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- Question
In the question given below, two equations are provided. Solve the equations and establish the relationship between x and y I. 2x2-13x-189=0 II. 2y2-3y-189=0
Options- A. x>y
- B. x?y
- C. x
- D. x?y
- Correct Answer
ExplanationI. 2x2 - 13x - 189 = 0 2x2 - 27x + 14x - 189 = 0 x(2x - 27) + 7(2x - 27) = 0 x = -7, 27/2
II. 2y2 - 3y - 189 = 0 2y2 - 21y + 18y - 189 = 0 y(2y - 21) + 9(2y - 21) = 0 y = -9, 21/2
When x, as well as y, have both positive and negative values then no relationship can be established between them because if we consider x to be positive then the negative value of y will be lesser than x. If we consider x to be negative then positive value of y will be greater than x.
Simplification problems
Search Results
- 1. What should come in place of question mark (?) in the following question? 65% × 700 + ?196 ? 9 × 3 = ?
Options- A. 522
- B. 442
- C. 402
- D. 362 Discuss
Correct Answer: 442
Explanation:
As per the BODMAS rule, Addition and subtraction can be treated on same priority (from left to right) when they are in consecutive order.
65% × 700 + 14 - 9 × 3 65 × (700/100) + 14 - 27 455 + 14 - 27 = 442
- 2. What should come in place of question mark (?) in the following question? 41% of 600 - 250 = ? - 77% of 900
Options- A. 889
- B. 589
- C. 789
- D. 689 Discuss
Correct Answer: 689
Explanation:
41% of 600 - 250 = ? - 77% of 900
? 246 - 250 = ? - 693
? 246 -250 + 693 = ?
? ? = 689
- 3. What should come in place of question mark (?) in the following question? 12.5 × 3.2 × 8.8 = ?
Options- A. 358
- B. 355
- C. 354
- D. 356 Discuss
Correct Answer:
Explanation:
12.5 × 3.2 × 8.8 = 352
- 4. What should come in place of question mark (?) in the following question? 52000 ÷ 40 ÷ 65 × 30 = ? - ?400
Options- A. 580
- B. 620
- C. 720
- D. 780 Discuss
Correct Answer: 620
Explanation:
52000 ÷ 40 ÷ 65 × 30 = ? - ?400
(52000 ÷ 40) ÷ 65 × 30 = ? - 20
(1300 ÷ 65) × 30 = ? - 20
20 × 30 = ? - 20
600 = ? - 20
? = 620
- 5. If 2x + 2(4 + 3x) < 2 + 3x > 2x + x/2; then x can take which of the following values?
Options- A. -3
- B. 1
- C. 0
- D. -1 Discuss
Correct Answer: -3
- 6. In each of the following questions two equations I and II are given. Solve both the equations and give answer: I. x2+2x-195=0II. y2+30y+225=0
Options- A. x = y or relation can?t be established between x and y
- B. x > y
- C. x < y
- D. x ? y Discuss
Correct Answer: x ? y
Explanation:
I. x2 + 2x - 195 = 0 = (x+15) (x-13) => x = -15, 13
II. y2 + 30y + 225 = 0 = (y+15) (y+15) => y = -15, -15
So x ? y
- 7. In each of these questions, two equations (I) and (II) are given. I. 2x2+19x+42 = 0II. 4y2+43y+30 = 0
Options- A. x > y
- B. x < y
- C. x ? y
- D. x ? y Discuss
Correct Answer:
Explanation:
I. 2x2 + 19x + 42 = 0
2x2 + 12x + 7x + 42 = 0
2x (x+6) + 7(x +6) = 0
(2x+7) (x+6) = 0 x = -7/2, -6 I
I. 4y2 + 43y + 30 = 0
4y2 +40y + 3y + 30 = 0
4y(y + 10) + 3(y + 10) (4y + 3)(y + 10) = 0
y = -3/4, -10
So answer is no relation.
- 8. 3x2-14x+16=05y2-16y+12=0
Options- A. x > y
- B. x < y
- C. x=y or relation cannot be established between x and y
- D. x ? y Discuss
Correct Answer: x=y or relation cannot be established between x and y
Explanation:
3x2 ? 14x + 16=0
3x2 ?6x ? 8x + 16=0
3x (x-2) ? 8 (x-2)
(3x-8) (x-2)=0
x=8/3 or 2
5y2 ? 16y + 12=0
5y2 ? 10y ? 6y + 12=0
5y (y-2) ? 6 (y-2)=0
(5y-6) (y-2)=0
y=6/5 or 2
Can't be determined.
- 9. In the question, two equations I and II are given. You have to solve both the equations and give answer x2-11x+28=0y2-18y+81=0
Options- A. x > y
- B. x < y
- C. x=y, or relation cannot be established between x and y
- D. x ? y Discuss
Correct Answer: x < y
Explanation:
x2 ? 11x + 28=0
x2 ? 7x ? 4x + 28=0
x (x-7) ? 4 (x-7)=0
(x-4) (x-7)=0 x=4, 7
y2 ? 18y + 81=0
y2 ?9y ? 9y + 81=0
y (y-9) ? 9 (y-9)=0
(y-9) (y-9)=0 y=9, 9
So, x<y.
- 10. What should come in place of question mark (?) in the following question? 115 ÷ 5 + 12 × 6 = ? + 64 ÷ 4 - 35
Options- A. 95
- B. 136
- C. 102
- D. 74 Discuss
Correct Answer:
Explanation:
As per the BODMAS rule, the priority in which the operations should be done is:
Priority wise operations Symbol B-Bracket () O-of of D-Division /,÷ M-Multiplication *,x A-Addition + S-Subtraction - Note: Addition and subtraction can be treated on same priority (from left to right) when they are in consecutive order.
(115/5) + 12 × 6 = ? + (64/4) ? 35 23 + 72 = ? + 16 ? 35 95 = ? - 19 95+19 = ? ? = 114
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