if X < Y

if X > Y

if X ≥ Y

if X ≤ Y

or no relation can be established

**6X**^{2}+ 31X + 35 = 0

2Y^{2}+ 3Y + 1 = 0Answer : Option D.

6X^{2}+ 31X + 35 = 0

Factorize 6X^{2}+ 21X +10X +35=0

So we get factors of X = -7/2 and -5/3

2Y^{2}+ 3Y + 1 = 0

After factorize we get

Y = -1 and -1/2

So conclusion D follows**2X**^{2}- (4 + 13) X + 2 13 = 0

10Y^{2}- (18 + 513) Y + 9 13 = 0Answer : Option D.2X^{2 }- (4 + √13) X + 2 √13 = 0After factorizing we get2X - √13X - 4 √13X+ 2 √13 = 0X = 2 and √13/210Y^{2 }- (18 + 5 √13) Y + 9 √13 = 0Y = √13/2 and 9/2Hence conclusion D follows**2X**^{2}+ 9X + 10 = 0

4Y^{2}+ 28Y + 45 = 0Answer : Option C.2X^{2}+ 9X + 10 = 0Factorizing2X^{2}+ 5X +4X +10=0We get X = -5/2 and -24Y^{2}+ 28Y + 45 = 0Factorizing we get4Y^{2}+ 18Y +10Y +45 = 0Y= -9/2 and -5/2Hence conclusion C follows**15X**^{2}- 11X - 12 = 0 20Y^{2}- 49Y + 30 = 0Answer : Option E.15X^{2 }- 11X - 12 = 0After factorizing we get15X^{2 }- 20X+9X - 12 = 0We get X=4/3 and -3/520Y^{2}- 49Y + 30 = 0After factorizing we get20Y^{2}- 25Y-24Y + 30 = 0We get Y = 5/4 and 6/5Hence conclusion E follows.**A and B are partners in a business. They invest in the ratio 5:6, at the end of 8 months A withdraws. If they receive profits in the ratio of 5 : 9, find how long B's investment was used?**- 12 months
- 10 months
- 15 months
- 14 months
- 18 months

Answer : Option A.

Ratio of profit is always distributed in the ratio of their investment and time.

5unit × 8 months:6 units × B’s months = 5:9

So B’s investment time = 12 monthsInfogain Preparation Links- Sample Aptitude Questions of Infogain
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**There are 3 red balls, 4 blue balls and 5 white balls. 2 balls are chosen randomly. Find probability that 1 is red and the other is white.**- 5/22
- 5/23
- 7/22
- 4/9
- None of These

Answer : Option E.

There are 3 red balls, 4 blue balls and 5 white balls. 2 balls are chosen randomly.

probability that 1 is red and the other is white = 3/12× 5/11 = 5/44**According to a new plan rolled out by H1SP Bank, the rate of simple interest on a sum of money is 8% p.a. for the first two years, 10% p.a. for the next three years and 6% p.a. for the period beyond the first five years. Simple interest accrued on a sum for a period of eight years is Rs. 12,800. Find the sum.**- Rs. 24,000
- Rs. 16,000
- Rs. 15,000
- Rs. 13,500
- None of These

Answer : Option E.

Let the sum of money be x.

So interest in first two years = 8×2 = 16% of x

Interest in next three years = 10×3 =30% of x

Interest in next five years = 6×3 = 18% of x

Total interest = 64% of x = Rs 12,800

We get x = Rs 20,000**Three Science classes A, B and C take a Life Science test. The average score of students of class A is 83. The average score of students class B is 76. The average score of class C is 85. The average score of class A and 8 is 79 and average score of class B and C is 81. Then the average score. Of classes A, B and C is**- 80
- 80.5
- 81
- None of these

Answer : Option D.

**A hemispherical bowl of internal diameter 54 cm contains a liquid. The liquid is to be filled in cylindrical bottles of radius 3 cm and height 9 cm. How many bottles are required to empty the bowl?**- 221
- 343
- 81
- 243
- None of these

Answer : Option E.

Area of a hemispherical bowl = 2/3 ×π ×r^{3}

Area of a cylinder = πr^{2}h

Area of a cylinder = n × Area of a hemispherical bowl

2/3 ×π ×27^{3}= n ×π×3^{2}×9

we get n = 162**Solve : (638 + 9709 - 216) ÷ 26 = ?**- 275
- 365
- 420
- 300
- 390

Answer : Option E.

(638 + 9709 - 216) ÷ 26 = 10131/26 = 389.65

Approx 290