Quantitative Aptitude - Arithmetic Ability Questions

Q:

If p and q are the roots of the equation x2 –15x + r = 0 and p –q = 1, then what is the value of r ?

A) 55 B) 56
C) 60 D) 64
 
Answer & Explanation Answer: B) 56

Explanation:

In the below equation,

x2–15x + r = 0

sum of roots = p + q = -(-15)/1 = 15 (sum of roots for equation ax2+ bx + c is -b/a)

product of roots = pq = r/1 = r     (product of roots for equation ax2+ bx + c is c/a)

given p –q = 1

also we know that p+q = 15

subtracting the squares of both

(p+q)2 + (p-q)2 = 15^2–1

p2 + q2 + 2pq –p2 –q2 +2pq = 225 -1

4pq = 224

4r = 224

r = 56

 

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Q:

What is the value of sin225°+ sin265°?

A) 0 B) 1
C) 2 D) 4
 
Answer & Explanation Answer: B) 1

Explanation:
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Q:

A student multiplied a number by 4/7 instead of 7/4. What is the percentage error in the calculation?

A) 206.25 percent B) 67.35 percent
C) 33.67 percent D) 103.13 percent
 
Answer & Explanation Answer: B) 67.35 percent

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Q:

P and Q can do a project in 150 and 100 days respectively. In how many days can they complete 60% of the project if they work together?

A) 12 days B) 72 days
C) 42 days D) 36 days
 
Answer & Explanation Answer: D) 36 days

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Q:

In a class of 50 students there are 22 girls who scored an average of 35 marks in the test. What is the average marks of the boys if the class average is 42 marks?

A) 50 B) 52.5
C) 47.5 D) 55
 
Answer & Explanation Answer: C) 47.5

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Q:

After deducting 60% from a certain number and then deducting 15% from the remainder, 1428 is left. What was the initial number?

A) 4200 B) 3962
C) 4150 D) 4300
 
Answer & Explanation Answer: A) 4200

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Q:

2 sec2A is equal to

A) (1 - tanA)2 - (1 + tanA)2 B) √[(1 - tanA)2 + (1 + tanA)2 ]
C) √[(1 - tanA)2 - (1 + tanA)2] D) (1 - tanA)2 + (1 + tanA)2
 
Answer & Explanation Answer: D) (1 - tanA)2 + (1 + tanA)2

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Q:

Rithika had Rs 8000. She invested some of it in savings scheme P and the rest of the money in savings scheme Q. She invested for 3 years in savings scheme P and for 2 years in savings scheme Q. savings scheme P offers SI at a rate of 20% pa while savings scheme Q compounded annually at the rate of 30% pa. The interest received from savings scheme P is 930 more than the interest received from savings scheme Q. If Rs 1500 is debited from the invested amount of savings scheme P then find the difference between the amount invested by Rithika in savings scheme P & savings scheme Q.

A) Rs 200 B) Rs 300
C) Rs 400 D) Rs 500
 
Answer & Explanation Answer: D) Rs 500

Explanation:
Amount invested in savings scheme P= Rs X

Amount invested in savings scheme Q= Rs (8000-X)

Compounding 30 % for 2 years , rate

30+30+ (30*30)/100= 69 %

60 % of X-69 % of (8000-X)=930

X= 5000

In savings savings scheme Q = 8000-5000=3000

5000 - 1500 = 3500

Difference =3500-3000=Rs 500

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