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Q:

The difference between two numbers is 1365. When larger number is divided by the smaller one, the quotient is 6 and the remainder is 15. The smaller number is ?

Answer

Let the numbers be x and 1365+x

Then 1365+x = 6x+15

=> x = 270

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Subject: Problems on Numbers

Q:

If sum of three consecutive numbers is 42 . What will the sum of the digits of middle number .

Answer

Let the numbers be x, x+1, x+2

Then x + x+1 + x+2 = 42

=> 3x + 3 = 42

=> 3x = 39

=> x = 13

The numbers would be 13, 14, 15

Therefore, Sum of the digits of middle number = 1+4 = 5

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Subject: Problems on Numbers

Q:

The planet with the maximum number of natural satellites (moons), so far discovered is

A) Jupiter	B) Neptune
C) Saturn	D) Uranus

Answer & Explanation Answer: A) Jupiter

Explanation:

Jupiter 63

Saturn 60

Uranus 27

Neptune 13

Pluto 3

Mars 2

Earth 1

Venus 0

Mercury 0

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Filed Under: World Geography

Q:

The Number of times the digit 8 will be written when listing the integers from 1 to 1000 is :

A) 100	B) 200
C) 300	D) 400

Answer & Explanation Answer: C) 300

Explanation:

Since 8 does not occur in 1000, we have to count the number of times 8 occurs when we list the integers from 1 to 999. Any number between 1 and 999 is of the form xyz, where $0 \leq x, y, z \leq 9 .$

Let us first count the numbers in which 8 occurs exactly once.

Since 8 can occur atone place in $3 C_{1}$ ways. There are $3 x 9 x 9$ such numbers.

Next, 8 can occur in exactly two places in $3 C_{2} \times 9$ such numbers. Lastly, 8 can occur in all three digits in one number only.

Hence, the number of times 8 occur is

$1 \times (3 \times 9^{2}) + 2 \times (3 \times 9) + 3 \times 1 = 300$

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Filed Under: Permutations and Combinations

Q:

The number of signals that can be generated by using 5 differently coloured flags, when any number of them may be hoisted at a time is:

A) 235	B) 253
C) 325	D) None of these

Answer & Explanation Answer: C) 325

Explanation:

Required number of signals = $5 P_{1} + 5 P_{2} + 5 P_{3} + 5 P_{4} + 5 P_{5}$

= 5 + 20 + 60 + 120 + 120 = 325

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Filed Under: Permutations and Combinations
Exam Prep: AIEEE , Bank Exams , CAT
Job Role: Bank Clerk , Bank PO

Q:

If a+b+c =21 what is the total number of positive integral solutions?

A) 109	B) 190
C) 901	D) 910

Answer & Explanation Answer: B) 190

Explanation:

Number of positive integral solutions = $n - 1_{C_{r - 1}}$ = ${}^{20}C_{2}$ = 190

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Filed Under: Permutations and Combinations
Exam Prep: CAT , Bank Exams , AIEEE
Job Role: Bank PO , Bank Clerk

Q:

If a+b+c = 21, what is the total number of non - negative integral solutions?

A) 123	B) 253
C) 321	D) 231

Answer & Explanation Answer: B) 253

Explanation:

Number of non - negative integral solutions = $n + r - 1 C_{r - 1} = {}^{23}C_{2}$ = 253

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Filed Under: Permutations and Combinations
Exam Prep: CAT , Bank Exams , AIEEE
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Q:

In how many different ways can 6 different balls be distributed to 4 different boxes, when each box can hold any number of ball?

A) 2048	B) 1296
C) 4096	D) 576

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