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Jaiswal Sunny

· started a discussion

· 1 Months ago

Option should have 2 (Question: 99480.0 )

This is Arun Sharma Question ,

1st AP should be 998 , 1000

2nd AP should be 664,666,668

How come 7?

Question:

A boy plays a mathematical game where he tries to write the number 1998 into the sum of 2 or more consecutive positive even numbers (e.g. 1998 = 998 + 1000). In how many different ways can he do so?

Options:
A) 5
B) 6
C) 7
D) 8
E) 10
Solution:

For answering this question we need to plan the use of the factors of 1998,

1998 = 2 × 33 × 37 → 16 factors viz. 1 × 1998, 2 × 999, 3 × 666, 6 × 333,9 × 222, 18 × 111, 27 × 74, 54 × 37.

Thus we could form 7 APs as follows:

(1)  An AP with 2 terms and average 999

(2)  An AP with 3 terms and average 666 and so on → 7 ways.

kanhaiya jha

· commented

· 1 Months ago

For answering this question we need to plan the use of the factors of 1998,
1998 = 2 × 33 × 37 → 16 factors viz. 1 × 1998, 2 × 999, 3 × 666, 6 × 333,9 × 222, 18 × 111, 27 × 74, 54 × 37.
Thus we could form 7 APs as follows:
(1) An AP with 2 terms and average 999
(2) An AP with 3 terms and average 666 and so on → 7 ways.
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