divelab/Sys2Bench huggingface dataset:
Question: The radius of a cylindrical vessel is 7cm and height is 3cm. Find the whole surface of the cylinder?
Options:
A)520 sq cm
B)840 sq cm
C)440 sq cm
D)120 sq cm
E)5 sq cm
Rationale: Explanation:
r = 7 h = 3
2πr(h + r) = 2 * 22/7 * 7(10) = 440 sq cm
Answer: C
Answer: C
Question: What will $2000 amount to in three years if it is invested at 20% per year compound interest, with the interest being compounded annually?
Options:
A)$3124
B)$3260
C)$3328
D)$3456
E)$3680
Rationale: After one year: 1.2 * $2000
After two years: (1.2)^2 * $2000
After three years: (1.2)^3 * $2000 = $3456
The answer is D.
Answer: D
Question: Solve the equation for x : 6x - 27 + 3x = 4 + 9 - x?
Options:
A)4
B)5
C)3
D)9
E)6
Rationale: 9 x + x = 13 + 27
10 x = 40 => x = 4
Answer:A
Answer: A
Question: Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in:
Options:
A)3 9/17 hours
B)1 13 /17 hours
C)2 8/11 hours
D)4 1/ 2 hours
E)5 1/ 2 hours
Rationale: Explanation:
Pipes A and B can fill the tank in 5 and 6 hours respectively. Therefore,
part filled by pipe A in 1 hour =1/5
part filled by pipe B in 1 hour = 1/6
Pipe C can empty the tank in 12 hours. Therefore,
part emptied by pipe C in 1 hour =1/12
Net part filled by Pipes A,B,C together in 1 hour
=1/5+1/6-1/12=17/60
i.e., the tank can be filled in 60/17=3 9/17 hours.
Answer: Option A
Answer: A
Question: In a certain store, the profit is 320% of the cost. If the cost increases by 40% but the selling price
remains constant, approximately what percentage of the selling price is the profit
Options:
A)67%
B)80%
C)90%
D)100%
E)None of above
Rationale: Explanation:
Let C.P.= Rs. 100.
Then, Profit = Rs. 320,
S.P. = Rs. 420.
New C.P. = 140% of Rs. 100 = Rs. 140
New S.P. = Rs. 420.
Profit = Rs. (420 - 140) = Rs. 280
Required percentage = (280/420) * 100
= 66.67%(approx) =67%
Answer: A
Answer: A
Question: A family consists of grandparents, parents and three grand children. The average age of the grandparents is 67 years, that of the parents is 37 years and that of the grandchildren is 6 years. What is the average age of the family?
Options:
A)28 4â„7 years
B)31 5â„7 years
C)32 2â„7 years
D)27 1â„2 years
E)None of these
Rationale: Required average = (67Ã—2+37Ã—2+6Ã—3/2+2+3)
=226/7
= 32 2â„7 years
Answer C
Answer: C
Question: A starts a business with a capital of Rs. 85,000. B joins in the business with Rs.42500 after some time. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1?
Options:
A)5 months
B)6 months
C)7 months
D)8 months
E)9 months
Rationale: Explanation:
Let B joined for x months. Then
85000×12:42500 × x = 3:1
⇒850×12:425x=3:1
⇒850×12×1=3×425x
Answer: Option D
⇒850×4=425x
⇒x=8
Answer: D
Question: A train 240 m in length crosses a telegraph post in 16 seconds. The speed of the train is?
Options:
A)77 kmph
B)55 kmph
C)54 kmph
D)58 kmph
E)76 kmph
Rationale: S = 240/16 * 18/5
= 54 kmph
Answer: C
Answer: C
Question: A & B throws a pair of dice and winner is one who gets a sum of 9 first.if A starts throwing first
Then what is the ratio of A winning over B?
Options:
A)8/9
B)9/8
C)7/8
D)6/9
E)5/9
Rationale: probability of a person throwing first and winning is given by 1/(2-p)
1/(2-(1/9))=9/17 prob of a
prob of b is 8/17
prob (a/b) 9/8
ANSWER:B
Answer: B
Question: A boy wants to go abroad by boat and return by flight. He has a choice of 8 different boat to go and 6 flight to return. In how many ways, can the boy perform his journey?
Options:
A)20
B)48
C)46
D)50
E)70
Rationale: Ans.(B)
Sol. Number of choices to go by ship = 8 Number of choices to return by airline = 6 From, fundamental principle, total number of ways of performing the journey = 8 x 6 = 48 ways
Answer: B
Question: A man is standing on a railway bridge which is 180 m long. He finds that a train crosses the bridge in 20 seconds but himself in 8 seconds. Find the length of the train and its speed.
Options:
A)10 m/sec
B)15 m/sec
C)18 m/sec
D)19 m/sec
E)25 m/sec
Rationale: If length of train is l and speed of train is s, then
l/s = 8
(l+180)/s = 20
(l+180)/l = 20/8 =5/2
2l+360 =5*l
3*l= 360
l=120 mtrs
s= l/8 = 120/8 = 15 m/sec
ANSWER:B
Answer: B
Question: How many ways are there to arrange the letters in the word accessibility ?
Options:
A)1
B)1260
C)3780
D)7560
E)778377600
Rationale: 13 total words, 2C, 2S, 2I
= 13! / 2! 2! 2! = 778377600 Answer E
Answer: E
Question: Sam and Nik start from A and B respectively at the same time and travel towards each other at constant speeds along the same route. Sam meets Nik at point C on the road which is 600m away from starting point A and 400m away from point B. The speed of Sam is 50 m/m(meter/minute). How much time did Sam take to cover the distance between A and B?
Options:
A)10 minutes
B)15 minutes
C)20 minutes
D)22 minutes
E)17 minutes
Rationale: total distance from A to B-
A - C = 600m, B - C = 400m;
therefore A-B = 1000m;
Vs=50 m/m;
therefore,
t = 1000/50 = 20 minutes.
option C
Answer: C
Question: A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent?
Options:
A)27%
B)20%
C)25%
D)40%
E)28%
Rationale: 900 ---- 180
100 ---- ? => 20%
Answer: B
Answer: B
Question: The present average age of a family of five members is 26 years. If the present age of the youngest member in the family is ten years, then what was the average age of the family at the time of the birth of the youngest member ? (Assume no death occurred in the family since the birth of the youngest)?
Options:
A)28 years
B)11 years
C)20 years
D)17 years
E)16 years
Rationale: Present total age of the members = 26(5) = 130 years.
Present age of the youngest member = 10 years
Present total age of the remaining four members = 130 -10 = 120 years
Their average age at the time of the birth of the youngest member
= [120 - (4 * 10)] / 4
= 30 - 10
= 20 years.
Answer: C
Answer: C
Question: In a school the number of girls is 15 more that that of the boys. now if 19% of the girls were newly joined and 25% of the boys were newly joined the number of girls is 9 more than that of the boys how many girls and boys were there?
Options:
A)156
B)157
C)158
D)159
E)160
Rationale: In a school the number of girls is 15 more that that of the boys.
Means G = 15 + B ------ 1
now if 19% of the girls were newly joined and 25% of the boys were newly joined
Total Girls are 1.19G
Total Boys are 1.25B
girls is 9 more than that of the boys.
1.19G = 9 + 1.25B ------ 1
Solving 1 and 2
B= 147
G= 147 + 9 = 156
ANSWER:A
Answer: A
Question: Rose made a part payment of $300 toward buying a brand new car, which represents 5% of the total cost of the car, how much remains to be paid?
Options:
A)$5700
B)$5500
C)$5800
D)$5200
E)$5880
Rationale: Explanation:
Let's start with what the total price of the car would be. If 5% is equal to $300 then 100% equals $x. We just have to multiply $300 by 20 to get total amount=$6000. Out of this amount we then need to deduct the amount already paid which was $300 so we have $6000-$300=$5700
Answer: Option A
Answer: A
Question: A certain list of 100 data has an average (arithmetic mean) of 7 and a standard deviation of d, where d is positive. Which of the following pairs of data, when added to the list, must result in a list of 104 data with standard deviation less than d?
Options:
A)-7 and 0
B)0 and 0
C)0 and 7
D)0 and 14
E)7 and 7
Rationale: Standard deviation shows how much variation there is from the mean. A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.
So when we add numbers, which are far from the mean we are stretching the set making SD bigger and when we add numbers which are close to the mean we are shrinking the set making SD smaller.
According to the above adding two numbers which are closest to the mean will shrink the set most, thus decreasing SD by the greatest amount.
Closest to the mean are 7 and 7 (actually these numbers equal to the mean) thus adding them will definitely shrink the set, thus decreasing SD.
Answer: E.
Answer: E
Question: If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is?
Options:
A)1/8
B)1/2
C)7/9
D)1/6
E)1/1
Rationale: The number of exhaustive outcomes is 36.
Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2
P(E) = 1 - 1/2
= 1/2.
Answer:B
Answer: B
Question: Pipe A can fill a tank in 16 hrs and pipe B can fill it in 24 hrs. If both the pipes are opened in the empty tank. In how many hours will it be fill 5/4th of that tank?
Options:
A)10
B)12
C)14
D)16
E)18
Rationale: Part filled A in 1 hr= (1/16)
Part filled B in 1 hr= (1/24)
Part filled by (A+B) together in 1 hr=(1/16)+(1/24)=5/48
So, The tank will be full in 48/5 hrs
Time taken to fill Exact quarter tank = (48/5) * (5/4) = 12 hrs
Answer : B
Answer: B
Question: The area of the Rest room is 40 m2 that of a longer wall 10 m2 and of the shorter wall 1 m2, find the edge of the new cube?
Options:
A)40 m3
B)10 m2
C)80 m3
D)20 m3
E)50 m3
Rationale: lb = 40 ; lh = 10 ; fh = 1
(lbh)2 = 40 * 10 * 1 => lbh = 20 m3
ANSWER:D
Answer: D
Question: A parts store is having a store-wide sale of 10% off all merchandise. An out-of-stock part can be backordered, but at a 20% fee. If a customer orders an out-of-stock part whose presale price was $40, how much will he pay?
Options:
A) $41.40
B) $42.00
C) $42.60
D) $43.20
E) $43.80
Rationale: price = (original price - 10% decrease) + 20% increase
price = [40 * (90/100)] * (120/100) = 40 * (.90) * (1.2) = 36 * 1.2 = 43.20
The answer is D.
Answer: D
Question: An ice cream store received shipments of ingredients on Tuesday and Wednesday. Tuesday's shipment had 6 different packages, with an average (arithmetic mean) of 11 and 2/3 pounds. Wednesday's shipment included 7 packages, weighing an average of 9 and 3/7 pounds. What was the average package weight, in pounds, of the shipments received on both days?
Options:
A)9 and 6/7 pounds
B)10 and 1/10 pounds
C)10 and 2/5 pounds
D)136/13 pounds
E)11 and 1/7 pounds
Rationale: Solution: Average weight = Total weight/number of packages. The total weight on Tuesday was 6 * (11 and 2/3 pounds), or 70 pounds. The total weight on Wednesday was 7 * (9 and 3/7 pounds), or 66 pounds. The sum of the weights for both days is 66 + 70, or 136 pounds. The average is 136 pounds/13 packages.
answer: D
Answer: D
Question: If 2464 / 1.12 = 2200, then 246.4 / 11.2 is equal to?
Options:
A)24
B)23
C)22
D)21
E)25
Rationale: Answer
Given expression 246.4 / 11.2 = 2464 / 112
= 2464 / (1.12 x 100)
= 2200 / 100
=22
Correct Option: C
Answer: C
Question: Fresh grapes contain 90% by weight while dried grapes contain 20% water by weight. What is the weight of dry grapes available from 25 kg of fresh grapes?
Options:
A)2 kg
B)2.4 kg
C)3.12 kg
D)10 kg
E)none of these
Rationale: The weight of non-water in 25 kg of fresh grapes (which is 100-90=10% of whole weight) will be the same as the weight of non-water in x kg of dried grapes (which is 100-20=80% of whole weight), so 25âˆ—0.1=xâˆ—0.8--> x=3.12
Answer: C.
Answer: C
Question: On flipping 3 coins together what is the outcomes for at least One tail and three heads?
Options:
A)1/7
B)3/8
C)3/11
D)4/8
E)5/13
Rationale: Sample space, S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}
Favorable outcomes for at least two heads
= favorable outcomes for exactly two heads and favorable outcomes for more than two heads
= {HHT, HTH, THH,HHH}
4/8
D
Answer: D
Question: An agent wants to sell x% of a list of 10,000 apartments in a residential area. After market price decreases, the agent must reduce this selection by (x − 8)%. In terms of x, how many apartments will he be able to sell?
Options:
A)x*x – 8x
B)(x)(108 – x)
C)(100)(108 – x)
D)(100)(92 – x)
E)(x-8)/100
Rationale: Based on the answer choices and the question, this question begs the use of x=8 as a sample number.
Initial = 8%*10000 = 800
Reduction = 8-8=0%, so no math required here to calculate the reduction; just make sure that you can calculate 800 in your answer.
A. x*x – 8x = 0; No
B. (x)(108 – x) = 800; Winner!
C. (100)(108 – x) > 800; No
D. (100)(92 – x) > 800; No
E. (x-8)/100 = 0; No
B
Answer: B
Question: If four coins are tossed, the probability of getting two heads and two tails i
Options:
A)3/8
B)3/6
C)3/9
D)3/1
E)3/2
Rationale: Since four coins are tossed, sample space = 24
Getting two heads and two tails can happen in six ways.
n(E) = six ways
p(E) = 6/24 = 3/8
Answer:A
Answer: A
Question: A boat crossed a lake from North to East at the speed of 7 km/h, entered a river and covered twice as much distance going upstream at 6 km/h. It then turned around and stopped at the south shore of the lake. If it averaged 3.8 km/h that day, what was its approximate downstream speed?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: One way of solving this is:
Speed of boat on still water (lake)=7kmph
Speed upstream = 6kmph = speed in still water - speed of river => speed of river = 1kmph
=>Speed downstream = speed in still water + speed of river = 7+1 =8kmph
Ans is E
Answer: E
Question: At a dinner party,3 people are to be seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group?
Options:
A)1) 5
B)2) 10
C)3) 24
D)4) 2
E)5) 120
Rationale: for number of distinct arrangements of 'n' items around a circular table, we get the arrangements by way of (n-1)!
in this case, there are 3 guests, so number of distinct arrangements = 2! = 2
Answer : D
Answer: D
Question: A man can swim in still water at 9 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
Options:
A)1.7
B)1.9
C)3
D)1.5
E)1.2
Rationale: M = 9
S = x
DS = 9 + x
US = 9 - x
9 + x = (9 - x)2
9 + x = 18 -2x
3x = 9
x = 3
Answer:C
Answer: C
Question: If w/x = 1/3 and w/y = 4/15, then (x + y)/y =
Options:
A)4/5
B)6/5
C)7/5
D)8/5
E)9/5
Rationale: W/X = 1/3=>x=3w and W/Y = 4/15=>y=15/4w
(X+Y)/Y = (3w+15/4w)/(15/4w) = (27/4w)/(15/4w) = 9/5
Correct Option: E
Answer: E
Question: In a city, 40% of the adults are illiterate while 85% of the children are literate. If the ratio of the adults to that of the children is 2 : 3, then what percent of the population is literate ?
Options:
A)20%
B)25%
C)50%
D)75%
E)80%
Rationale: ET POPULATION 100
RATIO IS 2:3
So adults=2*100/5=40 chldren=3*100/5=60
illterate adult 40*40/100=16
literate adult 24
literate chldren 51
so total literate is 75
ANSWER:D
Answer: D
Question: If x+y=4 and x2y3 + y2x3=36, what is the value of xy?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: xy=3
As x+y=4
x2y3+y2x3=36
x2y2(y+x)=36
Substituting x+y
x2y2=4
xy=4
ANSWER:D
Answer: D
Question: Trapezoid JKLM in the x-y plane has coordinates J = (–2, –1), K = (–2, 1), L = (6, 7), and M = (6, –1). What is its perimeter?
Options:
A) 34
B) 36
C) 31
D) 40
E)(F) 42
Rationale: JK =2
LM = 11
KL =using distance formula 10
JM = using distance formula 8
Sum of all is 31
C
Answer: C
Question: The two lines y = x and x = -2 intersect on the coordinate plane. If z represents the area of the figure formed by the intersecting lines and the x-axis, what is the side length of a cube whose surface area is equal to 6z?
Options:
A)16
B)8√2
C)8
D)√2
E)(√2)/3
Rationale: 800score Official Solution:
The first step to solving this problem is to actually graph the two lines. The lines intersect at the point (-2, -2) and form a right triangle whose base length and height are both equal to 4. As you know, the area of a triangle is equal to one half the product of its base length and height: A = (1/2)bh = (1/2)(2 × 2) = 2; so z = 2.
The next step requires us to find the length of a side of a cube that has a face area equal to 2. As you know the 6 faces of a cube are squares. So, we can reduce the problem to finding the length of the side of a square that has an area of 2. Since the area of a square is equal to s², where s is the length of one of its side, we can write and solve the equation s² = 2. Clearly s = √2 , oranswer choice (D).
Answer: D
Question: The average of runs of a cricket player of 20 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 6 ?
Options:
A)96
B)106
C)158
D)116
E)122
Rationale: Average = total runs / no.of innings = 32
So, total = Average x no.of innings = 32 * 20 = 640
Now increase in avg = 4 runs. So, new avg = 32+6 = 38 runs
Total runs = new avg x new no. of innings = 38 * 21 = 798
Runs made in the 11th inning = 798-640 = 158
ANSWER:C
Answer: C
Question: 300 × ? + (12 + 4) × 1/8 = 602
Options:
A)A)4
B)B)3
C)C)5
D)D)2
E)E)8
Rationale: Explanation:
=> 300 × ? + (12 + 4) × 1/8 = 602
=> 300 × ? = 602 - (12 + 4) × 1/8
=> 300 × ? = 602 - 2 = 600
=> ? = 600/300 = 2
Answer: Option D
Answer: D
Question: Walking at the rate of 4 kmph a man cover certain distance in 2 hr 45 min. Running at a
speed of 16.5 kmph the man will cover the same distance in.
Options:
A)12 min
B)25 min
C)40 min
D)60 min
E)None of these
Rationale: Explanation :
Distance = Speed * time
4*11/4 = 11km
New Speed = 16.5 kmph
Therefore time = D/S = 11/16.5 = 40min
Answer : C
Answer: C
Question: If C is a whole number, C+1 is a whole number after that. If A is a whole number, what is a whole number before that?
Options:
A)-1
B)1
C)0
D)2
E)-2
Rationale: Solution:
We know that the number ‘0’ together with the natural numbers gives us the numbers 0, 1, 2, 3, 4, 5, …………… which are called whole numbers.
If A is a whole number and it is greater than 0 then the whole number before that is A – 1, which will always be a whole number.
Again, when A is a whole number and it is equal to 0 then the whole number before that is A – 1 which means 0 – 1 = -1, which is not a whole number.
Therefore, if A is a whole number then the number before that will not always be a whole number.
Answer A
Answer: A
Question: A can do a piece of work in 4 hours; B and C together can do it in 2 hours, which A and C together can do it in 2 hours. How long will B alone take to do it?
Options:
A)2hours
B)3hours
C)4hours
D)5hours
E)6hours
Rationale: A's 1 hour work = 1/4;
(B + C)'s 1 hour work = 1/2;
(A + C)'s 1 hour work = 1/2
(A + B + C)'s 1 hour work = (1/4 + 1/2) = 3/4
B's 1 hour work = (3/4 - 1/2) = 1/4
B alone will take 4 hours to do the work.
Answer:C
Answer: C
Question: Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm.
Options:
A)289 cm2
B)285 cm2
C)287 cm2
D)267 cm2
E)207 cm2
Rationale: Area of a trapezium
= 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (20 + 18) * (15)
= 285 cm2
Answer: B
Answer: B
Question: Adam borrowed some money at the rate of 6% p.a. for the first two years, at the rate of 9% p.a. for the next three years, and at the rate of 14% p.a. for the period beyond four years. If he pays a total interest of 11,900 at the end of nine years, how much money did he borrow?
Options:
A)10,526
B)12,526
C)14,000
D)16,000
E)16,536
Rationale: Let the sum borrowed be x. Then,
(x×6×21/00)+(x×9×3/100)+(x×14×4/100)= 11900
⇒ (3⁄25x + 27⁄100x + 14⁄25x) = 11400 ⇒ 95⁄100x = 11900
⇒ x = (11900×100/95)= 12526
Hence, sum borrowed = 12,526
Answer B
Answer: B
Question: A man has Rs. 544 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
Options:
A)102
B)38
C)37
D)90
E)28
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 544
⇒ 16x = 544
∴ x = 34.
Hence, total number of notes = 3x = 102
Answer:A
Answer: A
Question: If r>0, which of the following must be true?
Options:
A)1 < r
B)0 < r < 2
C)-1 < r < 1
D)-10 < r
E)1/100 < r
Rationale: All we know is that r is some positive number. Right away we can see that D must be true: if r is positive then it MUST be true that it's greater than -10. Still let's check each option.
A. 1 < r. We don't know whether the number is greater than 1, it could be a positive number less than or equal to 1. Discard.
B. 0 < r < 2. The same here: we don't know whether the number is less than 2, it could be more than or equal to 2. Discard.
C. -1 < r < 1. The same as A. Discard.
E. 1/100 < r. We don't know whether the number is greater than 1/100, it could be a positive number less than or equal to 1/100. Discard.
Answer: D.
Answer: D
Question: A train of 24 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.5 km long?
Options:
A)6
B)3
C)4
D)9
E)2
Rationale: D = 25 * 60 + 1500 = 3000 m
T = 3000/60 * 18/5 = 180 sec = 3 mins
Answer:B
Answer: B
Question: A motorcyclist started riding at highway marker A, drove 120 miles to highway marker B, and then, without pausing, continued to highway marker C, where she stopped. The average speed of the motorcyclist, over the course of the entire trip, was 20 miles per hour. If the ride from marker A to marker B lasted 3 times as many hours as the rest of the ride, and the distance from marker B to marker C was half of the distance from marker A to marker B, what was the average speed, in miles per hour, of the motorcyclist while driving from marker B to marker C?
Options:
A)40
B)135
C)50
D)55
E)60
Rationale: A- B = 120 Miles
B - C = 60 Miles
Avg Speed = 20 Miles
Time taken for A-B 3t and B-C be t
avg speed = (120+60) / Total time
20 = 180/4t
t = 135
B-C = 135mph
Answer B
Answer: B
Question: The average weight of a class is x pounds. When a new student weighing 90 pounds joins the class, the average decreases by 1 pound. In a few months the student’s weight increases to 110 pounds and the average weight of the class becomes x + 4 pounds. None of the other students’ weights changed. What is the value of x?
Options:
A)85
B)86
C)88
D)90
E)99
Rationale: When the student weighs 90 pounds the average weight is x - 1 pounds;
When the student weighs 110 pounds the average weight is x + 4 pounds.
So, the increase in total weight of 110 - 90 = 20 pounds corresponds to the increase in average weight of (x + 4) - (x - 1) =5 pounds, which means that there are 20/5 = 4 students (including the new one). So, initially there were 5 student.
Total weight = 5x + 90 = 6(x-1) --> x = 96 pounds.
Answer: E.
Answer: E
Question: Margaret is 10 years more than twice the age of his son. The age of son is 12. Find the age of mother and find the difference between their ages
Options:
A)10yrs
B)22yrs
C)30yrs
D)40yrs
E)50yrs
Rationale: Let, age of son x=12
Margaret is 10 years more than twice the age of his son, y = 10+2(x)
=10+2(12)
=10+24
=34yrs
Difference = 34 - 12
=22yrs
ANSWER:B
Answer: B
Question: Tina’s cat weighs 2.6 kilograms. Her dog weighs 6 times as much as her cat. How much does her dog weigh in kilograms?
Options:
A)A)10.4kg
B)B)38kg
C)C)22kg
D)D)15.6kg
E)E)20kg
Rationale: 2.6*6=15.6kg.Answer is D.
Answer: D
Question: If it takes 70 workers 3 hours to disassemble the exhibition rides at a small amusement park, how many hours would it take 30 workers to do this same job?
Options:
A)40/3
B)11
C)7
D)7/3
E)9/7
Rationale: 70 Workers = 3 hours then,
1 Worker = 3*70 Hours
30 Workers = (3*70) /(30) = 7
ANSWER:C
Answer: C
Question: g(x) is defined as the product of all even integers k such that 0 < k ≤ x. For example, g(14) = 2 × 4 × 6 × 8 × 10 × 12 × 14. If g(e) is divisible by 4^11, what is the smallest possible value for e?
Options:
A) 22
B) 24
C) 28
D) 32
E) 44
Rationale: g(e)=4^11=2^22. So we have to find a product with atleast 22 2's in it.
in option 1 22 the total no of 2's = [22/2] + [22/4] +[22/8] +[22/16] = 11+5+2+1 = 19
in option 2 24 the total no of 2's = [24/2] + [24/4] +[24/8] +[24/16] = 12+6+3+1 = 22 . Hence B
Answer: B
Question: A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m?
Options:
A)2999
B)1350
C)2677
D)2898
E)2787
Rationale: Area = (l + b +2d) 2d
= (75 + 55 +2.5 * 2) 2*2.5 => 675
675 * 2 = Rs.1350
AnswerB
Answer: B