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Question (31)

QN0019682

Which of the following triples has hypotenuse 25?

(A) (7, 24, 25)
(B) (8, 15, 17)
(C) (5, 12, 13)
(D) (9, 40, 41)

Correct Answer: A

Explanation:

The largest number 25 is the hypotenuse.

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Question (32)

QN0019683

The triple (12, 35, 37) is primitive because:

(A) Its numbers are consecutive
(B) It has no common factor greater than 1
(C) Its hypotenuse is odd
(D) Its sides are equal

Correct Answer: B

Explanation:

The numbers 12, 35, and 37 have no common factor greater than 1.

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Question (33)

QN0019684

Which triple has all entries divisible by 3?

(A) (5, 12, 13)
(B) (8, 15, 17)
(C) (9, 12, 15)
(D) (7, 24, 25)

Correct Answer: C

Explanation:

9, 12, and 15 are all divisible by 3.

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Question (34)

QN0019685

Which of the following is a primitive triple with hypotenuse 17?

(A) (6, 8, 10)
(B) (8, 15, 17)
(C) (12, 16, 20)
(D) (15, 36, 39)

Correct Answer: B

Explanation:

(8, 15, 17) has no common factor greater than 1.

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Question (35)

QN0019686

If (6, 8, 10) is divided by their common factor 2, the resulting triple is:

(A) (2, 3, 4)
(B) (3, 4, 5)
(C) (4, 5, 6)
(D) (5, 6, 7)

Correct Answer: B

Explanation:

Dividing by 2 gives the primitive triple (3, 4, 5).

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Question (36)

QN0019687

There are infinitely many Baudhāyana triples because:

(A) Numbers never end
(B) (3k, 4k, 5k) forms a triple for every positive integer k
(C) Every integer forms a triple
(D) Triangles are infinite

Correct Answer: B

Explanation:

Multiples of a triple are also triples.

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Question (37)

QN0019688

Which triple has hypotenuse 61?

(A) (11, 60, 61)
(B) (9, 40, 41)
(C) (12, 35, 37)
(D) (20, 21, 29)

Correct Answer: A

Explanation:

11² + 60² = 61².

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Question (38)

QN0019689

The triple (30, 40, 50) is a scaled version of:

(A) (5, 12, 13)
(B) (3, 4, 5)
(C) (8, 15, 17)
(D) (7, 24, 25)

Correct Answer: B

Explanation:

Dividing by 10 gives (3, 4, 5).

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Question (39)

QN0019690

Which statement is true about primitive triples?

(A) They always have even hypotenuse.
(B) They cannot be scaled down further by a common factor greater than 1.
(C) They have equal sides.
(D) They contain zero.

Correct Answer: B

Explanation:

Primitive triples have no common factor greater than 1.

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Question (40)

QN0019691

The triple (300, 400, 500) is obtained by multiplying (3, 4, 5) by:

(A) 10
(B) 50
(C) 100
(D) 150

Correct Answer: C

Explanation:

100 × (3, 4, 5) = (300, 400, 500).

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Question (31)

Which of the following triples has hypotenuse 25?

Explanation:

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Question (32)

The triple (12, 35, 37) is primitive because:

Explanation:

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Question (33)

Which triple has all entries divisible by 3?

Explanation:

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Question (34)

Which of the following is a primitive triple with hypotenuse 17?

Explanation:

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Question (35)

If (6, 8, 10) is divided by their common factor 2, the resulting triple is:

Explanation:

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Question (36)

There are infinitely many Baudhāyana triples because:

Explanation:

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Question (37)

Which triple has hypotenuse 61?

Explanation:

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Question (38)

The triple (30, 40, 50) is a scaled version of:

Explanation:

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Question (39)

Which statement is true about primitive triples?

Explanation:

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Question (40)

The triple (300, 400, 500) is obtained by multiplying (3, 4, 5) by:

Explanation:

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