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1
Q:

For any two real numbers a and b.

a-b2+b-a2 is

A) always zero B) never zero
C) positive only if a ≠ b D) positive if an only if a > b

Answer:   C) positive only if a ≠ b



Explanation:
Subject: Quantitative Aptitude - Arithmetic Ability
Exam Prep: Bank Exams
Related Questions
Q:

Train A, travelling at 84 kmph, overtook train B, traveling in the same direction, in 10 seconds. If train B had been traveling at twice its speed, then train A would have taken 22.5 seconds to overtake it. Find the length of train B, given that it is half the length of train A.

A) 180 m B) 100 m
C) 200 m D) 150 m
 
Answer & Explanation Answer:

Explanation:

Let speed of train B be x m/s And length of train B be y m
Then length of train A is 2y m
Speed of train A = 84 × 5/18 = 210/9 m/s = 70/3 m/s
A.T.Q, (2y+y)/10 = 70/3 − x .............(i)
and (2y+y)/ 22.5 = 70/3 − 2x ................(ii)
solving (i) and (ii), y = 50 m

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Filed Under: Quantitative Aptitude - Arithmetic Ability
Exam Prep: Bank Exams , GATE

0 3324
Q:

A solid sphere of radius 6 cm is melted and re-casted into a hollow cylinder of uniform thickness. If the external radius of the base of the cylinder is 5 cm and its height is 32 cm, find the uniform thickness of the cylinder ?

A) 3 cm B) 1.5 cm
C) 1 cm D) 2.5 cm
 
Answer & Explanation Answer: C) 1 cm

Explanation:

Let, inner radius of cylinder be ‘x’ cm.
4/3 π(6)3 = π × 32 (52 − x2)

or, (4 × 6 × 6 × 6) / (3 × 32) = 25 − x2 or, x2 = 25 − 9
or, x = 4 cm
Hence, thickness = 5 – 4 = 1 cm.

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Exam Prep: Bank Exams , GATE

0 1033
Q:

X and Y entered into partnership with Rs. 700 and Rs. 600 respectively. After another 3 months, X withdrew two- sevenths of his stock but after 3 months, he puts back three-fifths of what he had withdrawn. The total profit at the end of the year is Rs. 726. How much of this should X receive?

A) Rs. 336 B) Rs. 366
C) Rs. 633 D) Rs. 663
 
Answer & Explanation Answer: B) Rs. 366

Explanation:

Profit ratio X & Y = (700 × 3) + (700 × 5/7× 3) + (700× 5/7 + 200 × 3/5 )× 6 : 600 ×12
X:Y= 7320 : 7200= 183:180
∴ X’s share from profit = 183 × 726/(183+180) = Rs. 366.

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Exam Prep: Bank Exams , GATE

1 4460
Q:

Cost price of a pen is 50 Rs. and that of notebook is 140 Rs. If pen is sold at 200% profit, then to purchase 10 such note books how many pens are required to sell if only profit money is used to buy notebooks?

A) 14 B) 18
C) 15 D) 20
 
Answer & Explanation Answer: A) 14

Explanation:

C.P. of 10 note books ⇒ 140 × 10 = 1400 Rs.
Profit on selling one pen ⇒ 50×200/100 = Rs 100
Number of pen required ⇒ 1400/100 = 14

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0 1602
Q:

Length of two trains are 150 m and 200 m respectively and the ratio (shorter: longer) of their speed is 2 : 5. If they cross each other in opposite direction in 15 second then in what time faster train will overtake the slower train.

A) 20 seconds B) 25 seconds
C) 32 seconds D) 35 seconds
 
Answer & Explanation Answer: D) 35 seconds

Explanation:

Let speed of slower train = 2x
⇒ speed of faster train = 5x
ATQ, (150 + 200)/(2x + 5x) = 15
x = 10/3
Time required=350/[50/3–20/3]= 35 seconds

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0 1403
Q:

If length of a rectangle is decreased by 6 cm we get a square and the area of square formed is 252 cm2 less than the area of square formed when breadth of the original rectangle is increased by 6 cm. Find the perimeter of the rectangle.

A) 66 cm B) 88 cm
C) 80 cm D) 72 cm
 
Answer & Explanation Answer:

Explanation:

Let length and breadth of rectangle be L cm
and B cm respectively So, ATQ
Area1= (L-6)×B
But this is square, so L-6=B
Area1= (L-6) × (L-6)
Case 2, Area2= L × (B+6),
L=B+6
So, Area2= L × L,
Given, Area2-Area1= 252(L)2-(L-6)2=252
Solving this, L= 24
B= 18
Perimeter= 2(L+B)= 2(24+18)= 84 cm

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Exam Prep: Bank Exams , GATE

2 2465
Q:

Breadth of a rectangle is equal to the diagonal of the square whose side is 2.5√2 cm. Ratio between length and breadth of rectangle is 3 : 1. Find the area of the rectangle (in cm2).

A) 75 B) 90
C) 85 D) 80
 
Answer & Explanation Answer: A) 75

Explanation:

Diagonal of Square = Side √2= 2.5√2 × √2= 5 cm
Breadth = 5 cm
Length of rectangle = 5 × 3 = 15 cm
Area of rectangle = 15 × 5 = 75 cm2

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0 1121
Q:

A and B entered into a partnership with Rs.800 and Rs.1600 respectively. From 9th months onward they each decided to invest Rs.100 more on starting of each month. If total annual profit is Rs.7700 then find the profit share of A.

A) Rs.2550 B) Rs.3200
C) Rs.2650 D) Rs.2450
 
Answer & Explanation Answer: C) Rs.2650

Explanation:

A : B = (800 × 8+ 900+ 1000+ 1100+ 1200): (1600 × 8+ 1700+ 1800+ 1900+ 2000)
A : B = 53 : 101
Profit of A ⇒ 7700 ×53/154 = 2650 Rs.

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Exam Prep: Bank Exams , GATE

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