Numbers problems
- 1. The sum of the digits of a two-digits number is 10,while when the digits are reversed, the number decreases by 54. Find the changed number ?
Options- A. 28
- B. 19
- C. 37
- D. 46 Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk
Correct Answer: 28
Explanation:
Let the original number is 82 i.e 8 + 2 = 10 and when the digits are reversed i.e 28
The difference is 82 - 28 = 54 i.e, the number is decreased by 54.
- 2. What is the value of 4 in 475?
Options- A. 4
- B. 400
- C. 475
- D. 40 Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO
Correct Answer: 400
Explanation:
The value of 4 in 475 means the place value of 4 in 475 and not its face value. Face value means the digit itself though it is at any place in the given number. But place value means the value of digit in its place in the given number.
Here the place value of 4 in 475 can be determined by as 4 is in 100's place in 475.
Hence, the place value of 4 in 475 is 4x100 = 400.
- 3. A six-digit number is formed by repeating a three-digit number; for example, 404404 or 415415 etc. Any number of this form is always exactly divisible by
Options- A. 101
- B. 901
- C. 1001
- D. 789 Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 1001
Explanation:
Here by trial and error method, we can obseve that
404404 = 404 x 1001; 415415 = 415 x 1001, etc.
So, any number of this form is divisible by 1001.
- 4. A teacher multiplies 987 by a certain number and obtains 556781 as her answer. If in the answer, both 6 and 7 are wrong but the other digits are correct, then the correct answer will be
Options- A. 553681
- B. 555181
- C. 556581
- D. 555681 Also asked in: AIEEE, Bank Exams, CAT, GATE, GRE, Analyst, Bank Clerk, Bank PO
Correct Answer: 555681
Explanation:
Given number is 987 = 3 x 7 x 47.
So, required number must be divisible by each one of 3, 7, 47.
None of the numbers in 553681 and 555181 are divisible by 3. While 556581 is not divisible by 7.
Correct answer is 555681.
- 5. What is the right most integer of the expression 65776759 + 54697467 ?
Options- A. 4
- B. 6
- C. 9
- D. 0 Also asked in: GRE, GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 9
Explanation:
Last digit for the power of 6 is 6 (always)
Power cycle of 7 is 7, 9, 3, 1.
Now 467/4 gives a remainder of 3
Then the last digit is = 3
Last digit is 6 + 3 = 9.
- 6. A box contains 90 screws each of 100 gms and 100 bolts each of 150 gms. If the entire box weighs 35.5 kg, then the weight of the empty box is ?
Options- A. 10.5 kgs
- B. 12 kgs
- C. 9.6 kgs
- D. 11.5 kgs Also asked in: AIEEE, Bank Exams, CAT, GATE, GRE, Bank PO
Correct Answer: 11.5 kgs
Explanation:
Screws weight = 90x100 = 9000gms
bolts weight = 100 x 150 = 15000gms
weight = screws + bolts => 24000 gms =>24 kg
Given entire box weight = 35.5kg
empty box = entire box weight - weight => 35.5kg - 24kg => 11.5kg
so the empty box is 11.5kg.
- 7. Which of the following is not a prime number?
Options- A. 5
- B. 11
- C. 21
- D. 37 Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO
Correct Answer: 21
Explanation:
A prime number is a whole number greater than 1 whose only factors are 1 and itself.
Factors of 5 are 1, 5
Factors of 11 are 1, 11
Factors of 21 are 1, 3, 7, 21
Factors of 37 are 1, 37.
Hence, according to the definition of a prime number, 21 is not a prime number as it has more than two factors.
- 8. There are several peacocks and deers in a cage (with no other types of animals). There are 72 heads and 200 feet inside the cage. How many peacocks are there, and how many deers ?
Options- A. 42 & 24
- B. 38 & 26
- C. 36 & 24
- D. 44 & 28 Also asked in: AIEEE, Bank Exams, CAT, GATE, GRE, Bank Clerk, Bank PO
Correct Answer: 44 & 28
Explanation:
Let
x = peacocks
y = deers
2x + 4y = 200
x + y = 72
y = 72 - x
2x + 288 - 4x = 200
x = 44 peacocks
y = 28 deers
- 9. If 1/a+1/b+1/c = 1/(a+b+c) where a+b+c not equals '0', abc not equals '0', What is the value of (a+b) (b+c) (a+c) ?
Options- A. 3
- B. 2
- C. 1
- D. 0 Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 0
Explanation:
Let assume the value of a,b &c that will satisfy the equation.
so a=1,b=1,c= -1 or a=1,b= -1 &c=1 or a= -1,b=1,c=1
here all three cases satisfy the equation
assume any one a=1,b=1,c= -1
Hence (a+b)(b+c)(c+a)=(1+1)(1-1)(-1+1) = 0
- 10. Which of the following is a rational number?
Options- A. 0.241
- B. 1.732
- C. 4
- D. All of the above Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO
Correct Answer: 4
Explanation:
Any number which can be expressed as a fraction of two integers like P & Q as P/Q where Q is not equal to zero.
Every integer is a rational number since Q can be 1.
Hence, in the given options, 4 can be expressed as a simple fraction as 4/1. And all other options cannot be expressed as fractions.
Hence, 4 is a rational number in the given options.
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