
2. If P is selected, U must also be selected.
3. R and S cannot both be selected.
Which of the following could be the team?
QRTV meets every condition.
RSTU breaks condition 1, 3.
PSTV breaks condition 1, 2.
PQRT breaks condition 2.
A team of 4 is to be chosen from 7 students, P, Q, R, S, T, U and V, under these conditions:
1. S and T cannot both be selected.
2. U and Q cannot both be selected.
3. Exactly one of R and P is selected.
Which student must be in every possible team?
The possible teams are: PQSV, PQTV, PSUV, PTUV, QRSV, QRTV, RSUV, RTUV.
V is in all of them.
A team of 3 is to be chosen from 7 students, P, Q, R, S, T, U and V, under these conditions:
1. If V is selected, U must also be selected.
2. Exactly one of V and P is selected.
3. If S is selected, R must also be selected.
4. If T is selected, S must also be selected.
Which student cannot be in any possible team?
The possible teams are: PQR, PQU, PRS, PRU, QUV, RUV.
T is in none of them.
A team of 4 is to be chosen from 6 students, P, Q, R, S, T and U, under these conditions:
1. Exactly one of U and P is selected.
2. If U is selected, Q must also be selected.
3. Exactly one of R and S is selected.
How many different teams are possible?
Check every group of 4: 15 groups in all.
The groups that meet every condition are: PQRT, PQST, QRTU, QSTU.
So 4 teams are possible.
A team of 3 is to be chosen from 8 students, P, Q, R, S, T, U, V and W, under these conditions:
1. Exactly one of W and V is selected.
2. If U is selected, S must also be selected.
3. At least one of R and V is selected.
4. If V is selected, S must also be selected.
Which of the following could be the team?
STV meets every condition.
PRV breaks condition 4.
PQW breaks condition 3.
PQU breaks condition 1, 2, 3.
A team of 3 is to be chosen from 6 students, P, Q, R, S, T and U, under these conditions:
1. If U is selected, Q must also be selected.
2. If P is selected, R must also be selected.
3. S and R cannot both be selected.
How many different teams are possible?
Check every group of 3: 20 groups in all.
The groups that meet every condition are: PQR, PRT, QRT, QRU, QST, QSU, QTU.
So 7 teams are possible.
A team of 4 is to be chosen from 7 students, P, Q, R, S, T, U and V, under these conditions:
1. At least one of T and U is selected.
2. T is selected only if S is not selected.
3. At least one of U and Q is selected.
4. Exactly one of S and P is selected.
How many different teams are possible?
Check every group of 4: 35 groups in all.
The groups that meet every condition are: PQRT, PQRU, PQTU, PQTV, PQUV, PRTU, PRUV, PTUV, QRSU, QSUV, RSUV.
So 11 teams are possible.
A team of 3 is to be chosen from 6 students, P, Q, R, S, T and U, under these conditions:
1. If U is selected, R must also be selected.
2. Q and P cannot both be selected.
3. If P is selected, U must also be selected.
4. Exactly one of S and Q is selected.
Which student cannot be in any possible team?
The possible teams are: QRT, QRU, RST, RSU.
P is in none of them.
A team of 4 is to be chosen from 7 students, P, Q, R, S, T, U and V, under these conditions:
1. If U is selected, P must also be selected.
2. At least one of S and R is selected.
3. Exactly one of U and Q is selected.
4. At least one of R and U is selected.
Which of the following could be the team?
QRST meets every condition.
RSUV breaks condition 1.
STUV breaks condition 1.
QTUV breaks condition 1, 2, 3.
A team of 4 is to be chosen from 6 students, P, Q, R, S, T and U, under these conditions:
1. If S is selected, T must also be selected.
2. P and Q cannot both be selected.
3. R and T cannot both be selected.
4. If Q is selected, S must also be selected.
Which of the following could be the team?
QSTU meets every condition.
PRSU breaks condition 1.
PQRS breaks condition 1, 2.
QRTU breaks condition 3, 4.
A team of 3 is to be chosen from 6 students, P, Q, R, S, T and U, under these conditions:
1. R is selected only if P is not selected.
2. At least one of Q and S is selected.
3. If T is selected, S must also be selected.
Which of the following could be the team?
QSU meets every condition.
PQR breaks condition 1.
PQT breaks condition 3.
PTU breaks condition 2, 3.
A team of 3 is to be chosen from 6 students, P, Q, R, S, T and U, under these conditions:
1. At least one of S and Q is selected.
2. U and Q cannot both be selected.
3. R and T cannot both be selected.
Which of the following could be the team?
RSU meets every condition.
QSU breaks condition 2.
PRT breaks condition 1, 3.
RTU breaks condition 1, 3.
These are original practice questions written by Target Campus in the pattern, syllabus and difficulty of IPMAT Indore, IPMAT Rohtak, JIPMAT, NPAT and SET. They are not previous-year papers.
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