mathewhe/aqua_rat huggingface dataset:
Question: The average of four positive integers is 69. The highest integer is 93 and the least integer is 39. The difference between the remaining two integers is 28. Which of the following integers is the higher of the remaining two integers?
(A) 32
(B) 86
(C) 44
(D) 22
(E) 55
Rationale: Let the four integers be A, B, C and D where A > B > C > D.
(A + B + C + D)/4 = 69 => A + B + C + D = 276 ---> (1)
A = 93, D = 39 and B - C = 28
(1) => B + C = 276 - (A + D) = 276 - 132 = 144.
B + B -28 = 144
B = (144 + 28)/2 = 86
Answer:Option B
Answer: (B) 86
Question: A man can row 8 km/hr in still water. If the river is running at 3 km/hr, it takes 3 hours more in upstream than to go downstream for the same distance. How far is the place?
(A) 32.5 km
(B) 25 km
(C) 27.5 km
(D) 22.5 km
(E) None of these
Rationale: Explanation :
Let the speed downstream = x and speed updstream = y
Then
(x+y)/2=8
=> x + y = 16 ---(Equation 1)
(x−y)/2=3
=> x - y = 6 ---(Equation 2)
(Equation 1 + Equation 2) = > 2x = 22
=> x = 11 km/hr
(Equation 1 - Equation 2) = > 2y = 10
=>y = 5 km/hr
Time taken to travel upstream = Time taken to travel downstream + 3
Let distance be x km
Then
x/5 = (x/11) + 3
=> 11x = 5x + 165
=> 6x = 165
=> 2x = 55
=> x = 27.5. Answer : Option C
Answer: (C) 27.5 km
Question: he total marks obtained by a student in Physics, Chemistry and Mathematics is 180 more than the marks obtained by him in Physics. What is the average mark obtained by him in Chemistry and Mathematics?
(A) 55
(B) 65
(C) 75
(D) 85
(E) 90
Rationale: Let the marks obtained by the student in Physics, Chemistry and Mathematics be P, C and M respectively.
P + C + M = 180 + P
C + M = 180
Average mark obtained by the student in Chemistry and Mathematics = (C + M)/2 = 180/2 = 90.
ANSWER:E
Answer: (E) 90
Question: Find the value of 72519 x 9999 = m?
(A) 345434667
(B) 246465757
(C) 465767867
(D) 725117481
(E) 645354643
Rationale: 72519 x 9999 = 72519 x (10000 - 1)
= 72519 x 10000 - 72519 x 1
= 725190000 - 72519
= 725117481
D
Answer: (D) 725117481
Question: If the personal income tax rate is lowered from 46% to 32%, what is the differential savings for a tax payer having an annual income before tax to the tune of $36000?
(A) $3500
(B) $5040
(C) $3150
(D) $7000
(E) $10000
Rationale: Saving = (46-32)% of 36000 = 5040.
Answer:B
Answer: (B) $5040
Question: When running a mile during a recent track meet, Nuria was initially credited with a final time of 7 minutes, 44 seconds. Shortly after her run, officials realized that the timing mechanism malfunctioned. The stopwatch did not begin timing her until 11/25 of a minute after she began to run. If the time was otherwise correct, how long did it actually take Nuria to run the mile?
(A) 8 minutes, 10.4 seconds
(B) 5 minutes, 21.8 seconds
(C) 5 minutes, 43.56 seconds
(D) 5 minutes, 44.44 seconds
(E) 5 minutes, 17.6 seconds
Rationale: One approach:
The watch starts to work after Nuria began his running. It means the time should be greater than credited 7 minutes, 44 seconds. The only number is 8 minutes, 10.4 seconds.
Another approach:
11/25 close to 30 second when added to the 7 minutes, 44 seconds, it means it passes 8 minute.
Answer: A
Answer: (A) 8 minutes, 10.4 seconds
Question: A man can row upstream at 25 kmph and downstream at 45 kmph, and then find the speed of the man in still water?
(A) 11
(B) 77
(C) 30
(D) 88
(E) 35
Rationale: US = 25
DS = 45
M = (45 + 25)/2 = 35
Answer:E
Answer: (E) 35
Question: Difference between two numbers is 5, six times of the smaller lacks by 6 from the four times of the greater. Find the numbers?
(A) 5,14
(B) 6,4
(C) 12,7
(D) 7,5
(E) 4,7
Rationale: Answer: Option C
x â€“ y = 5
4x â€“ 6y = 6
x = 12 y = 7
Answer: (C) 12,7
Question: In a village there are 20 men and 25 women. In how many ways can a man and a woman be selected?
(A) 200
(B) 300
(C) 500
(D) 600
(E) 650
Rationale: We can select one men from 20 women in 20 ways.
We select one woman from 25 women in 25 ways
We select a Men and women in 20 * 25 ways i.e., = 500 ways.
C
Answer: (C) 500
Question: A and B can do a work in 5 days, B and C in 15 days and C and A in 25 days. In how many days will the work be completed, if all three of them work together?
(A) 26/18
(B) 42/15
(C) 48/63
(D) 12/36
(E) 150/23
Rationale: One day work of A and B = 1/5
One day work of B and C = 1/15
One day work of C and A = 1/25
2(A + B + C) = 1/5+ 1/15 + 1/25
2(A + B + C) = 23/75
(A + B + C) = 23/150
Number of days required = 150/23 days.
Answer: E
Answer: (E) 150/23
Question: Martin bought 10 concert tickets, some at the full price of $2.00 per ticket, and some at a discounted price of $1.60 per ticket. If he spent a total of $19.20, how many discounted tickets did he buy?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 2
Rationale: Let x be the number of tickets he bought at $2 per ticket.
then 2 x + (10-x)1.6 = 19.2
0.4x = 3.2 => x = 8
discounted tickets = 10 -x = 2
Ans : E
Answer: (E) 2
Question: If an article is sold at 19% profit instead of 12% profit, then the profit would be $84 more. What is the cost price?
(A) $900
(B) $1200
(C) $1500
(D) $1800
(E) $2100
Rationale: 7% * cost price = $84
1% * cost price = $84 / 7 = $12
The cost price is $1200.
The answer is B.
Answer: (B) $1200
Question: In a survey of 350 employees, 104 of them are uninsured, 54 work part time, and 12.5 percent of employees who are uninsured work part time. If a person is to be randomly selected from those surveyed, what is the probability that the person will neither work part time nor be uninsured?
(A) 7/12
(B) 8/41
(C) 9/348
(D) 1/8
(E) 41/70
Rationale: ---------UI----------------NUI-------Total
PT----(12.5/100)*104 = 13----------- --54
NPT---104-13-------------- x--------296
Total--104----------------------------350
we have to find not part time and not uninsured . in other words not part time and insured = x/350 = (296-104+13)/350
= 41/70
Answer is E.
Answer: (E) 41/70
Question: A thief steals at a car at 2.30 p.m. and drives it at 60 km/hr. The theft is discovered at 3 p.m. and the owner sets off in another car at 80 km/hr. When will he overtake the thief?
(A) 6:30 p.m
(B) 9:30 p.m
(C) 4:30 p.m
(D) 2:30 p.m
(E) 1:30 p.m
Rationale: :
Suppose the thief is overtaken x hrs after 2.30 p.m.
Then, distance covered by the owner in (x - 1/2) hrs.
60x = 80(x - 1/2) => x = 2 hrs.
So, the thief is overtaken at 4:30 p.m.'
Answer: C
Answer: (C) 4:30 p.m
Question: The 540 students in a group are to be seated in rows so that there is an equal number of students in each row. Each of the following could be the number of rows EXCEPT
(A)  4
(B)  20
(C)  30
(D)  60
(E)  90
Rationale: Obviously the number of rows must be a factor of 540. The only option which is not a factor of 540 is A (4).
Answer: A.
Answer: (A)  4
Question: If Josh, Doug, and Brad have a total of $68 between them, and Josh has two times as much money as Brad but only three-fourths as much as Doug, how much money does Doug have?
(A) $8
(B) $9
(C) $27
(D) $32
(E) $36
Rationale: Josh+Doug+Brad = 68 ; Josh = 2 Brad, Josh =3/4 Doug
Josh+1/2 Josh+ 4/3 Josh = 68 (substituted the given values)
Josh = 24. 24= 3/4 Doug => Doug =32
Answer is D.
Answer: (D) $32
Question: A rectangular metallic piece of paper that covers exactly the area of a cube. The length of the piece of paper is 96 inches and the width is 72 inches. What is the volume of the cube in cubic feet is 1 feet is 12 inches?
(A) a 64
(B) b 22
(C) c 27
(D) d 40
(E) e 50
Rationale: l = 96 /12 = 8 ft
w = 72 / 12 = 6 ft
Area of paper = 48
Area of cube = 8 * side^2
side of cube = 4
V of cube = 64
Answer: (A) a 64
Question: A man invested Rs. 4455 in Rs. 10 shares quoted at Rs. 8.25. If the rate of dividend be 12%, his annual income is:
(A) 242
(B) 297
(C) 648
(D) 267
(E) 108
Rationale: Number of shares = 4455 = 540.
8.25
Face value = Rs. (540 x 10) = Rs. 5400.
Annual income = Rs. 12	x 5400 = Rs. 648.
100
Answer: C
Answer: (C) 648
Question: A train 110 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
(A) 5 sec
(B) 6 sec
(C) 7 sec
(D) 10 sec
(E) 12 sec
Rationale: Speed of train relative to man = 60 + 6 = 66 km/hr.
= 66 * 5/18 = 55/3 m/sec.
Time taken to pass the men = 110 * 3/55 = 6 sec.
ANSWER:B
Answer: (B) 6 sec
Question: In a partnership between A, B and C. A's capital is Rs.8000. If his share of a profit of Rs.800 is Rs.200 and C's share is Rs.130, what is B's capital?
(A) 19878
(B) 12798
(C) 26908
(D) 11750
(E) 18800
Rationale: 200 + 130 = 330
800 - 330 = 470
200 ---- 8000
470 ---- ? => 18800
Answer: E
Answer: (E) 18800
Question: If two sides of a triangle are 6 and 10, respectively, which of the following could NOT be the area of this triangle?
(A) 1
(B) 6
(C) 17
(D) 38
(E) 29
Rationale: For this question it would be helpful to know the largest area that this triangle could be, given the two sides of 6 and 10.
We know that the area of a triangle will be maximized when two sides are perpendicular to each other (consult Bunuel's drawing above). Thus we have a max area being equal to one half the base times the height, either (.5)10 * 6 -or- (.5)6 * 10 will result in a maximum area of 30 for the triangle; therefore, the triangle could never have an area of 38.
D
Answer: (D) 38
Question: What is the area of a triangle with the following vertices L(2, 3), M(5, 1), and N(3, 5) ?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: There is a direct formula to calculate the are of a triangle based on coordinates of its vertices and one could use it to solve this problem.
Though if you make a diagram minimum simple calculations will be needed:
Answer: B.
Answer: (B) 4
Question: The C.P of 17 books is equal to the S.P of 18 books. Find his gain% or loss%?
(A) 16 2/3%
(B) 16 2/8%
(C) 5 5/9%
(D) 16 2/1%
(E) 16 1/3%
Rationale: 17 CP = 18 SP
18 --- 1 CP loss
100 --- ? => 5 5/9% loss.Answer: C
Answer: (C) 5 5/9%
Question: 18 men working 8 hours per day dig 30 m deep. How many extra men should be put to dig to a depth of 50 m working 6 hours per day?
(A) 22
(B) 66
(C) 88
(D) 100
(E) 281
Rationale: (18 * 8)/30 = (x * 6)/50 => x =40
40 – 18 = 22
Answer: A
Answer: (A) 22
Question: Oranges are purchased for $15/bag at the Farmer's Market. A bag weighs 3 lbs. The oranges are peeled and the seeds removed (removing 1/6 of the weight). Then, these oranges are crushed and used for making marmalade. It takes 1 lb of oranges to make 3 cups of crushed oranges. If 4 cups of crushed oranges can make one jar of marmalade, how much money is needed to buy oranges to make x number of jars of marmalade, in dollars?
(A) 8x/3
(B) 4x
(C) 8x
(D) 2x
(E) 3x/2
Rationale: Initial cost for a bag = $15; since 1 bag = 3 lbs, 1 lb = $15/3, but ONLY 5/6 is used.
So the cost of 5/6 lb = $5, or 1 lb = $30/5,
and 1 lb of oranges = 2 cups of crushed oranges, so 2 cups of oranges costs $30/5, but 4 cups are needed for 1 jar, so cost of 4 cups = $(30/5)(4/3) = $120/15 = $8
If 1 jar costs $8, x number of jars will cost $8x.
Answer is C
Answer: (C) 8x
Question: If two numbers are in the ratio 2:3 and the numerator and denominator are added and subtracted by1 and 2 respectively, then the ratio becomes 6:2, then find the biggest number?
(A) 2
(B) 5
(C) 3
(D) 4
(E) 6
Rationale: 2:3
2x + 1 : 3x - 2 = 3 : 1
[2x + 1] = 3[3x - 2]
2x + 1= 9x -6
9x - 2x = 7
x = 1
Then smallest number is = 3x
3x = 3
C
Answer: (C) 3
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 190 m long?
(A) 40 sec
(B) 11 sec
(C) 88 sec
(D) 19 sec
(E) 44 sec
Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 190 = 550 m
Required time = 550 * 2/25 = 44 sec
Answer: E
Answer: (E) 44 sec
Question: The president of a country and 6 other dignitaries are scheduled to sit in a row on the 7 chairs represented above. If the president must sit in the center chair, how many different seating arrangements are possible for the 5 people?
(A)  720
(B)  5
(C)  20
(D)  24
(E)  120
Rationale: IMO A
Given that one chair is taken, i think the remaining 6 dignitaries can be arranged 6!. That is 6*5*4*3*2*1=720.
Answer: (A)  720
Question: A man swims downstream 45 km and upstream 25 km taking 5 hours each time, what is the speed of the man in still water?
(A) 17
(B) 24
(C) 7
(D) 24
(E) 20
Rationale: 45--- 5 DS = 9
? ---- 1
25 --- 5 US = 5
? ---- 1 M = ?
M = (9+ 5)/2 = 14/2=7
Answer: C
Answer: (C) 7
Question: A person completes half distance of marathon in 20 min including 7 minutes of break time.He runs at 5m/s. Then what is total distance covered if he runs at constant speed and takes only one break in entire marathon.
(A) 8km
(B) 7.8km
(C) 9km
(D) 6.1km
(E) 7km
Rationale: Considering and removing break he runs only for 13 min ie 780 s.So total time =780*2=1560.
Total distance =1560*5=7800m
Thus 7.8km
Answer:B
Answer: (B) 7.8km
Question: Pavan travelled for 11 hours. He covered the first half of the distance at 30 kmph and remaining half of the distance at 25 kmph. Find the distance travelled by Pavan?
(A) 288
(B) 266
(C) 129
(D) 300
(E) 276
Rationale: Let the distance travelled be x km.
Total time = (x/2)/30 + (x/2)/25 = 11 => x/60 + x/50 = 11 => (5x + 6x)/300 = 11
=> x
= 300 km
Answer:D
Answer: (D) 300
Question: A train ,130 meters long travels at a speed of 45 km/hr crosses a bridge in 30 seconds. The length of the bridge is
(A) 270 m
(B) 245 m
(C) 235 m
(D) 220 m
(E) 240 m
Rationale: Explanation:
Assume the length of the bridge = x meter
Total distance covered = 130+x meter
total time taken = 30s
speed = Total distance covered /total time taken = (130+x)/30 m/s
=> 45 × (10/36) = (130+x)/30
=> 45 × 10 × 30 /36 = 130+x
=> 45 × 10 × 10 / 12 = 130+x
=> 15 × 10 × 10 / 4 = 130+x
=> 15 × 25 = 130+x = 375
=> x = 375-130 =245
Answer: Option B
Answer: (B) 245 m
Question: A can do a piece of work in 10 days and B can do it in 15 days and C can do it 20 days. They started the work together and B leaves after 2 days and C leaves after 4 days from the beginning. How long will work lost?
(A) 3 2/3
(B) 5 2/3
(C) 6 2/3
(D) 4 2/3
(E) 7 2/3
Rationale: x/10 + 2/15 + 4/20 = 1
x = 40/60*10 = 6 2/3
Answer: C
Answer: (C) 6 2/3
Question: If 4XZ + YW = 5 and XW + YZ = 10, what is the value of the expression (2X + Y)(2Z + W)?
(A) 9.
(B) 12.
(C) 15.
(D) 16.
(E) 25
Rationale: (2x+y)*(2z+w) = 5+2(10) =25
Answer : E
Answer: (E) 25
Question: It is given that 2^32 + 1 is exactly divisible by a certain number. Which one of the following is also divisible by the same number Q?
(A) a. 2^96 + 1
(B) b. 2^16 - 1
(C) c. 2^16 + 1
(D) d. 7 * 2^33
(E) e. 2^64 + 1
Rationale: a³ + b³ =(a+b)(a² -ab +b²)
Now, let (2^32 + 1) be (a+b)
a³ + b³ = (2^96 + 1)
Now, as mentioned in formula above,
a³ + b³ is always divisible by (a+b)
So any factor of Q= (a+b) is a factor of (a³ + b³)
Henca A
Answer: (A) a. 2^96 + 1
Question: To be considered for “movie of the year,” a film must appear in at least 1/4 of the top-10-movies lists submitted by the Cinematic Academy’s 765 members. What is the smallest number of top-10 lists a film can appear on and still be considered for “movie of the year”?
(A) 191
(B) 192
(C) 193
(D) 212
(E) 213
Rationale: Total movies submitted are 765.
As per question we need to take 1/4 of 765 to be considered for top 10 movies = 191.25
approximate the value we 192.
Answer:option B is the correct answer..
Answer: (B) 192
Question: If a is a positive integer then 2^(2a) + (16^a)/(2^(2a)) =
(A) 4^a
(B) 8^a
(C) 10^a
(D) 2/4^a
(E) 2 × 4^a
Rationale: 2^(2a) + 16^a/ 2^(2a) = 4^a + 16^a/4^a = 4^a + (16/4)^a = 4^a + 4^a = 2 × 4^a
Answer : E
Answer: (E) 2 × 4^a
Question: A man can cover a distance in 1hr 24min by covering 2/3 of the distance at 4 km/h and the rest at 5km/h. The total distance is
(A) 5km
(B) 6km
(C) 7km
(D) 8km
(E) 9km
Rationale: Distance = 2/3S
distance=1-2/3S=1/3S
21/15 hr=2/3 S/4 + 1/3s /5
84=14/3S * 3
S= 6km
Answer : B
Answer: (B) 6km
Question: A certain quantity is measured on two different scales, the A-scale and the S-scale, that are related linearly. Measurements on the A-scale of 6 and 24 correspond to measurements on the S-scale of 30 and 60, respectively. What measurement on the A-scale corresponds to a measurement of 100 on the S-scale?
(A)  20
(B)  36
(C)  48
(D)  60
(E)  84
Rationale: First, we have to understand what linearly means. It's not a straight ratio (since 6:30 does NOT equal 24:60). We need to look at the increases in each measurement to see what the scalar actually is.
From 6 to 24 we have an increase of 18. From 30 to 60 we have an increase of 30. Therefore, the increase ratio is 18:30 or 3:5. In other words, for every 3 that A increases, S increases by 5.
We know that S is 100. To get from 60 to 100, we went up by 40, or 8 jumps of 5; therefore, A will go up by 8 jumps of 3.
24 + 8(3) = 24 + 24 = 48=C
Answer: (C)  48
Question: Find the compound interest on $10000 in 2years at 4% per annum, the interest being compounded half-yearly?
(A) $645.56
(B) $824.32
(C) $954.26
(D) $745.69
(E) $1020.45
Rationale: Principle = $10000
Rate = 2% half yearly = 4 half years
Amount = 10000*(1 + 2/100)^4 = 10000 * 51/50 * 51/50 * 51/50 * 51/50
= $10824.32
C.I. = 10824.32-10000 = $824.32
Answer is B
Answer: (B) $824.32
Question: The speed at which a woman can row a boat in still water is 30 kmph. If he rows downstream, where the speed of current is 6 kmph, what time will he take to cover 100 metres?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: Speed of the boat downstream = 30 + 6 = 36 kmph
= 36 * 5/18 = 10 m/s
Hence time taken to cover 100 m = 100/10 = 10 seconds. Answer: C
Answer: (C) 10
Question: In the faculty of Reverse-Engineering, 250 second year students study numeric methods, 423 second year students study automatic control of airborne vehicles and 134 second year students study them both. How many students are there in the faculty if the second year students are approximately 80% of the total?
(A) 515.
(B) 545.
(C) 618.
(D) 674.
(E) 666.
Rationale: Answer is D :674
Solution : Total number of students studying both are 423 + 250 - 134 = 539 (Subtracting the 134 since they were included in the both the other numbers already).
So 80% of total is 539, so 100% is approx. 674.
Answer: (D) 674.
Question: 8597-?=7429-4358
(A) 5426
(B) 5706
(C) 5526
(D) 5476
(E) None of them
Rationale: Let 8597-x=3071
Then x = 8597-3071
=5526
Answer is C
Answer: (C) 5526
Question: On dividing a number by 7, we get 5 as quotient and 0 as remainder. On dividing the same number by 11, what will be the remainder?
(A) 2
(B) 5
(C) 8
(D) 1
(E) 3
Rationale: Number = 7 * 5+ 0 = 35
11) 35 (3
33
--------
2
Required number = 2.
ANSWER:A
Answer: (A) 2
Question: An auto assembly plant performs six functions with each frame that arrives: add axles, add wheels to the axles, install the windshield to the frame, install the instrument panel, install the steering wheel, and install the interior seating. Once those six tasks are performed, each car goes to a separate building for finishing touches. If these tasks can be arranged along a linear assembly line in any order, except that the axles must be installed before the wheels can be added, how many R ways can the assembly line be arranged?
(A) 120
(B) 240
(C) 360
(D) 480
(E) 720
Rationale: C) 360
short way: there are 6C! ways to do the six tasks. Half will have wheels before axles and half will have axles before wheels. So we want R=6C!/2 -> 720/2 = 360
Answer: (C) 360
Question: The average age of a group of persons going for picnic is years. Sixteen new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years. The number of persons initially going for picnic is
(A) 5
(B) 10
(C) 16
(D) 45
(E) 52
Rationale: Solution
Let the initial number of persons be x. Then
16x + 16 x 15 = 15.5(x+20)
= 0.5x = 8
x = 16
Answer C
Answer: (C) 16
Question: In the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30. In the sport formulation, the ratio of flavoring to corn syrup is three times as great as in the standard formulation, and the ratio of flavoring to water is half that of the standard formulation. If a large bottle of the sport formulation contains 8 ounces of corn syrup, how many ounces of water does it contain?
(A) 45
(B) 50
(C) 55
(D) 60
(E) 120
Rationale: F:C:W
1:12:30
Sport version:
F:C
3:12
F:W
1:60
OR 3:180
So C:F:W = 12:3:180
C/W = 12/180 = 3 ounces/x ounces
x = 8*180/12 = 120 ounces of water
E
Answer: (E) 120
Question: P cando a work in 15 days and Q cando the same work in 20 days. If they can work together for 4 days, what is the fraction of work left?
(A) 1/15
(B) 2/13
(C) 8/15
(D) 7/15
(E) 5/13
Rationale: Amount of work P can do in 1 day = 1/15
Amount of work Q can do in 1 day = 1/20
Amount of work P and Q can do in 1 day = 1/15 + 1/20 = 7/60
Amount of work P and Q can together do in 4 days = 4 × (7/60) = 7/15
Fraction of work left = 1 – 7/15= 8/15
C
Answer: (C) 8/15
Question: If the height of a right cone C is 3 and the diameter of the base of C is 8, what is the distance from the apex of C to any point on the circumference of the base of C?
(A) 3√2
(B) 5
(C) 5√2
(D) √(67)
(E) √(73)
Rationale: height of cone=3
radius of base=4
so the distance from the apex of C to any point on the circumference of the base of C will be a right angled triangle
Hence the distance is sqrt(3^2+4^2)= 5
ANSWER:B
Answer: (B) 5
Question: Two pipes A and B can fill a tank in 4 and 5 hours respectively. If they are turned up alternately for one hour each, the time taken to fill the tank is?
(A) 4 hrs
(B) 4 hrs 24 min
(C) 4 hrs 26 min
(D) 4 hrs 04 min
(E) 4 hrs 22 min
Rationale: 1/4 + 1/5 = 9/20
20/9 = 2 2/9
9/20 * 2 = 9/10 ---- 4 hours
WR = 1 - 9/10 = 1/10
1 h ---- 1/4
? ----- 1/10
2/5 * 60 = 24 = 4 hrs 24 min
Answer:B
Answer: (B) 4 hrs 24 min
Question: What is 25% of 25% equal to
(A) 0.625
(B) 0.0625
(C) 6.25
(D) 0.00625
(E) None
Rationale: Solution
25% of 25% = 25 / 100 x 25 / 100
= 1 / 16
= 0.0625
Answer D
Answer: (D) 0.00625
Question: There are six cards in which it has two king cards. all cards are turned down and two cards are opened :
a) what is the possibility to get at least one king.
b) what is the possibility to get two kings.
(A) a = 1/15 , b = 3/5
(B) a = 3/5 , b = 1/15
(C) a = 2/15 , b = 4/5
(D) a = 6/15 , b = 3/5
(E) a = 6/15 , b = 7/5
Rationale: Explanation :
a)
POSSIBILITY TO GET AT LEAST ONE KING IS :
=> = 2C1* 4C1/6C2 + 2C2/6C2
=> = 8/15+1/15
=> = 3/5
b)
P0SSIBLITY TO GET TWO KINGS IS :
=> =2C2/6C2
=> =1/15
Hence (B) is the correct answer.
Answer : B
Answer: (B) a = 3/5 , b = 1/15
Question: A and B start a business, with A investing the total capital of Rs.10000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.1000 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year?
(A) A)59000
(B) B)37000
(C) C)48000
(D) D)59000
(E) E)67000
Rationale: Interest received by A from B = 10% of half of Rs.10000 = 10% * 5000 = 500.
Amount received by A per annum for being a working partner = 1000 * 12 = Rs.12000.
Let 'P' be the part of the remaining profit that A receives as his share. Total income of A = (500 + 12000 + P)
Total income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally.
Income of A = Twice the income of B
(500 + 12000 + P) = 2(P)
P = 12500
Total profit = 2P + 12000
= 2*12500 + 12000 = 37000
Answer:B
Answer: (B) B)37000
Question: The diagonals of a rhombus are 20 cm and 25 cm. Find its area?
(A) 158
(B) 129
(C) 250
(D) 123
(E) 117
Rationale: 1/2 * 20 * 25 = 250
Answer:C
Answer: (C) 250
Question: What missing numberin the Sequence 5 15 5 18 5 ? 14 20 5
(A) 23
(B) 76
(C) 12
(D) 55
(E) 24
Rationale: E
24
write the numbers in ascending order in words as
onE (Position of 'E' in alphabet is 5)
twO (Position of 'O' in alphabet is 15)
threE (Position of 'E' in alphabet is 5)
fouR (Position of 'R' in alphabet is 18)
and so one
Answer: (E) 24
Question: A trader lists his articles at 30% above cost price and allows a discount of 10% on cash payment. Find his gain percentage
(A) 117% Gain
(B) 100% Gain
(C) 17% Profit
(D) 17% Loss
(E) None of these
Rationale: Explanation:
(130 * 90)/100 = Rs.117/-
profit = 17 % profit
Answer: Option C
Answer: (C) 17% Profit