Directions: Each question or group of questions is based on a passage, graph, table, or set of conditions. In answering some of the questions, it may be useful to draw a rough diagram. For each question, select the best answer choice given.

Questions 1-7

In a game, exactly six inverted cups stand side by side in a straight line, and each has exactly one ball hidden under it. The cups are numbered consecutively 1 through 6. Each of the balls is painted a single solid color. The colors of the balls are green, magenta, orange, purple, red, and yellow. The balls have been hidden under the cups in a manner that conforms to the following conditions:

• The purple ball must be hidden under a lower-numbered cup than the orange ball.

• The red ball must be hidden under a cup immediately adjacent to the cup under which the magenta ball is hidden.

• The green ball must be hidden under cup 5.

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Detailed Explanation (in Bangla)

Answer Keys

Explanations

Conditions you should keep in mind

1. Green is locked in cup 5.

2. Red and magenta are side-by-side (adjacent).

3. Purple is somewhere to the left of orange (i.e., lower-numbered cup).

Write the six cups as: 1 2 3 4 5 6.

Write the six colors as: G M O P R Y

1. Which complete ordering works?

Test each answer choice against the three rules:

• A – puts green in cup 1 ❌

• B – puts green in cup 2 ❌

• C – order = M R P Y G O

  • Green in 5 ✔︎

  • M & R side-by-side (1-2) ✔︎

  • P (3) before O (6) ✔︎
    → Valid

• D – order = O Y R M G P

  • P (6) not before O (1) ❌

• E – R and M not adjacent ❌

✅ Answer 1: C

2. Magenta in cup 4 – where is red?

Magenta at 4 forces red into cup 3 or 5.
But 5 is already green, so red must sit in cup 3.

✅ Answer 2: C

3. Which colour could sit in cup 6?

Brute-forcing (or quick mental check) across all legal arrangements shows only orange or yellow ever reach cup 6. Among the options, only yellow appears.

• need to change this explanaion

✅ Answer 3: E

4. Purple in cup 4 – where is orange?

Orange must be to the right of purple (rule 3).
Cup 5 is fixed as green, leaving only cup 6.

✅ Answer 4: E

5. Which statement is guaranteed to be true?

Look at every legal arrangement (there are only 18).
We notice:

• Green is fixed at 5, so any ball in cups 1-4 is automatically “before” green.

• Purple is always somewhere in 1-4 (because orange must be to its right and green already occupies 5). Therefore purple is always in a lower-numbered cup than green.

Check the answer choices:

A. Green before yellow – not guaranteed.
B. Orange before green – not guaranteed.
C. Purple before green – always true. ✔︎
D. Purple before red – fails in some layouts.
E. Red before yellow – not guaranteed.

✅ Answer 5: C

6. Orange in cup 2 – which colour pair could be adjacent?

Try to slot the remaining balls while honouring the rules:

Two workable layouts pop out:

1. P O M R G Y

2. P O R M G Y

In layout 2, green (5) and magenta (4) are side-by-side.
No other option in the list ever forms an adjacent pair.

So the pair that can be adjacent is green & magenta.

✅ Answer 6: A

7. Magenta in cup 1 - which pair must be adjacent?

Magenta at 1 forces red into cup 2 (adjacency rule).
Now place the rest:

• Green is fixed at 5.

• Purple must be somewhere left of orange, and both must avoid cup 5.
  The only ways this works are:

  • M R P O G Y

  • M R P Y G O

  • M R Y P G O

In all of them, green (5) and orange (6) are neighbors, while every other pair in the answer list is sometimes adjacent and sometimes not.

Therefore the pair that must end up adjacent is green & orange.

✅ Answer 7: A