RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Find the C.I. on a sum of Rs.1600 for 9 months at 20% per annum, interest being compounded quarterly?
A.Rs.7288
B.Rs.2542
C.Rs.2522
D.Rs.2625
Answer: C.Rs.2522
Explanation: A = 1600(21/20)3
= 2522
Answer: C
Question: Johnson completes a piece of work in 10 days, Vincent completes the same work in 40 days. If both of them work together, then the number of days required to complete the work is
A.7 days
B.8 days
C.9 days
D.10 days
Answer: B.8 days
Explanation: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 10 × 40/50 = 8 days.
B)
Question: A restaurant meal cost $35.50 and there was no tax. If the tip was more than 10 percent but less than 15 percent of the cost of the meal, then the total amount paid must have been between
A.$40 and $42
B.$39 and $41
C.$38 and $40
D.$37 and $39
Answer: B.$39 and $41
Explanation: The total amount for the meal was between 35.5*1.1=39.05 and 35.5*1.15=~41. Only option which covers all possible values of the meal is B.
Answer: B.
Question: When 30 per cent of a number is added to another number the second number increases by its 20 per cent. What is the ratio between the first and the second number?
A.3 : 2
B.2 : 3
C.2 : 5
D.Data inadequate
Answer: B.2 : 3
Explanation: 30% of I + II = II × 120⁄100
or, 3⁄10I = 2⁄10II ⇒ I : II = 2 : 3.
Answer B
Question: what is the probability of getting sum of 10 on rolling three dices?
A.28/216
B.27/216
C.29/216
D.26/216
Answer: B.27/216
Explanation: The no of ways to roll three dies is 6^3=216
The possibles of getting sum as 10 is
631=3!=6
622=3!/2!=3
541=3!=6
523=3!=6
442=3!/2!=3
433=3!/2!=3
Total possibles for getting sum as 10 is 27
The probabilty is 27/216
ANSWER:B
Question: The last digit of the number obtained by multiplying the numbers 41 x 42 x 43 x 44 x 45 x 46 x 47 x 48 x 49 will be ?
A.0
B.1
C.4
D.5
Answer: A.0
Explanation: Solution
Last digit will be multiplication of 1x2x3x4x5x6x7x8x9.
It includes 5 & 2 so, 5x2=10, 0 will be the last digit.
Correct Option: A
Question: A club wants to mix 20 pounds of candy worth $8.00 per pound with candy worth $5.00 per pound to reduce the cost of the mixture to $6.00 per pound. How many pounds of the $5.00 per pound candy should be used?
A.20
B.30
C.40
D.50
Answer: C.40
Explanation: Let number of pounds of 5$ candy to be used be w
6 = (20*8 + 5*w)/(20 +w)
=>120 + 6w = 160 + 5w
=> w = 40
Answer C
Question: The remainder when K=1+3+3^2+3^3+..........+3^200 is divided 13.
A.12
B.7
C.0
D.5
Answer: C.0
Explanation: K=1+3+3^2+3^3+..................+3^200
Is a Geometric progression having common ratio as '3' and number of terms as '201'.
Since Sum to n terms in GP = a(r^n-1)/(r-1)
where a=First term and r =common ration
Hence,
1*(3^201 -1 )/(3-1)
Rem of (3^201-1)/2 divided by 13
3^201 -1 /26
WKT, 3^3 = 27 = 26+1
{(26+1)^67 - 1}/26
{1-1}/26
=>0.C
Question: In a room filled with 5 people, 3 people have exactly 2 siblings in the room and 2 people have exactly 1 sibling in the room. If two individuals are selected from the room at random, what is the probability that those two individuals are NOT siblings?
A.2/3
B.2/5
C.3/5
D.3/10
Answer: C.3/5
Explanation: The 5 people consist of one set of 2 siblings and one set of 3 siblings.
The number of ways to choose 2 people is 5C2 = 10.
The number of ways to choose 2 from the first group of siblings is 2C2 = 1.
The number of ways to choose 2 from the second group of siblings is 3C2 = 3.
The number of ways to choose 2 people who are siblings is 3+1 = 4.
The number of ways to choose 2 people who are not siblings is 10-4=6.
P(the two people are not siblings) = 6/10 = 3/5
The answer is C.
Question: How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length?
A.82.1 sec
B.12.1 sec
C.16.1 sec
D.13.1 sec
Answer: B.12.1 sec
Explanation: Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 110 + 132 = 242 m.
Required time = 242/20 = 12.1 sec.
Answer:B
Question: A 180 meter long train crosses a man standing on the platform in 9 sec. What is the speed of the train?
A.72
B.108
C.1266
D.188
Answer: A.72
Explanation: S = 180/9 * 18/5 = 72 kmph
Answer: A
Question: If the annual interest on a principal is 8%, how many years before the amount is double?
A.11.3
B.12
C.12.5
D.10.2
Answer: C.12.5
Explanation: P = (P*8*R)/100
R = 12.5
Answer: C
Question: The first doughnut is priced at $1 and then if you purchase additional doughnuts as dozens then the price is $6/dozen. What is the total number of doughnuts purchased if you paid $24?
A.44
B.46
C.48
D.50
Answer: C.48
Explanation: $24 = 4 * $6
The number of doughnuts is 4*12 = 48
The answer is C.
Question: A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current?
A.1.7
B.1.5
C.1.3
D.1.2
Answer: B.1.5
Explanation: 72 --- 9 DS = 8
? ---- 1
45 ---- 9 US = 5
? ---- 1 S = ?
S = (8 - 5)/2 = 1.5
Answer: B
Question: A envelop weight 8.2 gm,if 800 of these envelop are sent with an advertisement mail. How much wieght?
A.6.56kg
B.6.8kg
C.6.7kg
D.6.9kg
Answer: A.6.56kg
Explanation: 800*8.2
6560.0gm
6.56kg
ANSWER:A
Question: A table is bought for Rs.400/- and sold at Rs.550/- find gain or loss percentage
A.l10%oss
B.30%gain
C.37.5%gain
D.10%loss
Answer: C.37.5%gain
Explanation: Formula = (Selling price ~ Cost price)/Cost price * 100
= (550 - 400)/400 = 37.5% gain
C
Question: A can finish a work in 18 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work?
A.7
B.6
C.5
D.4
Answer: B.6
Explanation: B's 10 day's work = (10*1/15) = 2/3.
Remaining work =	(1- (2/3))=1/3
Now, 1/18 work is done by A in 1 day.
A= 18* 1/3 = 6 DAYS
ANSWER:B
Question: The breadth of a rectangular hall is two-thirds of its length. If the area of the hall is 2400 sq metres, what is the length in metres?
A.120
B.80
C.60
D.40
Answer: C.60
Explanation: Let the length of the rectangular hall be ‘x’ m, then the breadth of the rectangular hall = 2x⁄3 m.
Area of hall = 2x⁄3 × x = 2x2⁄3
or, 2x2⁄3 = 2400 or x = 60 m
Answer C
Question: A man can row 4 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
A.5.98
B.3.98
C.3.54
D.3.87
Answer: C.3.54
Explanation: M = 4
S = 1.2
DS = 4.8
US = 2.8
x/4.8 + x/2.8 = 1
x = 1.77
D = 1.77* 2 = 3.54
Answer:C
Question: A,B,C can complete a piece of work in 25,5,10 days. Working together, they complete the same work in how many days?
A.2
B.4/5
C.50/17
D.10
Answer: C.50/17
Explanation: A+B+C 1day work = 1/25 + 1/5 + 1/10 = 17/50
A,B,C together will complete the job in 50/17 days
Answer is C
Question: In 100 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by:
A.20 m
B.25 m
C.22.5 m
D.9 m
Answer: A.20 m
Explanation: Distance covered by B in 9 sec. =	100/45 x 9	m = 20 m.
A beats B by 20 metres.
Answer: Option A
Question: A fort of 4000 soldiers has provisions for 100 days. After 20 days some of them left and the food was now enough for the same period of 100 days as before. How many of them left?
A.650
B.700
C.750
D.800
Answer: D.800
Explanation: 2000 ---- 50
4000 ---- 80
x ----- 100
x*100 = 4000*80
x=3200
4000
-------
800
Answer: D
Question: Girl and Boy together can complete a piece of work in 35 days while Girl alone can complete the same work in 60 days. Boy alone will be able to complete the same working in:
A.72
B.75
C.84
D.88
Answer: B.75
Explanation: Subtraction of fraction
ab−cd=ad−cbbd
Girl
and Boy finish one work with company = 35
days
(Girl+Boy)′
s one day’s work = 135
Girl alone finish the same work = 60
days
Girl′
s one day’s work = 160
B′
s one day’s work = (A+B)′s one day’s work - A′
s one day’s work
135−160=184
Hence B alone can complete the work in 84 days
Question: A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is:
A.15 hours
B.20 hours
C.25hours
D.28 hours
Answer: A.15 hours
Explanation: Let the first pipe alone can fill the tank in x hours
Then the second pipe can fill the tank in (x-5) hours
and the third pipe can fill the tank in (x-5)-4 = (x-9) hours
part filled by first pipe and second pipe together in 1 hr = part filled by third pipe in 1 hr
(1/x)+1/(x−5)=1/(x−9)
(x−5)(x−9)+x(x−9)=x(x−5)
x^2−14x+45+x^2−9x=x^2−5x
−14x+45+x^2−9x=−5x
x^2−18x+45=0
(x−15)(x−3)=0
x=15 or 3
We can not take the value of x = 3 because, (x-9) becomes negative which is not possible
because the third pipe can fill the tank in (x-9) hours
Hence, x = 15
Answer is A
Question: It costs a man 75 dollars to buy the things that he needs to make hotdogs. The city allows him to sell his hotdog somewhere near the city hall. However, the city hall charges him 1 dollar for each hotdog sold
Calculate the break even point if the price he charges for 1 hotdog is $1.50
A.140
B.150
C.160
D.170
Answer: B.150
Explanation: Let x be the number of hotdogs sold
Let C be the cost of buying and selling x hotdogs
Let R be the revenue made for selling x hotdogs
R = selling price of 1 hotdog × number of hotdogs sold
R = 1.50x
C = fixed cost + variable cost
variable cost = fee charged for 1 hotdog × number of hotdogs sold
variable cost = 1x
C = 75 + 1x
R = C
1.50x = 75 + 1x
1.50x - 1x = 75 + 1x - 1x
0.5x = 75
x = 150 since 0.5 × 150 = 75
The break even point is to sell 150 hotdogs.
Answer B
Question: In what time will a railway train 60 m long moving at the rate of 36 kmph pass a telegraph post on its way?
A.3
B.5
C.4
D.6
Answer: D.6
Explanation: T = 60/36 * 18/5 = 6 sec
Answer:D
Question: A contractor is engaged for 30days on the condition that he receives Rs.25 for each day he works &is fined Rs.7.50 for each day is absent. He gets Rs.490 in all. For how many days was he absent?
A.8
B.10
C.15
D.17
Answer: A.8
Explanation: 30 * 25 = 750
490
-----------
260
25 + 7.50 = 32.5
260/32.5 = 8
A
Question: {-10, -6, -5, -4, -2.5, -1, 0, 2.5, 4, 6, 7, 10}
A number is to be selected at random from the set above. What is the probability that the number selected will be a solution of the equation (x-5)(x+8)(2x-5) = 0?
A.1/12
B.1/6
C.1/4
D.1/3
Answer: A.1/12
Explanation: Roots of the equation (x-5)(x+10)(2x-5)=0 are x=5,x=-8 and x=5/2=2.5. So, one solutions present in our set of 12 distinct numbers, therefore P=1/12
Answer: A.
Question: Find the arithmetic mean L of all roots of the following equation- see an attachment.
A.2
B.1
C.0.5
D.-1/3
Answer: C.0.5
Explanation: arithmetic mean L your answer C and E are same, can you correct one of them please. thanks.C
Question: If in a game of 80, P can give 16 points to Q and R can give 20 points to P, then in a game of 150, how many points can R give to Q?
A.48
B.60
C.54
D.90
Answer: B.60
Explanation: Explanation:
When P scores 80, Q scores 64.
When R scores 80, P scores 60
Hence, when R scores 150, Q scores (60 * 64 * 150) / (80 * 80) = 90
Therefore, in a game of 150, R can give 60 points to Q.
ANSWER B
Question: Find: S.l. on Rs 3000 at 18% per annum for the period from 4th
A.118
B.105
C.108
D.110
Answer: C.108
Explanation: Explanation:
(24 + 31 + 18) days = 73 days = 1/5 year .
P = Rs 3000 and R = 18 % p.a.
S.I=(3000 *18 * 1/5)/100
ANSWER IS C
Question: In how much time will interest on Rs. 2300 at 4 1/2 percent p/a be Rs.310.50
A.5years
B.2years
C.4years
D.3 years
Answer: D.3 years
Explanation: 310 = (2300*T*9/2)/100
T = (310.50x100x2)/(300x9)= 3 years.
Answer: D
Question: What will be the fraction of 8%
A.1/20
B.1/50
C.1/75
D.2/25
Answer: D.2/25
Explanation: Explanation:
8*1/100 = 2/25.
Option D
Question: Two boys picked up 30 mangoes .In how many ways can they divide them if all mangoes be identical?
A.A)4^30
B.B)2^30
C.C)1^30
D.D)3^30
Answer: B.B)2^30
Explanation: Each Mango can be given to any one of the two people or in other words..30 mango can be divided into 2 ways...so all 30 can be divided in 2^30 ways
ANS:B
Question: Compound interest earned on a sum for the second and the third years are Rs.12500 and Rs.14000 respectively. Find the rate of interest?
A.18% p.a.
B.22% p.a.
C.20% p.a.
D.12% p.a.
Answer: D.12% p.a.
Explanation: Rs.14000 - 12500 = Rs.1500 is the interest on Rs.12500 for one year.
Rate of interest = (1500/12500) * 100 = 12% p.a
ANSWER:D
Question: A bag contains six white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color?
A.15/8
B.8/15
C.5/6
D.5/3
Answer: B.8/15
Explanation: Two balls can be picked from ten balls in 10Câ‚‚ ways.
We select one white ball and one red ball from five white balls and four red balls. This can be done âµ ways.
The required probability = (6 * 4) = 24/45 = 8/15
Answer: B
Question: Joe needs to paint all the airplane hangars at the airport, so he buys 360 gallons of paint to do the job. During the first week, he uses 1/4 of all the paint. During the second week, he uses 1/7 of the remaining paint. How many gallons of paint has Joe used?
A.18
B.128
C.175
D.216
Answer: B.128
Explanation: Total paint initially = 360 gallons
Paint used in the first week = (1/4)*360 = 90 gallons.
Remaning paint = 270 gallons
Paint used in the second week = (1/7)*270 = 38 gallons
Total paint used = 128 gallons.
Option B
Question: Let d > c > b > q. If c is twice as far from q as it is from d, and b is twice as far from c as it is from q, then (d - b)/(d - q) = ?
A.2/9
B.1/3
C.2/3
D.7/9
Answer: D.7/9
Explanation: Draw a number line and label with x and y. You would have:
Before calculating recognize it would be more effcient to express x or y in terms of the other. here 2x = 3y so x =3/2 y.
Now you can calculate d -b and d -a
d - b= x +2y = 7/2 y
d - q = x + 2x = 3x = 9/2y
Dividing both you get: 7/9
Answer D
Question: The ratio of two numbers is 2/3, and if a 1 is subtracted from the numerator and a 1 is added to the remainder the ratio becomes 1/2, then the numbers are.
A.6 and 9
B.6 and 10
C.6 and 8
D.6 and 7
Answer: A.6 and 9
Explanation: a:b=2:3 b=3/2a
a-1/b+1=1/2
solving this we get a=6 and b=9
ANSWER:A
Question: A jar full of whiskey contains 40% alcohol. A part of
this whiskey is replaced by another containing 19% alcohol
and now the percentage of alcohol was found to be 26%.
The quantity of whiskey replaced is?
A.2/3
B.1/3
C.1/4
D.1/2
Answer: A.2/3
Explanation: Strength of first jar 40% Strength of 2nd jar 19%
Mean Strength 26%
7 14
So,ratio of 1st and 2nd quantities =7:14 =1:2
Therefore required quantity replaced =2/3.
ANSWER A
Question: The ratio of the ages of Mini and Minakshi is 4 : 3. The sum of their ages is 21 years. The ratio of their ages after 8 years will be
A.2 : 3
B.20 : 17
C.5 : 4
D.3 : 5
Answer: B.20 : 17
Explanation: Let Mini’s age = 4x and Minakshi’s age = 3x
Then 4x + 3x = 21
x = 3
Mini’s age = 12 years
And Minakshi’s age = 9 years
Ratio of their ages after 8 years = (12 + 8) : (9 + 8) = 20 : 17
ANSWER:B
Question: A goods train runs at the speed of 72 km/hr and crosses a 290 m long platform in 26 sec. What is the length of the goods train?
A.278
B.166
C.151
D.230
Answer: D.230
Explanation: Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 290)/26 = 20
x = 230 m.
Answer:D
Question: Find the difference between C.I and S.I on a sum of money Rs. 2000 for 2 years. at 4% p.a
A.Rs.2.20
B.Rs.3.20
C.Rs.4.20
D.Rs.5.20
Answer: B.Rs.3.20
Explanation: P9r/100)^2 =2000(4/100)^2 =Rs.3.20 Answer : B
Question: (786×74) ÷ ? = 4847
A.A)4.8
B.B)12
C.C)58
D.D)68
Answer: B.B)12
Explanation: Explanation:
58164/x = 4847 => x = 58164/4847 = 12
Answer: Option B
Question: If x^2−2ax+a^2=0 get value of x/a
A.1
B.2
C.3
D.4
Answer: A.1
Explanation: a is obviously non-zero. We divide the equation by
a^2
we get (x/a-1)^2=0
x/a=1
ANSWER A 1
Question: If (a-5)(b-2) =0, which of the following must be true ?
I. a=5 and b=2
II. if a is not 5, then b=2
III. if a=5, then b is not=2
A.I only
B.II only
C.III only
D.I and II
Answer: B.II only
Explanation: (a-5)(b-2)=0
So either a=5 or b=2 or both. It is 'or' not 'and', so it could be any of the three possibilities. Thus I and III are not necessarily true.
The answer is B.
Question: If the compound interest on a certain sum of money for 5 years at 10% per annum be Rs. 993, what would be the simple interest?
A.Rs. 1500
B.Rs. 890
C.Rs. 895
D.Rs. 900
Answer: A.Rs. 1500
Explanation: Let P = Principal
A - Amount
We have a = P(1 + R/100)3 and CI = A - P
ATQ 993 = P(1 + R/100)3 - P
? P = 3000/-
Now SI @ 10% on 3000/- for 5 yrs = (3000 x 10 x 5)/100
= 1500/-
Answer: A.
Question: 10 camels cost as much as 24 horses, 16 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants. If the cost of 10 elephants is Rs.150000, find the cost of a camel?
A.s.9800
B.s.3800
C.s.9800
D.s.6000
Answer: D.s.6000
Explanation: Cost of the camel = P
10 camels = 24 horses
16 horses = 4 oxen
6 oxen = 4 elephants
10 elephants = Rs.150000
P = Rs.[(24 * 4 * 4 * 150000)/(10 * 16 * 6 * 10)]
P = Rs.(57600000/9600) => P = Rs.6000
Answer:D
Question: √{(6.3)(10^9)} is closest to which of the following?
A.1,500
B.6,000
C.25,000
D.80,000
Answer: D.80,000
Explanation: √{(6.3)(10^9)} = √{(63)(10^8)} = √(63)√(10^8) = (√63) * 10,000 which is almost 80,000.
The answer is D.
Question: In an examination, there were 2,000 candidates, out of which 900 candidates were girls and rest were Boys. If 30% of the boys and 32% of the girls passed, then the total percentage of failed candidates is?
A.35.67%
B.64.75%
C.68.57%
D.69.10%
Answer: D.69.10%
Explanation: Girls = 900, Boys = 1100
Passed = ( 30% of 1100 ) + ( 32% of 900)
= 330 + 288 = 618
Failed = 2000 - 618 = 1382
Failed % = [(1382/2000) x 100]%
= 69.1%.
ANSWER:D
Question: If the average (arithmetic mean) of 5 positive temperatures is x degrees Fahrenheit, then the sum Q of the 3 greatest of these temperatures, in degrees Fahrenheit, could be
A. 6x
B. 4x
C. 5x/3
D. 3x/2
Answer: B. 4x
Explanation: Note that we have 5positivetemperatures.
Next, as the average is x then the sum of the temperatures is 5x and as all the temperatures are positive then the sum of the 3 greatest must be more than (or equal to) 3x (as the average of the 3 greatest must be at least x) and less than 5x: 3x<Q<5x --> only option B fits.
Answer: B.
Question: There are 79 people that own pets. 15 people own only dogs, 10 people own only cats, 5 people own only cats and dogs, 3 people own cats, dogs and snakes. How many total snakes are there?
A.2
B.4
C.8
D.49
Answer: D.49
Explanation: lets assign variables to all the areas in Venn Diagram of Three.
three different Units are DOG, Cat, Snake= Total = 79
Only Dog= d=15
Only Cat = c=10
Only Snake = s
Exactly Dog and Cat= 5
Exactly Dog and Snake = x
Exactly Cat and Snake = y
all three= 3
so 79=15+10+5+3+x+y+s
we need to know total snakes= x+y+s+3 = 49
answer:D
Question: A is 20% more efficient than B .how much time they will working together take to complete a job which A alone could have done in 15 days?
A.5 6/11 days
B.8 2/11 days
C.6 4/8 days
D.4 days
Answer: B.8 2/11 days
Explanation: The ratio of times taken by A and B=100:120=5:6
suppose B can do work in x days
then 5:6::15:x
x=6*15/5
x=18
A's 1 day's work=1/15
B's 1 day's work=1/18
(A+B)'s 1 day's work =1/15+1/18
A and B together can do work in 8 2/11 days
Answer(B)
Question: If the average (arithmetic mean) of a and b is 45 and the average of b and c is 60, what is the value of c âˆ’ a?
A.25
B.30
C.90
D.140
Answer: B.30
Explanation: the arithmetic mean of a and b =(a+b)/2=45 -- a+b=90 --1
similarly for b+c=120 --2
subtracting 1 from 2 we have
c-a=30;
ANSWER:B
Question: Two members of a club are to be selected to represent the club at a national meeting. if there are 190 different possible selections of the 2 members, how many members does the club have?
A.20
B.27
C.40
D.57
Answer: A.20
Explanation: Below is an answer to your question.
C2n=190Cn2=190 --> n!/2!∗(n−2)!=190. Now, notice that n!=(n−2)!∗(n−1)∗n so (n−2)!∗(n−1)∗n2!∗(n−2)!=190 --> (n−1)∗n/2=190 (n−1)n=380 --> n=20
Answer: A.
Question: In how many ways 3 boys and 3 girls can be seated in a row so that they are alternate.
A.144
B.288
C.36
D.256
Answer: C.36
Explanation: Solution: Let the Arrangement be,
B G B G B G B
34 boys can be seated in 3! Ways.
Girl can be seated in 3! Ways.
Required number of ways,
= 3!*3! = 36.
Answer: Option C
Question: A car driver travels from the plains to the hill station, which are 200 km apart at an average speed of 55km/hr. in return trip, he covers the same distance at an average speed of 20km/hr. the average speed of the car over the entire distance of 400 km is
A.8.95km/hr
B.26.7km/hr
C.27.8km/hr
D.29.3km/hr
Answer: D.29.3km/hr
Explanation: average speed = (2*55*20)/55+20 km/hr
=29.3 km/hr
Answer (D)
Question: Which of the following expressions CANNOT have a negative value
A.|a + b| – |a – b|
B.|a + b| – |a|
C.a^2 + b^2
D.|2a + b| – |a + b|
Answer: C.a^2 + b^2
Explanation: Whenever you are required to find if the equation is a perfect square or not, try to bring everything in the form of a perfect square as they are always positive.
Of the given options, only option D can be written in from of a perfect square.
a^2+b^2
This will always be positive.
Correct Option: C
Question: (2^2-1)(2^2+1)(2^4+1)(2^10+1)=
A.2^18 - 1
B.2^16 + 1
C.2^32 - 1
D.2^128 - 1
Answer: A.2^18 - 1
Explanation: A: is correct
(2^2-1)* (2^2+1)=(2^4-1)
(2^4-1)*(2^4+1)=2^8-1
(2^8-1)*(2^10 +1)=2^18-1
You can apply to this formula: a^2- b^2=(a-b)*(a+b)
Question: Ramesh can finish a piece of work in 12 days. Rohan is twice as efficient as Ramesh.If they work together how many days will they need to finish the same amount of work?
A.8/3 days
B.4 days
C.5 days
D.11/3 days
Answer: B.4 days
Explanation: Ramesh can finish a piece of work in 12 days. Rohan is twice as efficient as Ramesh.
So Rohan can finish a piece of work in 6 days.
days needed to finish the same amount of work = 1/(1/6+1/12)=4 days
ANSWER:B
Question: An article is bought for Rs.600 and sold for Rs.500, find the loss percent?
A.16 2/6%
B.16 8/3%
C.16 7/3%
D.16 2/3%
Answer: D.16 2/3%
Explanation: 600 ---- 100
100 ---- ? => 16 2/3%
Answer:D
Question: he population of a city is 130,000. If it increases at the rate of 6% per annum, then what will be its population 2 years hence?
A.146069
B.146067
C.156068
D.146068
Answer: D.146068
Explanation: Population after n years = P [1 + (R/100)]2
Population after 2 years = 130000 * [1 + 6/100]2 = (130000 x 53/50 x 53/50) = 146068
ANSWER: D
Question: In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?
A.1/10
B.2/5
C.2/7
D.5/7
Answer: C.2/7
Explanation: Solution
P(getting a prize)	= 10 / (10+25)
‹=› 10 / 35
‹=› 2 / 7.
Answer C
Question: The ages of two persons differ by 20 years. If 5 years ago, the elder one be 5 times as old as the younger one, their present ages (in years) are respectively
A.11 years
B.77 years
C.88 years
D.10 years
Answer: D.10 years
Explanation: Let their ages be x and (x + 20) years.
5 (x - 5) = (x + 20 - 5) or 4x = 40 or x = 10.
Their present ages are 30 years and 10 years
Answer: D
Question: A profit of Rs. 600 is divided between X and Y in the ratio of 1/2:1/3 . What is the difference between their profit shares ?
A.s. 220
B.s. 120
C.s. 320
D.s. 50
Answer: B.s. 120
Explanation: A profit of Rs. 600 is divided between X and Y in the ratio of 1/2 : 1/3 or 3:2.
so profits are 360 and 240.
difference in profit share = 360-240=120
ANSWER:B
Question: In the first 8 overs of a cricket game, the run rate was only 2.3 What should be the rate in the remaining 20 overs to reach the target of 260 runs?
A.12.08
B.12.18
C.12.0
D.6.19
Answer: A.12.08
Explanation: Required run rate
= [260- (2.3 * 8)]/20
= 241.60/20
= 12.08
Answer:A