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Q #26
:

Directions: Read the following information to answer the question.

What is the units’ digit of 1! + 2! + 3! + … + 19!?

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Answer:3 Solution :1!=1,2!=2,3!=6,4!=24,5!=120 factorials starting from 5! And end with digit 0 will have at least one 2 and one 5 in their product so they don’t contribute in the last digit. Last digit=1+2+6+4+0=13=3(last digit) hence proved.

Q #27
:

Directions: Read the following information to answer the question.

What is the remainder of (327 + 422 + 955) ÷ 9 ?

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Answer:3 Explanation:327/9 gives 3 remainder 422/9 gives 8 remainder and 955/9 gives 1 as a remainder.adding all 3 remainders wer Have 12 whwn divided by 9 it gives 3. Hence proved.

Q #28
:

Directions: Read the following information to answer the question.

What is the remainder of (273 x 549 x 977 )÷ 5 ?

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Answer:4 273/5 gives 3 as a remainder,549/5 gives 4 as a remainder,977/5 gives 2 as remainder then (3*4*2=24).when 24/5 gives 4 as a remainder. Hence proved.

Q #29
:

Directions: Read the following information to answer the question.

What is the remainder of (2^625) ÷ 5 ?

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Answer:2 Explanation: 2^1=2 so 2/5 gives 2 as a remainder. 2^2=4 ; 4/5 gives 4 as a remainder. 2^3=8 gives 3 as a remainder.2^54=16gives 1 as a remainder.so cyclicity is of4. .625/4=1 remainder son 2^1=2…

Q #30
:

Directions: Read the following information to answer the question.

What is the remainder of (8^5) ÷ 7?

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(8^5)/7…..here 8/7=1 remainder.