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Directions: Read the following information and choose the right alternate for the questions given afterwards.

One wedding card, two graduation cards, three anniversary cards and four birthday cards are to be arranged in a triangular display with one card in the first row, two cards in the second row, three cards in the third row and four cards in the fourth row. The arrangement is subject to the following conditions :

1. There is to be no birthday card in the fourth row.
2. There are to be no more than two cards of any type in any of the rows.
3. No birthday card is to be next to and in the same row as an anniversary card.

If all the birthday cards are in the second and third rows, which of these must be true?

1. There is a wedding card between two birthday cards.
2. There is an anniversary card in the second row.
3. There is a graduation card next to and in the same row as anniversary card in the fourth row.
4. There is a graduation card in the third row.

There is no card
18 points

### 1 comment

What do you mean?
• Row 1:
• Row 2: B, B
• Row 3: B, B
• Row 4:

Since Anniversary card cannot be near a Birthday card (condition iii), either Graduation card (G) or Wedding card (W) must be in row 3.

Since there are $3$ anniversary cards and based on condition (ii), two of them must go to row 4 and remaining one to row 1. Thus we get

• Row 1: A
• Row 2: B, B
• Row 3: B, B, W or G
• Row 4: A, A

So in the last row we can have either two G or one G and one W. Lets see the options:

1. There is a wedding card between two birthday cards. – not necessary even though this is possible (not always true)
2. There is an anniversary card in the second row. – false
3. There is a graduation card next to and in the same row as anniversary card in the fourth row – not a proper sentence as “same row” and “fourth row” are used. Ignoring this, this is not necessarily true as the fourth row can be A, A, W, G
4. There is a graduation card in the third row – not necessary as third row can be B, B, W

So, none of the options are necessarily true.

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