Discussion
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- Question
- When simplified, the product ( 2 - 1/3) (2 - 3/5) (2 - 5/7) ...... (2 - 997/999) is equal to?
Options- A. 5/999
- B. 1001/999
- C. 1001/3
- D. None of these
- Correct Answer
- 1001/3
ExplanationGiven Exp. ( 2 - 1/3) (2 - 3/5) (2 - 5/7) ...... (2 - 997/999)
= (5/3) x (7/5) x (9/7) x .......... x (1001/999)
= 1001/3. - 1. In a two digit number, the digital unit place is 1 more than twice of the digit at ten's place. If the digit at unit's and ten's place be interchanged, then the difference between the new number and original number is less than 1 to that of original number. what is the original number?
Options- A. 52
- B. 73
- C. 25
- D. 37 Discuss
- 2. The ratio of two number is 3:2, If 10 and the sum of the two numbers are added to their product, square of sixteen is obtained. What could be the smaller number?
Options- A. 14
- B. 12
- C. 16
- D. 18 Discuss
- 3. The numbers x, y, z are such that xy = 96050 and xz = 95625 and y is greater than z by one. Find out the number z?
Options- A. 425
- B. 220
- C. 525
- D. 225 Discuss
- 4. If a number is decreased by 4 and divided by 6 the result is 9. What would be the result if 3 is subtracted from the number and then it is divided by 5?
Options- A. 9 2/ 5
- B. 10 1/ 5
- C. 11 2/ 5
- D. 11 Discuss
- 5. A two-digit number is seven times the sum of its digits, If each digit is increased by 2, the number thus obtained is 4 more than six times the sum of its digits, Find the number?
Options- A. 42
- B. 24
- C. 48
- D. Data adequate Discuss
- 6. (1 - 1/3) (1 - 1/4) (1 - 1/5 )... (1 - 1/n ) =?
Options- A. 1/n
- B. 2/n
- C. 2(n - 1)/n
- D. 2(n + 1)/n Discuss
- 7. Which of the following numbers is exactly divisible by 99?
Options- A. 3572404
- B. 135792
- C. 913464
- D. 114345 Discuss
- 8. What least value must be given to * so that the number 91876 * 2 is divisible by 8?
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
- 9. What least value must be given to * so that the number 6135 * 2 is exactly divisible by 9?
Options- A. 0
- B. 1
- C. 2
- D. 3 Discuss
- 10. What least value must be given to * so that the number 97215*6 is divisible by 11?
Options- A. 1
- B. 2
- C. 3
- D. 5 Discuss
Number System problems
Search Results
Correct Answer: 37
Explanation:
Let the original number be 10p + q.
So from question,
q = 2p + 1 ...(i)
and (10q + p) - (10p + q ) = (10p + q) - 1
? 9q - 9p = 10p + q -1
? 19p - 8q = 1...(ii)
Putting the value of (i) in equation (ii) we get
19p - 8(2p + 1) = 1
? 19p - 16p - 8 = 1
? 3p = 9
? p = 3
So, q = 2 x 3 + 1 = 7
? Original number = 10 x 3 + 7 = 37
Correct Answer: 12
Explanation:
Let the two numbers be 3N and 2N
According to the question.
10 + (3N +2N ) + (3N x 2N) = 162
? 6N2 + 5N - 246 = 0
? 6N2 + 41N - 36N - 246 = 0
? N(6N + 41 ) - 6(6N + 41) = 0
? (6N + 41 ) (N - 6) = 0
? N = 6 or -41/6 (But -ve value cannot be accepted )
? Smaller number = 2N = 2 x 6 = 12 .
Correct Answer: 225
Explanation:
xy = 96050 ...(i)
and xz = 95625 ...(ii)
and y - z = 1 ... (iii)
Dividing (i) by (ii) we get
y/z = 96050 / 95625
= 3842 / 3825
= 226 / 225 ... (iv)
Combining (iii) and (iv) we get z = 225.
Correct Answer: 11
Explanation:
Let the number be x.
? (x - 4)/6 = 9
? x = 58
Again (x - 3)/5 = (58 - 3)/5 = 11
Correct Answer: 42
Explanation:
Let the two-digit number be 10x + y
10x + y = 7(x + y)
? x = 2y ...(i)
10(x +2 ) + (y + 2) = 6(x + y + 4) + 4
or 10x + y + 22 = 6x + 6y + 28
? 4x - 5y = 6 ...(ii)
Solving equations (i) and (ii)
We get x = 4 and y = 2
Correct Answer: 2/n
Explanation:
Given Exp.= (1 - 1/3) (1 - 1/4) (1 - 1/5)...(1 - 1/n)
= (2/3) x (3/4) x (4/5) x ... x (n-1/n)
= 2/n.
Correct Answer: 114345
Explanation:
To determine if a number is divisible by 99 it needs to be divisible by 9 and 11.
Divisible by 9 test. If sum of digits is divisible by 9 then the number is divisible by 9.
Divisible by 11 test. If sum of ODD positioned digits minus the sum of the EVEN positioned digits is divisible by 11 then the number is divisible by 11.
Clearly 114345 is divisible by 9 as well as 11. so,it is divisible by 99.
Correct Answer: 3
Explanation:
By hit and trial we find that 632 is divisible by 8. So, * must replaced by 3.
Correct Answer: 1
Explanation:
6 + 1 + 3 + 5 + x + 2 = 17 + x must be divisible by 9.
So, x =1.
Correct Answer: 3
Explanation:
If sum of ODD positioned digits minus the sum of the EVEN positioned digits is divisible by 11 then the number is divisible by 11.
Sum of odd positioned digits - sum of even positioned digits = (9 + 2 + 5 + 6) - (7 + 1 + x) =14 - x
It must be divisible by 11. So x = 3.
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