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Q #21
:

Directions: Read the following information to answer the question.

The integer 10133 and 12156 when divided by a three-digit integer n leave the same remainder. What is n?

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The required number will be the difference of the two given numbers or (a three digit) a factor of the difference 12156 – 10133 = 2033 2033 = 289 x 7 So The required three digit number = 289

Q #22
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Directions: Read the following information to answer the question.

How many three-digit numbers are there that are divisible neither by 6 nor by 7?

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First let’s find out number of 3 digit numbers divisible by 6 or 7 or both Number of 3 digit numbers divisible by 6 =166 –16 = 150 number of 3 digit numbers divisible by 7=142 –14 = 128 Number of 3-digit numbers divisible by 42 = 23 –2 = 21 number of 3-digit numbers divisible neither by 6 or 7 both =128+150-21=257 Hence, no .of 3-digit number divisible neither by 6 Nor by 7=900-257=643

Q #23
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Directions: Read the following information to answer the question.

How many two digit numbers exist such that the product of the two digits is a perfect square? Note that neither of the two digits are zeroes.

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A total of 17 numbers are possible. They are {11, 22, 33, 41 44, 55, 66, 77, 88, 99, 14, 19, 91, 28, 82, 94, 49}

Q #24
:

Directions: Read the following information to answer the question.

If 6440 soldiers were asked to stand in rows to form a perfect square, it was found that 40 soldiers were left out. What was the number of soldiers in each row?

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Reqd. no. of soldiers in each row =(6440 – 40)¹/² = 80

Q #25
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Directions: Read the following information to answer the question.

9^6 + 7 when divided by 8 would have a remainder of:

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