Simplification problems
- 1. 5/6 ÷ 6/7 x? - 8/9 ÷ 1 3/ 5 + 3/4 x 3 1/ 3 = 2 7/ 9
Options- A. 7/6
- B. 6/7
- C. 1
- D. None of these Discuss
Correct Answer: 6/7
Explanation:
Let 5/6 ÷ 6/7 x N - 8/9 ÷ 8/5 + 3/4 x 10/3 = 25 / 9
Then, 5/6 x 7/6 x N - 8/9 x 5/8 + 5/2 = 25/9
? 35N / 36 = 25/9 + 5/9 - 5/2
? 35N / 36 = (50 + 10 - 45) / 18 = 5/6
? N = (5/6 x 36/35) = 6/7
- 2. 15 2/ 3 x 3 1/ 6 + 6 1/ 3 = 11 7/ 18 +?
Options- A. 395/9
- B. 1374/9
- C. 297/9
- D. None of these Discuss
Correct Answer: None of these
Explanation:
Let 47/3 x 19/6 + 19/3 = 205 / 18 + N
Then, N = 893/18 + 19/3 - 205/18
? N = 893 + 114 - 205 / 18
? N = 802 / 18 = 445/9
- 3. 7 1/ 2 - [ 2 1/ 4 ÷ { 1 1/ 4 - 1/2(1 1/ 2 - 1/3 - 1/6)}] is equal to?
Options- A. 2/9
- B. 1
- C. 41/2
- D. 177/288 Discuss
Correct Answer: 41/2
Explanation:
Given expression = 15/2 -[9/4 ÷ {5/4 - 1/2(3/2 - 1/3 - 1/6)}]
= 15/2 -[9/4 ÷ {5/4 - 1/2 x 1}]
= 15/2 -[9/4 ÷ {5/4 - 1/2}]
= 15/2 -[9/4 ÷ 3/4] = 15/2 - [9/4 x 4/3]
= (15/2 - 3)
= 9 / 2 = 41/2
- 4. 50 /? =? / 12 1/ 2
Options- A. 25/2
- B. 4/25
- C. 4
- D. 25 Discuss
Correct Answer: 25
Explanation:
Let 50 / N = N / (25/2)
? N2 = 50 x 25/2 = 625
? N = ?625 = 25
- 5. If x/y = 4/5, then the value of 4/7 + (2y - x)/(2y + x) is?
Options- A. 3/7
- B. 1
- C. 11/7
- D. 2 Discuss
Correct Answer: 1
Explanation:
Given Exp. = 4/7 + (2y - x)/(2y + x)
= 4/7 + [(2 - (x/y)] / [2 + (x/y)]
= 4/7 + [2 - 4/5] / [2 + 4/5]
= 4/7 + ( 6/5 x 5/14 )
= 4/7 + 3/7
= 1
- 6. If x/2y = 3/2, the value of (2x + y) / (x - 2y) equals?
Options- A. 1/7
- B. 7
- C. 7.1
- D. None of these Discuss
Correct Answer: 7
Explanation:
Given expression = 2x + y / x - 2y
Dividing Num and Denom by y we get.
= [2(x/y) + 1] / [(x/y) - 2] = (2 x 3 + 1) / (3 - 2) = 7/1 = 7
[ ? x/2y = 3 / 2 ?x/y = (3 / 2 x 2) = 3 ]
- 7. (885 x 885 x 885 + 115 x 115 x 115) / (885 x 885 + 115 x 115 - 885 x 115) is equal to?
Options- A. 115
- B. 770
- C. 885
- D. 1000 Discuss
Correct Answer: 1000
Explanation:
Given expression = (a3 + b3) / (a2 + b2 - ab)
= (a + b)(a2 + b2 - ab) / (a2 + b2 - ab)
= (a + b) = (885 + 115)
= 1000
- 8. 4 2/ 17 ÷ 1 2/ 5 x 2 2/ 33 =?
Options- A. 42/13
- B. 62/33
- C. 61/11
- D. 81/11 Discuss
Correct Answer: 62/33
Explanation:
Give expression
= 70/17 ÷ 7/5 x 68/33
= 70/17 x 5/7 x 68/33
= 200/33
= 62/33
- 9. If a/b = 1/3, then (3a + 2b) / (3a - 2b) is equal to?
Options- A. 3
- B. -3
- C. -5
- D. -1 Discuss
Correct Answer: -3
Explanation:
Given expression = (3a + 2b) / (3a - 2b)
= [3(a/b) + 2] / [3(a/b) - 2]
= [3 x 1/3 + 2] / [3 x 1/3 - 2]
= 3 / -1
=-3
- 10. When Simplified, the product (2 - 1/3) (2 - 3/5) (2 - 5/7) ... (2 - 999/1001) is equal to?
Options- A. 991/1001
- B. 1001/13
- C. 1003/3
- D. None of these Discuss
Correct Answer: 1003/3
Explanation:
Given expression = 5/3 x 7/5 x 9/7 x ... x 1003/1001
= 1003/3
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