divelab/Sys2Bench huggingface dataset:
Question: Jimmy Bullard and his friend went for fishing.
They got six fishes without heads, nine fishes without the tail and eight fishes cut in two halves.
How many fishes did they caught ?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: Solution:
zero
6 without head => 0
9 without tail => 0
8 in two halves => 0 & 0
Answer A
Answer: A
Question: Two unbiased coin are tossed. What is the probability of getting almost
one head?
Options:
A)1/2
B)1/4
C)3/4
D)3/5
E)1/6
Rationale: Here S={HH,HT,TH,TT}
Let Ee=event of getting one head
E={TT,HT,TH}
P(E)=n(E)/n(S)=3/4
Answer option C) 3/4
Answer: C
Question: Mohit sold an article for Rs. 18000. Had he offered a discount of 10% on the selling price, he would have earned a profit of 8%. What is the cost price of the article?
Options:
A)15000
B)27767
C)16688
D)26678
E)19987
Rationale: Let the CP be Rs. x.
Had he offered 10% discount, profit = 8%
Profit = 8/100 x and hence his SP = x + 8/100 x = Rs. 1.08x = 18000 - 10/100(18000) = 18000 - 1800 = Rs. 16200
=> 1.08x = 16200
=> x = 15000
\Answer: A
Answer: A
Question: The sum of two numbers is 44. Five times one number is equal to 6 times the other. The smaller of the two numbers is
Options:
A)10
B)12
C)16
D)22
E)20
Rationale: Sol.
Let the numbers be x and (44 - x).
Then, 5x = 6(44 - x)
⇔ 11x = 264⇔ x = 24.
So, the numbers are 24 and 20.
Answer E
Answer: E
Question: Which of the following equations represents a line that is perpendicular to y=1/5*x+2?
Options:
A)y−2x=8
B)2x+4y=10
C)3y+6x=12
D)4y−8x=16
E)5x−10y=20
Rationale: For two lines to be perpendicular, the product of slopes should be equal to -1.
Slope of line 1 = 1/2
Slope of the line perpendicular to line 1 must be -2. Option C can be rewritten as y = -2x + 4 --> Slope = -2
Answer: B
Answer: B
Question: If x and y are integers such that x^2+2x+2y+3=2x^2+3x+y+1, we can deduce that y is
Options:
A)not an even
B)an even
C)a perfect square
D)an odd
E)a prime
Rationale: x^2 + 2x + 2y + 3 = 2x^2 + 3x + y + 1
y = x^2 + x - 2
y = (x+2)(x-1) (Note that one factor is even and one factor is odd.)
Then y must be even.
The answer is B.
Answer: B
Question: A meal cost $ 34.50 and there was no tax. If the tip was more than 10 pc but less than 15pc of the price, then the total amount paid should be:
Options:
A)40-42
B)39-41
C)38-40
D)37-39
E)36-37
Rationale: 10%(34.5) = 3.45
15%(34.5) = 5.175
total amount could have been 34.5+3.45 and 34.5+5.175
=> could have been between 37.95 and 39.675
=> approximately between 38 and 40
Answer is C.
Answer: C
Question: What is the angle between the minute hand and the hour hand when the time is 1540 hours?
Options:
A)150
B)160
C)140
D)130
E)None
Rationale: Solution:
The total angle made by the minute hand during an hour is 360o. If it takes 360o for an hour, it will take (40/60) * 360 = 240o. The angle between the hour hand the minute hand will therefore, be somewhere between 240 - 90 = 150o, as the hour hand is between 3 and 4.
The angle made by the hour hand when it moves from say 3 to 4 will be 30o. That is the hour hand makes 30o during the course of an hour.
The hour hand will therefore, move (40/60) * 30 = 20o.
Therefore, the net angle between the hour hand and the minute hand will be 150 - 20 = 130o.
Answer D
Answer: D
Question: During a Pizza buffet where A eats more times 1.8 than B, and B eats 8 times less than C.find the leat number of times all the three has to eat
Options:
A)350
B)260
C)360
D)380
E)285
Rationale: A eats more than B if B eats 1 times than the ratio of A and B is A:B is 1.8:1 or 9:5 and as B eat 8 times less the C the the ratio of B : C is 5:40 the the least number of times all three has eat is the LCM of A,B,C that is 360 ..
ANSWER:C
Answer: C
Question: 504 can be expressed as a product of primes as
.
Options:
A)2 × 2 × 3 × 3 × 7 × 7
B)2 × 3 × 3 × 3 × 7 × 7
C)2 × 3 × 3 × 3 × 3 × 7
D)2 × 2 × 2 × 3 × 3 × 7
E)NONE OF THE ABOVE
Rationale: It is clear that 504 = 2 × 2 × 2 × 3 × 3 × 7
Answer: Option D
Answer: D
Question: Nancy works 3 days per week at a rate of x dollars per day. If Nancy works more than 3 days per week, any extra days are paid at double her normal rate. Nancy worked 4 weeks with no overtime, and then worked 2 more weeks, each with y days of overtime. Which of the following represents Nancy’s total earnings over this period?
Options:
A)a) 3y(7x+2xy)
B)b) 3x+12y
C)c) 2x(2y+9)
D)d) 3x(2y+7)
E)e) 4x(y+8)
Rationale: Payment of a week for 3 days a week = $3x
Payment of 4 weeks for 3 days a week = $3x*4 = $12x
Payment of a week for y days overtime a week = $3x+$2xy
Payment of 2 weeks for y days overtime a week = ($3x+$2xy)*2
Total Earnings = $12x + ($3x+$2xy)*2 = 18x+4xy =2x(2y+9)
Answer: option C
Answer: C
Question: If f is a positive integer, and if the units' digit of f^2 is 4 and the units' digit of (f + 1)^2 is 1, what is the units' digit of (f + 2)^2 ?
Options:
A)	0
B)	2
C)	4
D)	6
E)	8
Rationale: A for me.
_1² = _1
_2² = _4
_3² = _9
_4² = _6
_5² = _5
_6² = _6
_7² = _9
_8² = _4
_9² = _1
_0² = _0
On the list, the only number that squared has the units digit = 4 preceding a number that squared has the units digit = 1 is the _8.
So, f = _8, that has square 4. The next square is 1 andnext nextsquare is 0.
Answer: A
Question: Which of the following is not a leap year?
Options:
A)700
B)800
C)1200
D)2000
E)2012
Rationale: The century divisible by 400 is a leap year.
The year 700 is not a leap year.
Answer: Option A
Answer: A
Question: The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 60 kmph, find the speed of the stream?
Options:
A)18 kmph
B)19 kmph
C)21 kmph
D)22 kmph
E)20 kmph
Rationale: The ratio of the times taken is 2:1.
The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1
Speed of the stream = 60/3 = 20 kmph.
Answer: E
Answer: E
Question: A can do a piece of work in 24 days. B in 15 days and C in 12 days. In how many days can A finish the work if he is assisted by B on one day and C on the next, alternately?
Options:
A)8 2/5days
B)10 2/5days
C)6 2/5days
D)18 2/5days
E)17 2/5days
Rationale: A + B = 1/24 + 1/15 = 13/120
A + C = 1/24 + 1/12 = 1/8
13/120 + 1/8 = 28/120
4 1/5 days * 2 = 8 2/5days
ANSWER:A
Answer: A
Question: In how many ways letters of the word OCCUPAY be arranged?
Options:
A)6178
B)9456
C)387
D)2520
E)9812
Rationale: OCCUPAY has 7 letters, out of which C repeated 2 times. Hence total ways = 7! / (2!) = 2520 ways
D
Answer: D
Question: A family has two children. find the probability that both the children are girls given that at least
one of them is a girl?
Options:
A)1/5
B)1/3
C)1/7
D)1/9
E)1/12
Rationale: Let b stand for boy and g for girl. The sample space of the experiment is
S = {(g, g), (g, b), (b, g), (b, b)}
Let E and F denote the following events :
E : ‘both the children are girls’
F : ‘at least one of the child is a girl’
Then E = {(g,g)} and F = {(g,g), (g,b), (b,g)}
Now E n F = {(g,g)}
Thus P(F) = 3/4
and P (E n F )= 1/4
Therefore P(E|F) = P(E ∩ F)/P(F) = (1/4)/(3/4) = 1/3
B)
Answer: B
Question: What is the time required for a vehicle to cover a distance of 480 km with a speed of 60 kmh?
Options:
A)6 hours
B)12 hours
C)9 hours
D)10 hours
E)8 hours
Rationale: Time= Distance / Speed
Time = 480 / 60 = 8
Answer: E
Answer: E
Question: In a group of people, if 30 people were made to stand in each column, 16 columns could be formed. If 12 people were made to stand in a column, how many columns could be formed?
Options:
A)20
B)30
C)40
D)50
E)60
Rationale: 16*30 = 12*n
n = 40
The answer is C.
Answer: C
Question: The average age of all the student of a class is 18 years. The average age of boys of the class is 20 years and that of the girls is 15 years. If the number of girls in the class is 20, then find the number of boys in the class.
Options:
A)15
B)45
C)30
D)50
E)60
Rationale: Let Boys in class = B
Girls in class = 20
Now, (20B+15*20)/(B+20) = 18 => B = 30
Answer: C
Answer: C
Question: If a particular is never chosen, in how many ways can a cricketbe chosen out of 15 players?
Options:
A)245
B)256
C)364
D)370
E)390
Rationale: A particular players is never chosen, it means that 11 players are selected out of 14 players.
=> Required number of ways = 14C11
= 14!/11!x3! = 364
C
Answer: C
Question: A case of 12 rolls of paper towels sells for $9. The cost of one roll sold individually is $1.What is the percent Q of savings per roll for the 12-roll package over the cost of 12 rolls purchased individually?
Options:
A)9%
B)11%
C)15%
D)25%
E)90%
Rationale: Cost of 12 paper towels individually = 1*12=12
Cost of a set of 12 paper towels = 9
Cost of one roll = 9/12 = 3/4 = 0.75
Savings per roll = 1-.75 = 0.25
% of savings is Q= .25/ 1 *100 = 25% D is the answer.
Answer: D
Question: Visitors to show were charged Rs.15 each on the first day. Rs.7.50 on the second day, Rs.2.50 on the third day and total attendance on the three days were in ratio 2:5:13 respectively. The average charge per person for the whole show is?
Options:
A)1
B)4
C)5
D)6
E)8
Rationale: 2: 5: 13
2x 5x 13x
15 7.5 2.5
30x + 37.5x + 32.5x = 100x/20x
Average = 5
Answer: C
Answer: C
Question: A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is:
Options:
A)100 Kmph
B)110 Kmph
C)120 Kmph
D)130 Kmph
E)150 Kmph
Rationale: Let speed of the car be x kmph.
Then, speed of the train =150X/100 = 3X/2 Kmph.
75/X - 75/(3X/2) = 125/(10 *60)
75/X - 50/X = 5/24
X = 25 * 24/5 = 120 Kmph.
Answer C) 120 Kmph
Answer: C
Question: A man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
Options:
A)1.0
B)1.7
C)1.2
D)1.5
E)1.2
Rationale: M = 4.5
S = x
DS = 4.5 + x
US = 4.5 + x
4.5 + x = (4.5 - x)2
4.5 + x = 9 -2x
3x = 4.5
x = 1.5.Answer:D
Answer: D
Question: The sum of two numbers is 232 and their H.C.F is 29. How many pairs of such numbers are
Options:
A)1
B)2
C)0
D)3
E)None of these
Rationale: Explanation:
HCF of two numbers = 29
Let the numbers = 29x, 29y
x and y are prime to each other
According to the question,
29x + 29y = 232, 29(x+y) = 232, x + y = 8,
Possible pairs of x and y = (1,7) and (3,5)
numbers are = (29, 203) and (87,145)
Answer: Option B
Answer: B
Question: What will come in place of the x in the following Number series? 2, 3, 6, 6, 18, 12, 54, 24, x
Options:
A)162
B)96
C)78
D)144
E)180
Rationale: There are two series here
2, 6, 18, 54, ... (Multiply by 3)
3, 6, 12, 24 (Multiply by 2)
Hence, next term is 54 x 3 = 162
Correct Answer is A
Answer: A
Question: Ratio of ages of three persons is 4:7:9, Eight years ago, the sum of their ages was 56. Find their
present ages
Options:
A)16,35,36
B)12,28,36
C)16,28,27
D)16,28,36
E)None of these
Rationale: Explanation:
Let the present ages are 4x, 7x, 9x.
=> (4x-8) + (7x-8) + (9x-8) = 56
=> 20x = 80
=> x = 4
So their present ages are: 16,28,36
Answer: Option D
Answer: D
Question: Rahim is able to sell a hand-carved statue for $840 which was a 20% profit over his cost. How much did the statue originally cost him?
Options:
A)$496.30
B)$512.40
C)$555.40
D)$574.90
E)$700
Rationale: Cost price = 840/120*100 = 700
Answer : E
Answer: E
Question: An express traveled at an average speed of 150 km/hr, stopping for 3 min after every 80 kn. How long did it take to reach its destination 750 km from the starting point?
Options:
A)5 hrs 24 min
B)4 hrs 24 min
C)6 hrs 44 min
D)6 hrs 21 min
E)4 hrs 34 min
Rationale: A
5 hrs 24 min
Time taken to cover 750 km = 750/150 = 5 hrs.
Number of stoppages = 750/80 - 1 = 8
Total time of stoppages = 3 * 8 = 24 min
Hence, total time taken = 6 hrs 21 min.
Answer: A
Question: A 600 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 1.8 kilometer long bridge, at the same speed?
Options:
A)4 min
B)2 min
C)8 min
D)9 min
E)3 min
Rationale: S = 600/40 = 15 mps
S = 1800/15 = 120 sec = 2 min.Answer: B
Answer: B
Question: Rooney, Hernandez, and Robin race each other in a 100 meters race. All of them run at a constant speed throughout the race.
Rooney beats Hernandez by 20 meters.
Hernandez beats Robin by 20 meters.
How many meters does Rooney beat Robin by ?
Options:
A)33 meters.
B)29 meters.
C)25 meters.
D)36 meters.
E)30 meters.
Rationale: D
36 meters.
100/v1 = 80/v2
100/v2 = 80/v3
20+(20/v2)*v3=20+16 = 36
Answer: D
Question: A man can row 7 Â½ kmph in still water.if in a river running at 1.5 km/hr an hour,it takes him 50 minutes to row to a place and back,how far off is the place?
Options:
A)4 km
B)2 km
C)5 km
D)3 km
E)1 km
Rationale: Speed downstream =(7.5+1.5)km/hr=9 km/hr;
Speed upstream=(7.5-1.5)kmph=6kmph.
Let the required distance be x km.then,
x/9+x/6=50/60.
2x+3x=(5/6*18)
5x=15
x=3.
Hence,the required distance is 3km.
ANSWER D
Answer: D
Question: How many times are the hands of a clock at right angle in a day?
Options:
A)22
B)44
C)41
D)21
E)40
Rationale: Correct Answer : B
In 12 hour hands of clock are at right angle 22 times
In 24 hour hands of clock are at right angle 44 times
Answer: B
Question: If 7^k + 7^k = (7^9)^(7^9) - 7^k, then k = ?
Options:
A) 11/3
B) 11/2
C) 242
D) 3^10
E) 7^11 - 1
Rationale: 7^k + 7^k = (7^9)^7^9 - 7^k
7*(7^k) = 7 ^ (49 * 7^9 ) = 7^(7^2 * 7^9) = 7^(7^11)
7^k+1 = 7^(7^11)
So k+1 = 7^11
So k = 7^11 -1
Answer is E
Answer: E
Question: If a number is 60% more than the another, how much % is the smaller number less than the first ?
Options:
A)32(1/3)%
B)16(2/3)%
C)37(1/2)%
D)36(4/3)%
E)none of these
Rationale: Take a number 100,
Then the other number is 160
% the smaller number is less than the first = [(60/(160)) x 100]% = 37(1/2)%.
ANSWER:C
Answer: C
Question: S = { 8,4,7,3,2,9}
T = { 4,5,6,3,1,7}
what is the probability that x chosen from S and y chosen from T will result x*y = even
Options:
A)2/5
B)4/7
C)5/3
D)5/6
E)1/6
Rationale: p: the probability that x*y is even, then p=1-p(x*y is odd)
p(x*y odd)=p(x odd)*p(y odd)=3/6*4/5=1/3
And p=1-6/10=2/5
Option: A
Answer: A
Question: Working together, printer A and printer B would finish the task in 24 minutes. Printer A alone would finish the task in 60 minutes. How many pages does the task contain if printer B prints 4 pages a minute more than printer A ?
Options:
A)600
B)480
C)1000
D)1200
E)1500
Rationale: Answer: B.
Answer: B
Question: The average age of 15 men of a group is 15 years. Out of these, the average age of 5 men is 15 years and that of the other 9 men is 16 years. The age of the 15th man is?
Options:
A)11 years
B)17 years
C)6 years
D)14 years
E)12 years
Rationale: Age of the 15th student
=[15 * 15 - (15 * 5 + 16 * 9)]
= (225 - 219)
= 6 years.
Answer:C
Answer: C
Question: A password of a computer used seven digits where they are from 0 and 9. What is the probability that the password solely consists of prime numbers and zero?
Options:
A)1/32
B)1/16
C)1/8
D)2/5
E)1/128
Rationale: We have seven digits can be used for password -0,2,3,5,7.
Assuming that the numbers can be repeated any number of times in the password, probability of selecting any one of them is 5/10 (out of 10 digits from 0-9)
So, 5/10 * 5/10 * 5/10 * 5/10 * 5/10 * 5/10 * 5/10=1/128 (E)
Answer: E
Question: A rectangular field 30 m long and 20 m broad. How much deep it should be dug so that from the earth taken out, a platform can be formed which is 8 m long, 5.5 m broad and 1.5 m high where as the earth taken out is increase by 10/5?
Options:
A)77 cm
B)10 cm
C)88 cm
D)12 cm
E)13 cm
Rationale: 30 * 20 * x = (8 * 5.5 * 1.5)/2
Answer: B
Answer: B
Question: The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?
Options:
A)18%
B)19%
C)28%
D)38%
E)16%
Rationale: 1500 ---- 270
100 ---- ? => 18%
Answer:A
Answer: A
Question: At what price must an article costing Rs.47.50 be marked in order that after deducting 12% from the list price. It may be sold at a profit of 25% on the cost price?
Options:
A)62.5
B)67.5
C)62.7
D)62.2
E)62.9
Rationale: CP = 47.50
SP = 47.50*(125/100)
= 59.375
MP*(88/100)
= 59.375
MP = 67.5
Answer:B
Answer: B
Question: The perimeter of a triangle is 32 cm and the inradius of the triangle is 3.5 cm. What is the area of the triangle?
Options:
A)22
B)35
C)56
D)54
E)23
Rationale: Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 3.5 * 32/2
= 56 cm2
Answer:C
Answer: C
Question: The average of five numbers is 27. If one number is excluded, the average becomes 23. The excluded number is?
Options:
A)46
B)45
C)44
D)43
E)42
Rationale: Excluded number = (27 * 5) - (23 * 4)
= 135 - 92
= 43.
Answer: D
Answer: D
Question: 1/2, 1/4, 1/8 ....
In the sequence above each term after after the first one-half the previous term. If x is the tenth term of the sequence, then x satisfies which of the following inequalities?
Options:
A)0.1 < x < 1
B)0.01 < x < 0.1
C)0.001 < x < 0.01
D)0.0001 < x < 0.001
E)0.00001 < x < 0.0001
Rationale: In the Sequence notice that the sequence is just the 1/(2^n) ...
so for 1st term=1/2^1=1/2
2nd term=1/(2^2)1/4, 3rd term=1/(2^3)=1/8 and so on...
Thus the 10th term will be 1/(2^10)=1/1024
Roughly, 1/1024 can be 1/1000=0.001 but since denominator is a bit more than 1000 therefore the actual value will be a bit less than 0.001.
thus the ans will lie btw. 0.01 and 0.1.(B)
Answer: B
Question: A, B and C enter into a partnership and their shares are in the ratio 1/2 : 1/3 : 1/4. After 2 months, A withdraws half of his capital and after 10 months, a profit of Rs. 378 is divided among them. What is B's share ?
Options:
A)144
B)166
C)186
D)199
E)161
Rationale: Ratio of initial investments = 1/2 : 1/3 : 1/4 = 6 : 4 : 3.
Let their initial investments be 6x, 2x and 3x respectively.
A : B : C = (6x * 2 + 3x * 10) : (4x * 12) : (3x * 12) = 42 : 48 : 36 = 7 : 8 : 6.
B's share = = Rs. 144.
Answer: A
Answer: A
Question: A can do a work in 9 days and B can do the same work in 18 days. If they work together, in how many days will they complete the work?
Options:
A)4 days
B)6 days
C)8 days
D)2 days
E)9 days
Rationale: B
6 days
One day's work of A and B = 1/9 + 1/8 = (2+1)/18 = 1/6 So, the time taken to complete the work is 6 days.
Answer: B
Question: It takes John 25 minutes to walk to the car park and 45 to drive to work. At what time should he get out of the house in order to get to work at 9:00 a.m.?
Options:
A)8:50 a.m
B)5:50 a.m
C)7:50 a.m
D)6:50 a.m
E)9:50 a.m
Rationale: The time it takes John to get to work: time to walk to car park + time to drive
25 + 45 = 70 minutes = 1 hour and 10 minutes
John needs to get out of the house 1 hour and 10 minutes before 9:00 am at
9:00 - 1:10 = 7:50 a.m
correct answer C
Answer: C
Question: A train 140 m in length crosses a telegraph post in 16 seconds. The speed of the train is?
Options:
A)30.5 kmph
B)31.5 kmph
C)32.5 kmph
D)33.5 kmph
E)21.5 kmph
Rationale: S = 140/16 * 18/5 = 31.5 kmph
ANSWER:B
Answer: B
Question: How many integers between 100 and 1000 are there such that their unit digit is odd?
Options:
A)400
B)420
C)500
D)450
E)350
Rationale: 900 numbers between - 100 and 1000
Out of which half would be even, half odd.
Number of odd unit digit number = 450.
correct option is D
Answer: D
Question: A person works on a project and completes 5/8 of the job in 10 days. At this rate, how many more days will he it take to finish the job?
Options:
A)7
B)6
C)5
D)4
E)3
Rationale: Explanation:
Number of days he worked = 10
Work completed =5/8
Let the required number of days =x
Remaining Work to be completed =1−5/8=3/8
More work, more days(direct proportion)
Hence we can write as
(Work) 5/8 : 3/8:: 10 : x
⇒5/8×x=3/8×10
⇒5×x=3×10
⇒x=3×2=6
Answer: Option B
Answer: B
Question: What is the difference between the place value of 3 in the numeral 7339?
Options:
A)170
B)160
C)180
D)190
E)210
Rationale: 300 - 30 = 170
A
Answer: A
Question: Mr. Jones sold two pens at $1 each. Based on the cost, his profit one was 50% and his loss on the other was 40%. On the sale of the pipes. Find the amount of his profit or loss?
Options:
A)lost 10 cents
B)lost 4 cents
C)broke even
D)gained 4 cents
E)gained 40 cents
Rationale: 50 % profit on $ 1
= $ 50/100 × 1
= $ 0.50× 1
= $ 0.50
Similarly, 40 % loss on $ 1
= $ 40/100 × 1
= $ 0.40× 1
= $ 0.40
Therefore, in one pen his profit is $ 0.50 and in the other pipe his loss is $ 0.40
So profit by amount $0.40.
Answer is E.
Answer: E
Question: If d=1/(2^3*5^10) is expressed as a terminating decimal, how many nonzero digits will d have?
Options:
A)One
B)Two
C)Three
D)Seven
E)Ten
Rationale: Another way to do it is :
We know x^a*y^a=(X*Y)^a
given = 1/(2^3*5^10)
= Multiply and divide by 2^7
=2^7/(2^3*2^7*5^10)
=2^7/10^10
=> non zero digits are 128 => Ans C
Answer: C
Question: Let exp(m,n) = m to the power n. If exp(10, m) = n exp(2, 2) where to and n are integers then n =
Options:
A)27
B)272
C)98
D)25
E)72
Rationale: Given 10m=n.2210m=n.22
⇒⇒ 2m×5m=n.22⇒2m−2×5m=n2m×5m=n.22⇒2m−2×5m=n
For m = 2 we get least value of n = 25, and for m > 2 we get infinite values are possible for n.
Answer:D
Answer: D
Question: A, B and C started a shop by investing Rs. 10,000, Rs. 10,000 and Rs. 20,000 respectively. At the end of the year, the profits were distributed among them. If Câ€™s share of profit be Rs. 4,000, then the total profit was :
Options:
A)30,000
B)60,000
C)8,000
D)120,000
E)None
Rationale: Sol.
A : B : C = 10000 : 10000 : 20000 = 1: 1 : 2. so, Câ€™s share : Total Profit = 2 : 4
Let the total profit be Rs. x. Then, 2/4 = 36000/x or x
= 4000 * 4 / 2 = 8000.
Answer C
Answer: 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:
Options:
A)20
B)99
C)88
D)27
E)21
Rationale: Distance covered by B in 9 sec. = \inline \fn_jvn {\color{Black} \left ( \frac{100}{45}\times 9 \right )m} = 20m
\fn_jvn {\color{Black} \therefore } A beats B by 20 metres.
Answer: A) 20m
Answer: A
Question: If a+b=−6, and a=10/b, what is the value of a^2+b^2?
Options:
A)22
B)24
C)16
D)18
E)20
Rationale: a^2 + b^2 should make you think of these formulas:
(a+b)(a+b) = a^2+b^2+2ab
We already know (a+b) = -6 and a*b = 10
(a+b)(a+b) = (-6)(-6) = a^2+b^2+2*(10)
a^2+b^2 = 36 - 20 = 16
Answer : C
Answer: C
Question: A boy standing idle sounds a whistle to his friend at a distance of 1200 m moving away from him in a speeding car at 108 kms /hr. Find the duration after which his friend is going to hear him. (Speed of sound = 330m/sec).
Options:
A)3.6 secs
B)4.00 secs
C)40 secs
D)45 secs
E)None of these
Rationale: If friend hears sound after t secs, then
330*t = 1200 +(108*5/18)*t
300t =1200
t= 4 secs
ANSWER:B
Answer: B
Question: In a certain math department, students are required to enroll in either Calculus or Trigonometry, each of which is offered in beginner and advanced courses. The number of students enrolled in Trigonometry is 50% greater than the number of students enrolled in Calculus, and 80% of Calculus students are enrolled in the beginner course. If 4/5 of students are in the beginner courses, and one student is selected at random, what is the probability that a beginner Trigonometry student is selected?
Options:
A)40%
B)44%
C)48%
D)52%
E)56%
Rationale: Let x be the number of students in calculus.
Then the number of students in trigonometry is 1.5x
The number of students on beginner calculus is 0.8x
The number of students in beginner trigonometry is 4/5*(2.5x) - 0.8x = 1.2x
The percentage in beginner trigonometry is 1.2x / 2.5x = 48%
The answer is C.
Answer: C
Question: If each term in the sum E=a1+a2+a3+...+an either 2 or 22 and the sum equals 100, which of the following could be equal to n?
Options:
A)38
B)39
C)40
D)41
E)42
Rationale: Min value of 'n' can be 10 i.e 4*22+6*12=E => 22+22+22+22+2+2+2+2+2+2 = 100
Since we don't have 10 in the options proceed further, (10-1)+22/2 => 20 digits, which is again not in the options
(20-1) + 22/2 = 30 digits ( not in options)
(30-1) + 22/2 = 40 digits
Hence C.
Answer: C
Question: The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on atleast one ticket is?
Options:
A)0.5907
B)0.5904
C)0.5902
D)0.5901
E)0.59023
Rationale: P(winning prize atleast on one ticket)
= 1 - P("Losing on all tickets")
= 1 - (0.8)4 = (1 + (0.8)2)(1 - (0.8)2)
= (1.64)(0.36) = 0.5904.Answer: B
Answer: B