mathewhe/aqua_rat huggingface dataset:
Question: Sixty five percent of a number is 21 less than four fifth of that number. What is the number ?
(A) 240
(B) 180
(C) 120
(D) 220
(E) 140
Rationale: Let the number be x.
Then, 4*x/5 –(65% of x) = 21
4x/5 –65x/100 = 21
5 x = 2100
x = 140.
Answer is E.
Answer: (E) 140
Question: For every order, a certain mail-order company charges a shipping fee of $3 plus an additional $2 if the value of the order is over $50 but not over $100 or an additional $3 if the value of the order is over $100. How much greater are the total shipping fees for 2 orders of $75 each than the total shipping fee for 2 order of $250 ?
(A)  $1
(B)  $2
(C)  $3
(D)  $4
(E)  $5
Rationale: Total cost involved for each 75 $ shipment: 3+2 = 5 $. Thus, for two such orders = 10$
Total cost involved for a 250$ shipment: 3+3 = 6$. Thus, for two such orders = 12$
The difference = 2$.
B
Answer: (B)  $2
Question: A watch was sold at a loss of 10%. If the watch was sold for $24 more, there would have been a gain of 6%. What is the cost price?
(A) $120
(B) $150
(C) $180
(D) $210
(E) $240
Rationale: 0.9x + 24 = 1.06x
0.16x = 24
x = 150
The answer is B.
Answer: (B) $150
Question: What is the absolute value of twice the difference of the roots of the equation D=5y^2 − 20y + 15 = 0 ?
(A)  0
(B)  1
(C)  2
(D)  3
(E)  4
Rationale: D=5y^2 − 20y + 15 = 0 --> y^2 − 4y + 3 = 0 --> y=1 or y=3. The difference is 2, twice the difference is 4.
Answer: E.
Answer: (E)  4
Question: If (2x + 2)(x + 3) = 2x^2 + x, what is a possible value of x?
(A)  -6/7
(B)  -6/8
(C)  -5/7
(D)  8/7
(E)  6/8
Rationale: Rearranging the given expression:
(2x + 2)(x + 3) = 2x^2 + x
i.e. 2x^2 + 8x + 6 = 2x^2 + x
i.e. 7x = -6
i.e. x = -6/7
Answer: Option A
Had it been a difficult expression to solve further, then we could have used options to check which one satisfies the expression after solving it as further as possible.
Answer: (A)  -6/7
Question: The water from one outlet, flowing at a constant rate, can fill a swimming pool in 12 hours. The water from a second outlet, flowing at a constant rate, can fill the same pool in 8 hours. If both outlets are used at the same time, approximately what is the number of hours required to fill the pool?
(A)  0.22
(B)  0.31
(C)  2.50
(D)  3.21
(E)  4.8
Rationale: Always remember RT=W i.e Rate*Time = Work
Also remember that rate can be added or subtracted. For e.g if A do a work in 2 day and B do a work in 2 day.
They both of them together will do a work in 1 day.
So now your question first determine both outlets rate.
1st outlet rate = 1/12 (R=W/T here W=1 work, T = 12hrs)
2nd outlet rate = 1/8 (R=W/T here W=1 work, T = 8hrs)
Both of them working together rate = 1st outlet rate + 2nd outlet rate = 1/12+1/8 = 5/24
again apply the formula RT=W
T = W/R = 1/5/24 = 24/5 =4.8
Answer is E.
Answer: (E)  4.8
Question: If (2a + 3b)/(5a - 3b) = 23/5 , then the value of b : a is ?
(A) 4 : 1
(B) 1 : 4
(C) 4 : 5
(D) 5 : 4
(E) 1 : 2
Rationale: (2a + 3b)/(5a - 3b) = 23/5
=> 10a + 15b = 115a - 69b
=> 105a = 84b => 5a = 4b
a/b = 4/5
ANSWER:D
Answer: (D) 5 : 4
Question: Two trains are moving at 50 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?
(A) 3 sec
(B) 5 sec
(C) 6 ½ sec
(D) 7 ½ sec
(E) 5 ½ sec
Rationale: D
7 ½ sec
70 + 50 = 120 * 5/18 = 100/3 mps
D = 150 + 100 = 250 m
T = 250 * 3/100 = 15/2 = 7 ½ sec
Answer: (D) 7 ½ sec
Question: Income and expenditure of a person are in the ratio 5 : 4. If the income of the person is Rs. 14000, then find his savings?
(A) 3600
(B) 2800
(C) 3608
(D) 3602
(E) 3603
Rationale: Let the income and the expenditure of the person be Rs. 5x and Rs. 4x respectively.
Income, 5x = 14000 => x = 2800
Savings = Income - expenditure = 5x - 4x = x
So, savings = Rs. 2800.
Answer:B
Answer: (B) 2800
Question: In how many ways can the letters of the word ARRANGED be arranged in a row so that the vowels appear in alphabetic order?
(A) 6720
(B) 5280
(C) 6240
(D) 5202
(E) 4020
Rationale: three letters can be arranged in 3! ways.
only one combination AEI is required.
8 letters can be arranged in 8! ways.
thus 8!/ 3! * 1 = 6720.
A
Answer: (A) 6720
Question: Two numbers are respectively 71% and 80% more than a third number. The percentage that is first of the second is?
(A) 4%
(B) 5%
(C) 6%
(D) 7%
(E) 8%
Rationale: I II III
171 180 100
180----------171
100-----------? => 5%
Answer:B
Answer: (B) 5%
Question: A wire can be bent in the form of a circle of radius 56cm. If it is bent in the form of a square, then its area will be
(A) 7744
(B) 8844
(C) 5544
(D) 4444
(E) 3444
Rationale: length of wire = 2 PieR= 2 *(22/7 )*56 = 352 cm
side of the square = 352/4 = 88cm
area of the square = 88*88 = 7744 sq cm Answer: A
Answer: (A) 7744
Question: Machine M, N, O working simultaneously Machine M can produce x units in 3/4 of the time it takes machine N to produce the same amount of units. Machine N can produce x units in 1/3 the time it takes machine O to produce that amount of units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N?
(A) 1/2
(B) 1/3
(C) 4/13
(D) 8/29
(E) 6/33
Rationale: Now ultimately the speed of every machine is given with respect to Mach O.
So lets assume the speed of O, say 12 hrs to make x units (assuming 6 because we can see we will need to divide by 3 and 4
Mach O makes x units in 12 hrs
So, Mach N = 1/3 of O = 1/3*12 = 4 hrs to make x units
and Mach M = 3/4 of N = 3/4*4 = 6 hrs to make x units
No they are running simultaneously. Lets see how much each mach makes in 1 hr
Mach O = x/12 units
Mach N = x/4 units
Mach M = x/6 units
In 1 hr, together they make - x/12+x/4+x/6 = x/2
So what ratio of this has Mach N made?
(x/4) / (x/2) = 1/2
Ans:A=1/2
Answer: (A) 1/2
Question: What is the area of a square field whose diagonal of length 40 m?
(A) 287
(B) 269
(C) 750
(D) 200
(E) 800
Rationale: d2/2 = (40 * 40)/2
= 800
Answer:E
Answer: (E) 800
Question: A circular mat with radius 10 inches is placed on a square tabletop, each of whose sides is 24 inches long. Which of the following is closest to the fraction of the tabletop covered by the mat?
(A) 5/12
(B) 2/5
(C) 0.5451
(D) 3/4
(E) 5/6
Rationale: C.
It is a circle inscribed in a square.
Square side=24---> square(table) area=24^2
Circle diameter=20---> Circle area=PiR^2=100Pi (where Pi=~3.14)
covered fraction=100*3.14/24*24=~314/24*24=0.5451
C
Answer: (C) 0.5451
Question: A and B complete a work in 6 days. A alone can do it in 10 days. If both together can do the work in how many days?
(A) 3.75 days
(B) 3.78 days
(C) 3.25 days
(D) 3.15 days
(E) 2.75 days
Rationale: 1/6 + 1/10 = 8/30 = 4/15
15/4 = 3.75 days
Answer: A
Answer: (A) 3.75 days
Question: In a certain company, a third of the workers do not have a retirement plan. 20% of the workers who do not have a retirement plan are women, and 40% of the workers who do have a retirement plan are men. If 128 of the workers of that company are men, how many of the workers are women?
(A) 80
(B) 95
(C) 105
(D) 112
(E) 210
Rationale: Set up equation:
x = total number of workers
128 = 0,4 * 2/3 * x + 0,8 * 1/3 * x
128 = 16/30 x
x = 240
240 - 128 = 112
Answer D
Answer: (D) 112
Question: Excluding stoppages, the speed of a bus is 82 kmph and including stoppages, it is 75 kmph. For how many minutes does the bus stop per hour?
(A) 5.12
(B) 4.13
(C) 6.15
(D) 7.5
(E) None of these
Rationale: Due to stoppages, it covers 7 km less.
Time taken to cover 7 km = ((7/82)Ã—60) = 5.12 min.
Option(A) is correct
Answer: (A) 5.12
Question: A man can row his boat with the stream at 26 km/h and against the stream in 12 km/h. The man's rate is?
(A) 1 kmph
(B) 4 kmph
(C) 5 kmph
(D) 7 kmph
(E) 8 kmph
Rationale: DS = 26
US = 12
S = ?
S = (26 - 12)/2 = 7 kmph
Answer: D
Answer: (D) 7 kmph
Question: A car takes 6 hours to cover a distance of 504 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
(A) 48 Kmph
(B) 50 Kmph
(C) 52 Kmph
(D) 56 Kmph
(E) 60 Kmph
Rationale: Time = 6
Distence = 504
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 504/9 = 56 Kmph
D
Answer: (D) 56 Kmph
Question: A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 4 cm. What is the length of the wire?
(A) 116 cm
(B) 144 cm
(C) 168 cm
(D) 173 cm
(E) 189 cm
Rationale: Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere.
π(4)^2 * h = (4/3)π (12)^3 => h
= 144 cm
Answer:B
Answer: (B) 144 cm
Question: A man can row a distance of 5 km in 60 min with the help of the tide. The direction of the tide reverses with the same speed. Now he travels a further 40 km in 10 hours. How much time he would have saved if the direction of tide has not changed?
(A) 2
(B) 8
(C) 1
(D) 6
(E) 5
Rationale: Explanation:
He covered 5 km in 1 hour , so he might cover 40 km in 8 hours.
But he took 10 hours.
He would have saved 10 â€“ 8 = 2 hours.
Answer: A
Answer: (A) 2
Question: Given positive even integer y, which of the following CAN be evenly divisible by y?
(A) y + 1
(B) 2y - 2
(C) 2y + 1
(D) 3y - 1
(E) y + 1⁄2
Rationale: This can be easily solved by substituting values:
Assume y to be 2
A. y + 1: 3 is not evenly divisible by 2
B. 2y - 2: 2 is evenly divisible by 2
C. 2y + 1: 5 is not evenly divisible by 2
D. 3y − 1: 5 is not evenly divisible by 2
E. y + 1⁄2: 5/2 is not evenly divisible by 2
Option B
Answer: (B) 2y - 2
Question: Given that there are 6 basketball players per team, how many ways can you select 2 basketball players from 3 teams if no more than one player can be selected from each team?
(A)  15
(B)  30
(C)  60
(D)  108
(E)  90
Rationale: 2 teams can be selected from 3 teams in 3C2 ways = 3 ways
as the condition is that the 2 players should be from different teams
one player can be chosen from 1st team in 6 ways
similarly another player can be chosen from 2nd team in 5 ways
Total number of ways to choose the player = 6 * 6 * 3 = 108 ways
Correct Answer - D
Answer: (D)  108
Question: A and B together can do a piece of work in 6 days and A alone can do it in 14 days. In how many days can B alone can do it?
(A) 12 days
(B) 15 days
(C) 21/2 days
(D) 21 days
(E) 22 days
Rationale: Explanation:
A and B can do work 1/6 in 1 day
A alone can do 1/14 work in 1 day
B alone can do (1/6 -1/14) =2/21 work in 1 day
=> complete work can be done in 21/2 days by B
Answer: Option C
Answer: (C) 21/2 days
Question: A number x is multiplied with itself and then added to the product of 4 and x. If the result of these two operations is 0, what is the value of x?
(A) -4 and 0
(B) -2
(C) 2
(D) 4
(E) Cannot be determined.
Rationale: A number x is multiplied with itself --> X^2
added to the product of 4 and x --> X^2+4X
If the result of these two operations is 0 --> X^2+4X=0
i.e X^2+4X=0 is the Quadratic equation which needs to be solved.
X(X+4) = 0
Hence X=0. X=-4
IMO A
Answer: (A) -4 and 0
Question: Working individually, Amy can hang picture frames for 5 hours and John can hang picture frames in 4 hours. If Amy and John work together but independently at the task for 1 hour, at which point John leaves, how many remaining hours will it take Amy to complete the task alone?
(A) 11/20
(B) 55/20
(C) 5/2
(D) 30/10
(E) 3/22
Rationale: B
Answer: (B) 55/20
Question: In a games hour 4 different types of players came to the ground? cricket 16, hokey 12, football 18, softball 13. How many players are present in the ground?
(A) 70
(B) 52
(C) 62
(D) 59
(E) 50
Rationale: total number of players= 16+12+18+13= 59
Answer is D
Answer: (D) 59
Question: If P is a prime number greater than 3, find the remainder when P^2 + 16 is divided by 12.
(A) 5
(B) 1
(C) 0
(D) 8
(E) 7
Rationale: Every prime number greater than 3 can be written 6N+1 or 6N-1.
If P = 6N+1, then P^2 + 16 = 36N^2 + 12N + 1 + 16 = 36N^2 + 12N + 12 + 5
If P = 6N-1, then P^2 + 16 = 36N^2 - 12N + 1 + 16 = 36N^2 - 12N + 12 + 5
When divided by 12, it must leave a remainder of 5.
The answer is A.
Answer: (A) 5
Question: A meal cost $ 32.50 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:
(A) 40-42
(B) 39-41
(C) 38-40
(D) 37-39
(E) 36-37
Rationale: 10%(32.5) = 3.25
15%(32.5) =4.875
total amount could have been 32.5+3.25 and 32.5+4.875
=> could have been between 35.75 and 37.375
=> approximately between 36 and 37
Answer is E.
Answer: (E) 36-37
Question: x and y are integers. a+ b< 11 , and a> 6. What is the smallest possible value of a- b?
(A) 1
(B) 2
(C) 4
(D) -2
(E) -4
Rationale: Focus on the transition points and plug in the values.
a> 6 so a could be 7, 8, 9, 10, 11 etc
Look at a= 7
7 + b< 11
b< 4
b could be 3, 2, 1, 0, -1 etc
When b is 3, we get a- b= 4
This must be the smallest value because as a increases, b reduces so a- b increases.
Take another example. a= 11 so b< 0.
a- b will give a value greater than 11.
Answer (C).
Answer: (C) 4
Question: Today Joelle opened an interest-bearing savings account and deposited $5,000. If the annual interest rate is 5 percent compounded interest, and she neither deposits nor withdraws money for exactly 2 years, how much money will she have in the account?
(A) $6512.50
(B) $7512.50
(C) $5512.50
(D) $4512.50
(E) $5250.00
Rationale: Interest for 1st year = 5000*5/100 = 250
Interest for 2nd year = 5250 *5/100 = 262.50
Total =5000+250+262.50 = 5512.50
Answer : C
Answer: (C) $5512.50
Question: One train is traveling 36 kmph and other is at 15 meters a second. Ratio of the speed of the two trains is?
(A) 5:4
(B) 5:6
(C) 5:0
(D) 2:3
(E) 5:1
Rationale: 36 * 5/18 = 15
10:15 => 2:3
Answer: D
Answer: (D) 2:3
Question: How many pairs (r, r+1) have one or more prime factors common, where r is an integer and 2 ≤ r ≤9 ?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: r and r+1 are consecutive integers.
Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1. For example 20 and 21 are consecutive integers, thus only common factor they share is 1.
Answer: A.
Answer: (A) 0
Question: A juice manufacturer organized taste-testing sessions featuring four brands of orange juice, A, B, C and D. All customers who participated told the organizer which variety they thought was the most similar to freshly-squeezed orange juice. 61% preferred brand A and exactly half as many preferred brand B. Only 60 chose brand C. Which of the following could be the number of customers who preferred brand D?
(A)  1
(B)  8
(C)  18
(D)  20
(E)  27
Rationale: I get D, but I'm not sure that my method is sound.
You have A + B + C + D = total testers. Stating the variety they think is most similar to freshly squeezed orange juice means each person should get 1 vote.
x = total number of testers
A + B + C + D
.61x + (.5)(.61x) + 65 + D = x
.61x + .305x + 65 + D = x
I took total testers = 1000 because that gives me nice numbers to deal with. Also, if I use 200 total testers, that gives me A = 122, B = 61, C = 65...that's over 200 without considering D.
x = 400
A = 244, B = 122, C = 65..also over 400
x = 600
A = 366, B = 183 C = 65....also over 600
x = 800
A = 488, B = 244, C = 65...D = 3...not an option on the list.
x = 1000
A = 610 B = 305 C = 65 D = 18....the first time I get an answer that is an option in the question.
C
Answer: (C)  18
Question: The perimeter of one square is 48 cm and that of another is 20 cm. Find the perimeter and the diagonal of a square which is equal in area to these two combined?
(A) 13√6
(B) 13√2
(C) 13√9
(D) 13√1
(E) 13√5
Rationale: 4a = 48 4a = 20
a = 12 a = 5
a2 = 144 a2 = 25
Combined area = a2 = 169 => a = 13
d = 13√2
Answer: B
Answer: (B) 13√2
Question: The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles?
(A) 2898 sq m
(B) 1788 sq m
(C) 4312 sq m
(D) 7656 sq m
(E) 1786 sq m
Rationale: Let the radii of the smaller and the larger circles be s m and l m respectively.
2∏s = 264 and 2∏l = 352
s = 264/2∏ and l = 352/2∏
Difference between the areas = ∏l2 - ∏s2
= ∏{1762/∏2 - 1322/∏2}
= 1762/∏ - 1322/∏
= (176 - 132)(176 + 132)/∏
= (44)(308)/(22/7) = (2)(308)(7)
= 4312 sq m
Answer:C
Answer: (C) 4312 sq m
Question: P is 40% more efficient than Q. P can complete a work in 24 days. If P and Q work together, how many days will it take to complete the same work?
(A) 8
(B) 9
(C) 11
(D) 14
(E) 15
Rationale: The work done by P in 1 day = 1/24
Let work done by Q in 1 day = q
q × (140/100) = 1/24
q = 100/(24×140) = 10/(24×14)
The work done by P and Q in 1 day = 1/24 + 10/(24×14) = 24/(24×14)= 1/14
P and Q together can do the work in 14 days.
The answer is D.
Answer: (D) 14
Question: The average of five consecutive odd numbers A, B, C, D and E is 33. What percent of A is D ?
(A) 86.8
(B) 88.6
(C) 89.2
(D) 90.1
(E) 92.2
Rationale: Explanation :
In such a case the middle number (C) is the average
∴ C = 33 and A = 31 and D = 35
Required percentage = 31/35 x 100 = 88.6
Answer : Option B
Answer: (B) 88.6
Question: Three photographers, Lisa, Mike and Norm, take photos of a wedding. The total of Lisa and Mikes photos is 40 less than the sum of Mike's and Norms. If Norms photos number 10 more than twice the number of Lisa's photos, then how many photos did Norm Take?
(A) 40
(B) 50
(C) 70
(D) 80
(E) 90
Rationale: L+M=M+N-40 / N=2L+10
40=M+N-L-M
40=N-L
40=2L+10-L
30=L
2(30)+10=70
C
Answer: (C) 70
Question: A is twice as good a workman as B and they took 7 days together to do the work B alone can do it in.
(A) 23 days
(B) 25 days
(C) 21 days
(D) 26 days
(E) 29 days
Rationale: C
21 days
WC = 2:1
2x + x = 1/7
x = 1/21 => 21 days
Answer: (C) 21 days
Question: A pupil's marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half (1/2). The number of pupils in the class is:
(A) 32
(B) 50
(C) 40
(D) 20
(E) 10
Rationale: Let there be x pupils in the class.
Total increase in marks = x x 1/2 = x/2
x/2 = (83 - 63)
x/2	= 20
x= 40.
Answer: C
Answer: (C) 40
Question: Present ages of X and Y are in the ratio 5:6 respectively. Ten years hence this ratio will become 6:7 respectively. What is X's present age in years?
(A) 35
(B) 36
(C) 50
(D) 39
(E) 40
Rationale: Let the present ages of X and Y be 5x and 6x years respectively.
Then, (5x + 10)/(6x + 10) = 6/7
7(5x +10) = 6(6x +10) => 35x+70= 36x+60 => x=10
X's present age = 5x = 5*10 = 50
ANSWER:C
Answer: (C) 50
Question: A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 250 km of the tour is:
(A) 55.55 km/hr
(B) 35.55 km/hr
(C) 71.11 km/hr
(D) 36 km/hr
(E) 71 km/hr
Rationale: Total time taken = 160/64 + 160/80 = 9/2 hours
--> Average speed = 250 x 2/9 = 55.55 km/hr.
Answer : A.
Answer: (A) 55.55 km/hr
Question: A man rows his boat 75 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
(A) 6
(B) 7
(C) 5
(D) 8
(E) 9
Rationale: Speed downstream = d/t = 75/(2 1/2) = 30 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (30 - 18)/2
= 6 kmph
Answer: A
Answer: (A) 6
Question: The average of six numbers is 3.85. The average of two of them is 3.4, while the average of the other two is 3.85. What is the average of the remaining two numbers ?
(A) 4.3
(B) 4.6
(C) 4.2
(D) 4.1
(E) 4.9
Rationale: Explanation:
Sum of the remaining two numbers = (3.85 * 6) - [(3.4 * 2) + (3.85 * 2)]
= 23.10 - (6.8 + 7.7) = 23.10 - 14.5 = 8.60.
Required average = (8.6 / 2) = 4.3.
Answer: A) 4.3
Answer: (A) 4.3
Question: A small beaker is 1/2 filled with salt water. Another beaker, which has five times the capacity of the small beaker, is 1/4 filled with fresh water. After dumping all of the salt water from the small beaker into the large beaker, to what fraction of its capacity will the large beaker be filled?
(A) 7/20
(B) 9/20
(C) 11/20
(D) 13/20
(E) 17/20
Rationale: 1/2 of the small beaker is 1/10 of the large beaker.
1/10 + 1/4 = 7/20
The answer is A.
Answer: (A) 7/20
Question: What will be remainder when (67^67 + 67) is divided by 68 ?
(A) 5
(B) 9
(C) 87
(D) 66
(E) 12
Rationale: Explanation:
(x^n + 1) will be divisible by (x + 1) only when n is odd.
(67^67 + 1) will be divisible by (67 + 1)
(67^67 + 1) + 66, when divided by 68 will give 66 as remainder.
D
Answer: (D) 66
Question: In how many ways can the letters of the english alphabet be arranged so that there are seven letter between the letters A and B, and no letter is repeated
(A) 24P7 * 2 * 18!
(B) 24P7 * 2 * 17!
(C) 24P7 * 2 * 16!
(D) 24P7 * 2 * 13!
(E) 24P7 * 2 * 12!
Rationale: We can fix A and B in two ways with 7 letters in between them. Now 7 letters can be selected and arranged in between A and B in 24P724P7 ways. Now Consider these 9 letters as a string. So now we have 26 - 9 + 1 = 18 letters
These 18 letters are arranged in 18! ways. So Answer is 2 x 24P724P7 x 18!
Infact, 2 x 24P724P7 x 18! = 36 x 24!. So go for Option B as it was given as OA.
Answer:A
Answer: (A) 24P7 * 2 * 18!
Question: A train 600 m long can cross an electric pole in 20 sec and then find the speed of the train?
(A) 76 Kmph
(B) 108 Kmph
(C) 72 Kmph
(D) 34 Kmph
(E) 91 Kmph
Rationale: Length = Speed * time
Speed = L/T
S = 600/20
S = 30 M/Sec
Speed= 30*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 108 Kmph
Answer: B
Answer: (B) 108 Kmph
Question: The amount of principal Rs.8000 at compound interest at the ratio of 5% p.a. for 1 year is
(A) s.9621
(B) s.6921
(C) s.8400
(D) s.6261
(E) s.6361
Rationale: c.i=p(1+r/100)^n
=8000(1+5/100)
=Rs8400
ANSWER:C
Answer: (C) s.8400
Question: The equation (M )/42 = (p – 7)/21 relates two temperature scales, where M is the number of degrees on one scale and P is the number of degrees on the other scale. Which of the following equations can be used to convert temperatures from the P scale to the M scale?
(A) P
(B) P-7
(C) (P-7)*2
(D) (P-7)62
(E) P-5
Rationale: M/42 =(P-7)/21
M = (P-7)*42/21
=(P-7)*2
C
Answer: (C) (P-7)*2
Question: If 2^5, 4^3, and 13^2 are all factors of the product of 936 and w where w is a positive integer, what is the smallest possible value of w?
(A) 26
(B) 39
(C) 42
(D) 208
(E) 156
Rationale: Here 156 has three two's
two three's
and one 13
rest of them must be in w
so w= 13*4*4 = 208
Smash D
Answer: (D) 208
Question: A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of the son is?
(A) 11
(B) 25
(C) 27
(D) 22
(E) 91
Rationale: Let the son's present age be x years.
Then, man's present age = (x + 24) years.
(x + 24) + 2 = 2(x + 2) x + 26 = 2x + 4 => x = 22.
Answer: D
Answer: (D) 22
Question: If 9/(5 + 3/x) = 1, then x =
(A) 3
(B) 1
(C) 3/4
(D) -1/3
(E) -3
Rationale: The expression 9/(5 + 3/x) = 1 should have been equal to something .
If 9/(5 + 3/x) = 1
=> 9x/(5x+3)= 1
=> 9x= 5x + 3
=>4x = 3
=>x = 3/4
Correct Option : C
Answer: (C) 3/4
Question: In how many ways can the integer 15 be expressed as a product of two different positive integers?
(A) 10
(B) 8
(C) 5
(D) 4
(E) 2
Rationale: 15=3*5
Since 15 is not a perfect square, no of ways=2
Answer E
Answer: (E) 2
Question: The average amount with a group of seven numbers is Rs. 20. If the newly joined member has Rs. 62 with him, what was the average amount with the group before his joining the group?
(A) s.13
(B) s.12
(C) s.15
(D) s.22
(E) s.14
Rationale: Total members in the group = 7
Average amount = Rs. 20
Total amount with them = 7 * 20 = Rs. 140
One number has Rs. 62. So, the amount with remaining 6 people = 140 - 62 = Rs. 78
The average amount with them = 78/6 = Rs.13.
Answer:A
Answer: (A) s.13
Question: A train , 800 meter long is running with a speed of 78 km/hr. It crosses a tunnel in 1 minute. What is the length of the tunnel (in meters)?
(A) 440 m
(B) 500 m
(C) 260 m
(D) 430 m
(E) 450 m
Rationale: Explanation:
Distance = 800+x meter where x is the length of the tunnel
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78×10/36 m/s = 130/6 = 65/3 m/s
Distance/time = speed
(800+x)/60 = 65/3
=> 800+x = 20×65 = 1300
=> x = 1300 - 800 = 500 meter
Answer: Option B
Answer: (B) 500 m
Question: The diagonals of two squares are in the ratio of 3:7 then find the ratio of its areas?
(A) 7:37
(B) 6:46
(C) 9:49
(D) 8:68
(E) 6:61
Rationale: Let the diagonals of the squares be 3x and 7x
Ratio of their areas = 1/2 (3x)^2 : 1/2 (7x)^2 = 9x^2 : 49x^2 = 9:49
Answer is C
Answer: (C) 9:49