Simplification problems
- 1. A 120 m long rope is cut into 3 equal parts. What is the length of each part?
Options- A. 40 m
- B. 30 m
- C. 50 m
- D. 25 m Discuss
Correct Answer: 40 m
Explanation:
Required length = 120/3 = 40 m
- 2. A number when multiplied by five times of itself give the value equal to 1445. What is the number?
Options- A. 18
- B. 15
- C. 19
- D. 17 Discuss
Correct Answer: 17
Explanation:
Let the number = a
According to the question,
a x 5a = 1445
5a2 = 1445
? a2= 1445/5 =289
? a= ?289 = 17
- 3. A board 80 inches long is divided into 4 equal parts. What is the length of each part?
Options- A. 20 inches
- B. 25 inches
- C. 15 inches
- D. 18 inches Discuss
Correct Answer: 20 inches
Explanation:
Required length = 80/4 = 20 inches
- 4. If a * b = a + b + a/b, Then the value of 12 * 4 is
Options- A. 48
- B. 19
- C. 20
- D. 21 Discuss
Correct Answer: 19
Explanation:
Since a * b = a + b + a/b
? 12 * 4 = 12 + 4 + 12/4
= 12 + 4 + 3 = 19
- 5. [137 x 137 + 137 x 133 + 133 x 133] / [137 x 137 x 137 - 133 x 133 x 133] =?
Options- A. 4
- B. 270
- C. 1/4
- D. 1/270 Discuss
Correct Answer: 1/4
Explanation:
Given exp. = [ a2 + ab + b2 ] / [a3 - b3] where a = 137, b = 133
= 1/(a - b)
= 1/(137- 133)
=1/4
- 6. (117 x 117 x 117 - 98 x 98 x 98) / (117 x 117 + 117 x 98 + 98 x 98) =?
Options- A. 215
- B. 311
- C. 19
- D. 29 Discuss
Correct Answer: 19
Explanation:
Given expression = (a3 - b3) / (a2 + ab + b2), where a=117, b =98
= [(a-b)(a2 + ab + b2)] / (a2+ab+b2)
=(a-b)
=117 - 98
= 19.
- 7. (343 x 343 x 343 + 257 x 257 x 257 ) / (343 x 343 - 343 x 257 + 257 + 257) =?
Options- A. 8600
- B. 800
- C. 600
- D. 2600 Discuss
Correct Answer: 600
Explanation:
Given Exp. = ( a3 + b3 ) / ( a2 - ab + b2 ), where a =3 42, b = 257
= [(a + b )(a2 - ab +b2)] / (a2 - ab + b2)
= a + b
= 343+257
= 600.
- 8. 3 ÷ [(8 - 5) ÷ {(4 - 2) ÷ (2 + 8/13)}] =?
Options- A. 13/17
- B. 68/13
- C. 17/13
- D. 13/68 Discuss
Correct Answer: 13/17
Explanation:
Given expression = 3 ÷ [(8 - 5) ÷ {(4 - 2) ÷ (2 + 8/13)}]
= 3 ÷ [3 ÷ { 2 ÷ 34/13}]
= 3 ÷ [3 ÷ { 2 x 13/34}]
= 3 ÷ [ 3 x 17/13]
= 3 x 13/51
= 13/17
- 9. {7 1/ 2 + 1/2 ÷ 1/2 of 1/4 - 2/5 x 2 1/ 3 ÷ 1 7/ 8 of (1 2/ 5 - 1 1/ 3) } =?
Options- A. 31/5
- B. 21/24
- C. 41/30
- D. None of these Discuss
Correct Answer: 41/30
Explanation:
Given expression = 15/2 + 1/2 ÷ 1/8 - 2/5 x 7/3 ÷ 15/8 x (7/5 - 4/3)
= 15/2 + 4 - 2/5 x 7/3 ÷ 15/8 x 1/15
= 15/2 + 4 - 2/5 x 7/3 ÷ 1/8
= 15/2 + 4 - 2/5 x 7/3 x 8/1
= 15/2 + 4 - 112/15
= 23/2 - 112/15
= 121/30
= 41/30
- 10. 3/4 ÷ 2 1/ 4 of 2/3 - [(1/2 - 1/3) / (1/2 + 1/3) x 3 1/ 3 + 5/6 =?
Options- A. 7/18
- B. 49/54
- C. 2/3
- D. 1/6 Discuss
Correct Answer: 2/3
Explanation:
Given expression = 3/4 ÷ 9/4 of 2/3 - [(1/6) / (5/6)] x 10/3 + 5/6
= 3/4 x 2/3 - 1/6 x 6/5 x 10/3 + 5/6
= 1/2 - 2/3 + 5/6
= (3 - 4 + 5) / 6
= 4 / 6
= 2 /3
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