Order of Magnitude problems
- 1. If x = (?2 + 1)/(?2 - 1) and y = (?2 - 1)/(?2 + 1), then 3 (xy + 1) is euqal to?
Options- A. x + y
- B. x - y
- C. 2 (x + y)
- D. None of above Discuss
Correct Answer: x + y
Explanation:
xy = [(?2 + 1)/(?2 - 1)] x [(?2 - 1)/(?2 + 1)] = 1
? 3(xy + 1) = 3(1 + 1) = 6
Now, x + y = [(?2 + 1)/(?2 - 1)] + [(?2 - 1)/(?2 + 1)]
= (?2 + 1)2 + (?2 - 1)2 / (?2 - 1) (?2 + 1)
= (2 + 1 +2?2) + (2 + 1 - 2?2) / (2 - 1) = 6
? 3(xy + 1) = x + y
- 2. The least perfect square which is divisible by each of 21, 36 and 66 is equal to?
Options- A. 213444
- B. 223444
- C. 213442
- D. 223445 Discuss
Correct Answer: 213444
Explanation:
Ans. LCM of 21, 36 and 66 = 2772
Now, 2772 = 2 x 2 x 3 x 3 x 7 x 11
To make it a perfect square, it must be multiplied by 77 [for (7 x 11)].
? Required number = 22 x 32 x 72 x 112 = 213444
- 3. In an opera house, there are 7777 chairs to be placed but the organizer of the event arranged all the chair in such a way that these were as many columns as there were rows, so he had to remove minimum n chairs from the total 7777 chairs. The minimum value of n is?
Options- A. 121
- B. 44
- C. 33
- D. 25 Discuss
Correct Answer: 33
Explanation:
7777 - N must be a perfect square.
Now, using the option, we find that N = 33
7777 - 33 = 7744 is perfect square.
- 4. In a bangel shop, the shopkeeper displays the bangels in the form of a square, then he is left with 38 bangles with him. If he wants to increse the size of square by one unit each side of the square, he found that 25 bangles fall short of in completing the square. The actual number of bangles which he had with him in the shop was?
Options- A. 1690
- B. 999
- C. 538
- D. Cannot be determined Discuss
Correct Answer: 999
Explanation:
Let the number of bangles be x. Then, x - 38 is a perfect square and x + 25 is a perfect square.
Now, using the option, we find that x = 999
999 - 38 = 961 is a perfect square.
999 + 25 = 1024 is a perfect square
- 5. The sum of two number, when multiplied with each of the number separately, then the results of these multiplication are 2418 and 3666, respectively. Find the difference between the numbers.?
Options- A. 16
- B. 21
- C. 19
- D. 23 Discuss
Correct Answer: 16
Explanation:
Let the number be x and y.
Now, according to the question,
x(x + y) = 2418 .....(i)
and y(x + y) = 3666 .....(ii)
On adding Eqs. (i) and (ii), we get
x2 + xy + yx + y2 = 6084
? x2 + 2xy + y2 = 6084
? (x + y)2 = 6084
? x + y = ?6084 = 78
On subtracting Eq. (ii) from Eq. (i), we get
x2 + xy - yx - y2 = -1248
? x2 - y2 = -1248
? (x + y) (x - y) = -1248
? 78(x - y) = -1248
? x - y = - 1248 / 78 = -16
? (y - x) = 16
- 6. One-fourth of a herd of camels was seen in the forest. Twice the square root of the herd had gone to mountains and the remaining 15 camels were seen on the bank of a river. Find the total number of camels.
Options- A. 32
- B. 34
- C. 35
- D. 36 Discuss
Correct Answer: 36
Explanation:
Let the total number of camels be x.
Then, acording to the question,
x/4 + 2?x + 15 = x
? x - x/4 - 2 ?x = 15
? 3x - 8?x - 60 = 0
? ?x = [8 ± ?64 + 720] / 6
= (8 ± 28) / 6
? x = 36
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