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- Question
(963 + 476)2 + (963 - 476)2 =? (963 x 963 + 476 x 476)
Options- A. 1449
- B. 497
- C. 2
- D. 4
- E. None of these
- Correct Answer
- 2
ExplanationGiven Exp. = (a + b)2 + (a - b)2 = 2(a2 + b2) = 2 (a2 + b2) (a2 + b2) - 1. How many terms are there in the G.P. 3, 6, 12, 24, ... , 384?
Options- A. 8
- B. 9
- C. 10
- D. 11
- E. 7 Discuss
- 2. (35423 + 7164 + 41720) - (317 x 89) =?
Options- A. 28213
- B. 84307
- C. 50694
- D. 56094
- E. None of these Discuss
- 3. The sum of all two digit numbers divisible by 5 is:
Options- A. 1035
- B. 1245
- C. 1230
- D. 945
- E. None of these Discuss
- 4. In dividing a number by 585, a student employed the method of short division. He divided the number successively by 5, 9 and 13 (factors 585) and got the remainders 4, 8, 12 respectively. If he had divided the number by 585, the remainder would have been
Options- A. 24
- B. 144
- C. 292
- D. 584 Discuss
- 5. The difference of the squares of two consecutive odd integers is divisible by which of the following integers?
Options- A. 3
- B. 6
- C. 7
- D. 8 Discuss
- 6. Which of the following number is divisible by 24?
Options- A. 35718
- B. 63810
- C. 537804
- D. 3125736 Discuss
- 7. If the number 5 * 2 is divisible by 6, then * =?
Options- A. 2
- B. 3
- C. 6
- D. 7 Discuss
- 8. On dividing a number by 5, we get 3 as remainder. What will the remainder when the square of the this number is divided by 5?
Options- A. 0
- B. 1
- C. 2
- D. 4 Discuss
- 9. 35 + 15 x 1.5 =?
Options- A. 85
- B. 51.5
- C. 57.5
- D. 5.25
- E. None of these Discuss
- 10. (12 + 22 + 32 + ... + 102) =?
Options- A. 330
- B. 345
- C. 365
- D. 385 Discuss
Numbers problems
Search Results
Correct Answer: 8
Explanation:
| Here a = 3 and r = | 6 | = 2. Let the number of terms be n. |
| 3 |
Then, tn = 384 ⟹ arn-1 = 384
⟹ 3 x 2n - 1 = 384
⟹ 2n-1 = 128 = 27
⟹ n - 1 = 7
⟹ n = 8
∴ Number of terms = 8.
Correct Answer: 56094
Explanation:
35423 317 x 89 = 317 x (90 -1 ) + 7164 = (317 x 90 - 317) + 41720 = (28530 - 317) ----- = 28213 84307 - 28213 ----- 56094 -----
Correct Answer: 945
Explanation:
Required numbers are 10, 15, 20, 25, ..., 95
This is an A.P. in which a = 10, d = 5 and l = 95.
tn = 95 ⟹ a + (n - 1)d = 95
⟹ 10 + (n - 1) x 5 = 95
⟹ (n - 1) x 5 = 85
⟹ (n - 1) = 17
⟹ n = 18
| ∴Requuired Sum = | n | (a + l) | = | 18 | x (10 + 95) = (9 x 105) = 945. |
| 2 | 2 |
Correct Answer: 584
Explanation:
5 | x z = 13 x 1 + 12 = 25
--------------
9 | y - 4 y = 9 x z + 8 = 9 x 25 + 8 = 233
--------------
13| z - 8 x = 5 x y + 4 = 5 x 233 + 4 = 1169
--------------
| 1 -12
585) 1169 (1
585
---
584
---
Therefore, on dividing the number by 585, remainder = 584.
Correct Answer: 8
Explanation:
Let the two consecutive odd integers be (2 n + 1) and (2 n + 3). Then,
(2n + 3)2 - (2n + 1)2 = (2n + 3 + 2n + 1) (2n + 3 - 2n - 1)
= (4n + 4) x 2
= 8(n + 1), which is divisible by 8.
Correct Answer: 3125736
Explanation:
24 = 3 x8, where 3 and 8 co-prime.
Clearly, 35718 is not divisible by 8, as 718 is not divisible by 8.
Similarly, 63810 is not divisible by 8 and 537804 is not divisible by 8.
Consider option (D),
Sum of digits = (3 + 1 + 2 + 5 + 7 + 3 + 6) = 27, which is divisible by 3.
Also, 736 is divisible by 8.
∴ 3125736 is divisible by (3 x 8), i.e., 24.
Correct Answer: 2
Explanation:
6 = 3 x 2. Clearly, 5 * 2 is divisible by 2. Replace * by x
Then, (5 + x + 2) must be divisible by 3. So, x = 2.
Correct Answer: 4
Explanation:
Let the number be x and on dividing x by 5, we get k as quotient and 3 as remainder.
∴ x = 5k + 3
⟹ x2 = (5k + 3)2
= (25k2 + 30k + 9)
= 5(5k2 + 6k + 1) + 4
∴On dividing x2 by 5, we get 4 as remainder.
Correct Answer: 57.5
Explanation:
| Given Exp. = 35 + 15 x | 3 | = 35 + | 45 | = 35 + 22.5 = 57.5 |
| 2 | 2 |
Correct Answer: 385
Explanation:
| We know that (12 + 22 + 32 + ... + n2) = | 1 | n(n + 1)(2n + 1) |
| 6 |
| Putting n = 10, required sum = | ❨ | 1 | x 10 x 11 x 21 | ❩ | = 385 |
| 6 |
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