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Home ‣ Aptitude ‣ Surds and Indices Comments
- Question
❨ xb ❩ (b + c - a) . ❨ xc ❩ (c + a - b) . ❨ xa ❩ (a + b - c) =? xc xa xb
Options- A. xabc
- B. 1
- C. xab + bc + ca
- D. xa + b + c
- Correct Answer
- 1
ExplanationGiven Exp. = x(b - c)(b + c - a) . x(c - a)(c + a - b) . x(a - b)(a + b - c) = x(b - c)(b + c) - a(b - c) . x(c - a)(c + a) - b(c - a)
. x(a - b)(a + b) - c(a - b)= x(b2 - c2 + c2 - a2 + a2 - b2) . x-a(b - c) - b(c - a) - c(a - b) = (x0 x x0) = (1 x 1) = 1. - 1. (25)7.5 x (5)2.5 ÷ (125)1.5 = 5?
Options- A. 8.5
- B. 13
- C. 16
- D. 17.5
- E. None of these Discuss
- 2. If 3(x - y) = 27 and 3(x + y) = 243, then x is equal to:
Options- A. 0
- B. 2
- C. 4
- D. 6 Discuss
- 3. A sum of Rs. 1360 has been divided among A, B and C such that A gets ⅔ of what B gets and B gets ¼ of what C gets. B's share is:
Options- A. Rs. 120
- B. Rs. 160
- C. Rs. 240
- D. Rs. 300 Discuss
- 4. The price of 2 sarees and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay?
Options- A. Rs. 1200
- B. Rs. 2400
- C. Rs. 4800
- D. Cannot be determined
- E. None of these Discuss
- 5. To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two-fifth of its present?
Options- A. 10
- B. 35
- C. 62.5
- D. Cannot be determined
- E. None of these Discuss
- 6. If m and n are whole numbers such that mn = 121, the value of (m - 1)n + 1 is:
Options- A. 1
- B. 10
- C. 121
- D. 1000 Discuss
- 7. Given that 100.48 = x, 100.70 = y and xz = y2, then the value of z is close to:
Options- A. 1.45
- B. 1.88
- C. 2.9
- D. 3.7 Discuss
- 8.
If ❨ a ❩ x - 1 = ❨ b ❩ x - 3 , then the value of x is: b a
Options- A. 1⁄2
- B. 1
- C. 2
- D. 7⁄2 Discuss
- 9.
(243)n/5 x 32n + 1 =? 9n x 3n - 1
Options- A. 1
- B. 2
- C. 9
- D. 3n Discuss
- 10.
1 + 1 =? 1 + a(n - m) 1 + a(m - n)
Options- A. 0
- B. 11⁄2
- C. 1
- D. am + n Discuss
Surds and Indices problems
Search Results
Correct Answer: 13
Explanation:
Let (25) 7.5 x (5) 2.5 ÷ (125) 1.5 = 5 x
| Then, | (52)7.5 x (5)2.5 | = 5x |
| (53)1.5 |
| ⟹ | 5(2 x 7.5) x 52.5 | = 5x |
| 5(3 x 1.5) |
| ⟹ | 515 x 52.5 | = 5x |
| 54.5 |
⟹ 5x = 5(15 + 2.5 - 4.5)
⟹ 5x = 513
∴ x = 13.
Correct Answer: 4
Explanation:
3 x - y = 27 = 3 3 ⟺ x - y = 3 ....(i)
3x + y = 243 = 35 ⟺ x + y = 5 ....(ii)
On solving (i) and (ii), we get x = 4.
Correct Answer: Rs. 240
Explanation:
Let C's share = Rs. x
| Then, B's share = Rs. | x | , A's share = Rs. | ❨ | 2 | x | x | ❩ | = Rs. | x |
| 4 | 3 | 4 | 6 |
| ∴ | x | + | x | + x = 1360 |
| 6 | 4 |
| ⟹ | 17x | = 1360 |
| 12 |
| ⟹ x = | 1360 x 12 | = Rs. 960 |
| 17 |
| Hence, B's share = Rs. | ❨ | 960 | ❩ | = Rs. 240. |
| 4 |
Correct Answer: Rs. 2400
Explanation:
Let the price of a saree and a shirt be Rs. x and Rs. y respectively.
Then, 2x + 4y = 1600 .... (i)
and x + 6y = 1600 .... (ii)
Divide equation (i) by 2, we get the below equation.
=> x + 2y = 800. --- (iii)
Now subtract (iii) from (ii)
x + 6y = 1600 (-)
x + 2y = 800
----------------
4y = 800
----------------
Therefore, y = 200.
Now apply value of y in (iii)
=> x + 2 x 200 = 800
=> x + 400 = 800
Therefore x = 400
Solving (i) and (ii) we get x = 400, y = 200.
∴ Cost of 12 shirts = Rs. (12 x 200) = Rs. 2400.
Correct Answer: 62.5
Explanation:
Let the capacity of 1 bucket = x
Then, the capacity of tank = 25x.
| New capacity of bucket = | 2 | x |
| 5 |
| ∴ Required number of buckets = | 25x |
| (2x/5) |
| = | ❨ 25x | x | 5 | ❩ |
| 2x |
| = | 125 |
| 2 |
= 62.5
Correct Answer: 1000
Explanation:
We know that 11 2 = 121.
Putting m = 11 and n = 2, we get:
(m - 1)n + 1 = (11 - 1)(2 + 1) = 103 = 1000.
Correct Answer: 2.9
Explanation:
x z = y 2 ⟺ 10 (0.48z) = 10 (2 x 0.70) = 10 1.40
⟹ 0.48z = 1.40
| ⟹ z = | 140 | = | 35 | = 2.9 (approx.) |
| 48 | 12 |
Correct Answer: 2
Explanation:
| Given ❨ | a | ❩ | x - 1 | = | ❨ | b | ❩ | x - 3 |
| b | a |
| ⟹ | ❨ | a | ❩ | x - 1 | = | ❨ | a | ❩ | -(x - 3) | = | ❨ | a | ❩ | (3 - x) |
| b | b | b |
⟹ x - 1 = 3 - x
⟹ 2x = 4
⟹ x = 2.
Correct Answer: 9
Explanation:
| Given Expression |
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Correct Answer: 1
Explanation:
| 1 | + | 1 | = |
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| 1 + a(n - m) | 1 + a(m - n) |
| = | am | + | an |
| (am + an) | (am + an) |
| = | (am + an) |
| (am + an) |
= 1.
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