CAT Exam Model Paper 8 with solutions for free online practice

Question : 14 of 60

Marks: +1, -0

In a sequence of 100 positive integers, the sum of any six consecutive terms is the same. If the values of the 11th, 22nd, 33rd, 44th and 55th terms are 11,22, 33,44 and 55 respectively, then which of the following is definitely true about the sum of the 19th and the 99th terms of the sequence?

It is less than 60.
It is greater than 59 and less than 76.
It is greater than 75 and less than 90.
None of the above is true.

Validate

Solution:

Let us assume the sequence to be

a_{1}, a_{2}, a_{3}, ... a_{100}

According to the question:

a_{1}+a_{2}+... a_{6}=a_{2}+a_{3}+... a_{7}

⇒

a_{1}=a_{7}

. Similarly we can prove that

a_{2}=a_{8}

a_{3}=a_{9}

and so on. Combining these equations we get

a_{k}=a_{k+6}=a_{k+12}=

.....for 3,1 natural numbers k.
Therefore

a_{19}=a_{25}=....=a_{55}=55

Also

a_{33}=a_{39}=....=a_{99}=33

So the required sum is 55 + 33 = 88.

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