Six items U, V, W, X, Y and Z are being separated into 3 Groups - Group 1, Group 2 and Group 3, according to the following conditions.
(i) The number of items in Group 1 is less than or equal to the number of items in Group 2.
(ii) The number of items in Group 2 is less than or equal to the number of items in Group 3.
(iii) V and W cannot be in the same group.
(iv) X can be in Group 3 only if Y is in Group 3.
Which one of the following is an acceptable grouping of the six items?
- Group I - UVGroup 2-WXYGroup 3 - Z10
- Group I-XGroup 2 - YGroup 3-VZUW
- Group I - VGroup 2 - YWGroup 3 - XUZ
- Group I-VGroup 2-ZGroup 3-XYUW
The Correct Option is D
Solution and Explanation
Six items (U, V, W, X, Y, and Z) need to be split into three groups with these rules:
* Group 1 size ≤ Group 2 size ≤ Group 3 size
* V and W can't be in the same group
* X can be in Group 3 only if Y is there too
The correct grouping is:
* Group 1: V
* Group 2: Z, G
* Group 3: X, Y, U, W
The correct answer is (D) : Group I-VGroup 2-ZGroup 3-XYUW
If Group 1 contains only the item Y, then which of the following must be true?
- Group 3 contains four items
- Group 2 contains the same number of items as Group 3
- V is in Group 3
- X is in Group 2
The Correct Option is D
Solution and Explanation
* Condition (iv): X can only be in Group 3 if Y is also in Group 3. Since Y is in Group 1, X cannot be in Group 3.
* Condition (i) and (ii): With Y in Group 1, to satisfy the size conditions, Group 2 must have at least one item, and Group 3 must have at least two.
To keep V and W separate (condition iii), and since X cannot be in Group 3, the only option is to place X in Group 2.
The correct answer is (D) : X is in Group 2
If W and Y are in the same group and V is in Group 3, then which of the following must be false?
- W and Y are in Group 2
- U is the only item in Group 1
- X is the only item in Group 1
- U is in Group 3
The Correct Option is B
Solution and Explanation
* Condition (iv): If W and Y are together, they must be in Group 3 (because X can only be in Group 3 with Y).
* Condition (iii): V and W cannot be together, and V is already in Group 3, so W and Y cannot be in Group 3. This creates a contradiction.
Since the initial statement (W and Y are in the same group and V is in Group 3) leads to a contradiction with the given rules, it must be false. Therefore, any conclusions derived from that statement are also likely to be false. In this case, option B states that U is the only item in Group 1. This could be true or false, but it's not a definite outcome of the initial false statement.
The correct answer is (B) : U is the only item in Group 1
If Group 2 contains only one item, which is neither W nor V, then which of the following must be true?
- Group 1 contains only V or only W
- Group 3 contains W
- Group 1 contains both U and V
- Group 2 contains Z
The Correct Option is A
Solution and Explanation
Six items need to be sorted into three groups with these rules:
* Group 1 must have the fewest items, Group 3 the most.
* V and W can't be together.
* X and Y must be together in Group 3.
If Group 2 has just one item, and it's not V or W, then Group 1 MUST contain either only V or only W. This is the only way to keep V and W apart while following the other rules about group sizes and X and Y being together.
The correct answer is (A) : Group 1 contains only V or only W
Top Questions on Multi-Dimensional Arrangements
- Answer the questions based on the following information.
P drank more at the party than W and left later than V.
T drank more than P and less than V and left later than P and earlier than S.
U drank less than Q and more than V and left later than S.
W drank more than R and left earlier than V.- MAT - 2018
- Logical Reasoning
- Multi-Dimensional Arrangements
- Study the following information to answer these questions. A blacksmith has five iron articles A, B, C, D and E, each having a different weight.
(i)A weighs twice as much as B.
(ii) B weighs four and- a-half times as much as C.
(iii)C weighs half as much as D.
(iv) D weighs half as much as E.
(v) E weighs less than A but more than C.- MAT - 2008
- Logical Reasoning
- Multi-Dimensional Arrangements
- From a group of six boys M, N, O, P, Q, R and five girls G, H, I, J, K; a team of six is to be selected.
Some of the criteria of selection are as follows:
M and J go together.
O cannot be placed with N.
I cannot go with J.
N goes with H.
P and Q have to be together.
K and R go together.
Unless otherwise stated, these criteria are applicable to all the below questions:- MAT - 2006
- Logical Reasoning
- Multi-Dimensional Arrangements
- Study the information given below to answer these questions.
There are four friends A, B, C, D. One of them is a cricketer and studies Chemistry and Biology. A and play football. Both football players study Maths D is a boxer. One football player also studies physics. The boxer studies Matsha and Accounts.All the friends study two subjects each and play one game each.- MAT - 2005
- Logical Reasoning
- Multi-Dimensional Arrangements
- A set of eight candidates A, B, C, D, E, F, G and H are being interviewed by two panels of interviewers: Panel I and Panel II-from 9.30 to 10.50 on a particular day. Each panel will spend about 10 minutes per candidate and at no time during the interview process will a panel be without any candidate. The original schedules of interviews for the eight candidates are shown in the following table:
Candidate Panel-I Time Panel-II Time A
9.30 to 9.40
10.10 to 10.20
B
9.40 to 9.50
10.20 to 10.30
C
9.50 to 10.00
10.30 to 10.40
D
10.00 to 10.10
10.40 to 10.50
E
10.10 to 10.20
9.30 to 9.40
F
10.20 to 10.30
9.40 to 9.50
G
10.30 to 10.40
9.50 to 10.00
H
10.40 to 10.50
10.00 to 10.10
Due to requests from the candidates, the interview schedule was altered for several candidates. The alterations were made in such a way that whenever a change was made, the time schedule for both the panels of a particular candidate was exchanged in entirety with the time schedule of another candidate. The following alterations were made:
I. A's place was taken by G
II. A in turn was accommodated in C's place
III. C in turn was accommodated in E's place
IV. E took H's place
V. H took G's place- MAT - 2003
- Logical Reasoning
- Multi-Dimensional Arrangements
Questions Asked in MAT exam
- In the following sentence, a part of the sentence is underlined. Beneath each sentence four different ways of phrasing the underlined part are indicated. Choose the best alternative among the four options.
There \(\underline {\text{have}\ \text{been}\ \text{heavy}\ \text{rainfall}}\) yesterday- MAT - 2018
- Sentence Correction
- Who among the following cannot be impeached?
- MAT - 2018
- Politics and Government
- Who is leading the LTTE delegation for the peace process with Sri Lanka?
- MAT - 2018
- International Organizations
- Who was the first UN Secretary General?
- MAT - 2018
- Politics and Government
- Which of the following sources yields the maximum revenue to the Union Government?
- MAT - 2018
- Politics and Government