mathewhe/aqua_rat huggingface dataset:
Question: 189. The inside dimensions of a rectangular wooden box
are 10 inches by 12 inches by 14 inches. A cylindrical
canister is to be placed inside the box so that it stands
upright when the closed box rests on one of its six
faces. Of all such canisters that could be used, what is
the radius, in inches, of the one that has maximum
volume?
(A)  3
(B)  4
(C)  5
(D)  6
(E)  8
Rationale: Since the radius is squared, the biggest volume cylinder will have the biggest possible radius. To achieve that, let the smaller dimension of the rectangular box be the height. So, it will have 14x12 width x length. The biggest cylinder must fit both dimensions, so it must have at most a diameter of 12, so the radius will be 6.
D
Answer: (D)  6
Question: The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8463 for a computer table, then what was the cost price of the computer table?
(A) 6727
(B) 6825
(C) 6728
(D) 6725
(E) 2871
Rationale: :
CP = SP * (100/(100 + profit%))
= 8463(100/124) = Rs. 6825.
Answer: B
Answer: (B) 6825
Question: A student was asked to find 4/5 of a number. But the student divided the number by 4/5, thus the student got 9 more than the correct answer. Find the number.
(A) 16
(B) 18
(C) 20
(D) 22
(E) 24
Rationale: Let the number be x.
(5/4) * x = (4/5)*x + 9
25x = 16x + 180
9x = 180
x = 20
The answer is C.
Answer: (C) 20
Question: if 5+6+4=010530
and 2+4+8=021040
and 3+5+9=021155
and 4+6+7=020954....
then 2+7+5=??????
(A) 051070
(B) 051770
(C) 051074
(D) 151070
(E) 071070
Rationale: if 5+6+4=010530
and 2+4+8=021040
and 3+5+9=021155
and 4+6+7=020954....
then 2+7+5=??????
051070
ANSWER:A
Answer: (A) 051070
Question: A coin is tossed four times. What is the probability that there is at the least one tail?
(A) 15/16
(B) 15/37
(C) 15/67
(D) 15/17
(E) 15/31
Rationale: Let P(T) be the probability of getting least one tail when the coin is tossed four times.
= There is not even a single tail.
i.e. all the outcomes are heads.
= 1/16 ; P(T) = 1 - 1/16
= 15/16
Answer: A
Answer: (A) 15/16
Question: Carrie, Liz and Michael are playing cards. Together they have all won $400 total. Carrie and Liz have won $150 total. Michael and Liz have won $300 total. How much money as Carrie won?
(A) 50
(B) 250
(C) 350
(D) 100
(E) 150
Rationale: Carrie + Liz + Michael = $400
C + L = $150
M + L = $300 <<Plug into original formula
C + (M + L) = 400
C + 300 = 400
Subtract 300 from each side
c = $100
Answer: D
Answer: (D) 100
Question: The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is:
(A) 15
(B) 16
(C) 18
(D) 25
(E) 24
Rationale: Explanation:
Let C.P. of each article be Re. 1 C.P. of x articles = Rs. x.
S.P. of x articles = Rs. 20.
Profit = Rs. (20 - x).
(20-X/X X100=25)
2000 - 100x = 25x
125x=2000
x=16
ANSWER IS B
Answer: (B) 16
Question: In 1995, the Johnsons spent $800 on the family’s water bills. Anticipating that water rates would increase in 1996 by 50%, the Johnsons cut back their water usage. By how much must the Johnsons have reduced their 1996 water usage to pay exactly the same amount N in 1996 as they paid in 1995?
(A) 33 1⁄3%
(B) 40%
(C) 50%
(D) 66 2⁄3%
(E) 100%
Rationale: water rate increases by 50 % in 1996 means 150% of rate in 1995. to pay exactly the same amount N in 1996 as they paid in 1995, water use should decrease in the same ratio
150-> 100 means 1/3 rd= 33(1/3) %.A
Answer: (A) 33 1⁄3%
Question: A mixture of 70 litres of milk and water contains 10% water. How many litres of water should be added to the mixture so that the mixture contains 12 1/2% water?
(A) 2
(B) 8
(C) 4
(D) 5
(E) None of these
Rationale: Quantity of milk in the mixture = 90/100 (70) = 63 litres.
After adding water, milk would form 87 1/2% of the mixture.
Hence, if quantity of mixture after adding x liters of water, (87 1/2) / 100 x = 63 => x = 72
Hence 72 - 70 = 2 litres of water must be added.
ANSWER:A
Answer: (A) 2
Question: The ratio of the adjacent angles of a parallelogram is 4 : 11. Also, the ratio of the angles of quadrilateral is 5 : 6 : 7 : 12. What is the sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral?
(A) 132°
(B) 228°
(C) 156°
(D) 224°
(E) None of these
Rationale: The measures of the adjacent angles of a parallelogram add up to be 180°
Given
So, 4x + 11x = 180°
Or, 15x = 180°
Or, x = 12°
Hence the angles of the parallelogram are 48° and 132°
Further it is given
We know sum of all the four angles of a quadrilateral is 360°
So, 5y + 6y + 7y + 12 y = 360°
Or, 5y + 6y + 7y + 12 y = 360°
Or, 30y = 360°
Or, y = 12°
Hence the angles of the quadrilateral are 60° , 72, 84° and 144°
Will be 48° + 84° = 132°
Answer : A
Answer: (A) 132°
Question: How many seconds will a 400 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
(A) 11 sec
(B) 24 sec
(C) 77 sec
(D) 14 sec
(E) 12
Rationale: Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 400 * 3/50
= 24 sec.
Answer: B
Answer: (B) 24 sec
Question: Let C be defined as the sum of all prime numbers between 0 and 35. What is C/3
(A) 155
(B) 129
(C) 64.3
(D) 47
(E) 43
Rationale: Prime numbers between 0 and 30 - 2 , 3 , 5 , 7, 11 , 13 , 17 , 19 , 23 , 29, 31, 33
Sum,C = 193
C/3 = 64.3
Answer C
Answer: (C) 64.3
Question: A family pays $800 per year for an insurance plan that pays 85 percent of the first $1,000 in expenses and 100 percent of all medical expenses thereafter. In any given year, the total amount paid by the family will equal the amount paid by the plan when the family's medical expenses total.
(A) $1,100
(B) $1,200
(C) $1,400
(D) $1,800
(E) $2,200
Rationale: Upfront payment for insurance plan = 800$
Family needs to pay 15 % of first 1000 $ in expense = 150$
Total amount paid by family when medical expenses are equal to or greater than 1000 $ = 800 + 150 = 950 $
Total amount paid by insurance plan for first 1000 $ = 800 $
Total amount paid by family will equal amount paid by plan when medical expense = 1100 $
(Since insurance plan will pay 100% of amount that exceeds 950$ )
Answer A
Answer: (A) $1,100
Question: A train 280 m long can cross an electric pole in 20 sec and then find the speed of the train?
(A) 88 Kmph
(B) 89 Kmph
(C) 72 Kmph
(D) 50 Kmph
(E) 18 Kmph
Rationale: Length = Speed * time
Speed = L/T
S = 280/20
S = 14 M/Sec
Speed= 14*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 50 Kmph
Answer: D
Answer: (D) 50 Kmph
Question: The probability of rain showers in Barcelona on any given day is 0.5. What is the probability that it will rain on exactly one out of three straight days in Barcelona?
(A) 0.144
(B) 0.072
(C) 0.375
(D) 0.72
(E) 0.288
Rationale: IMO This is just for first day! It can rain on 2nd day or 3 rd day (and not rain on other days) in 3 consecutive days!
Hence,
0.5*0.5*0.5 + 0.5*0.5*0.5 + 0.5*0.5*0.5 = 0.375
Option - C
Answer: (C) 0.375
Question: Ram has 490 chocolates. 70 members work in his office. He would like to give each person the same amount of chocolates, how much should he give to each person?
(A) 7
(B) 12
(C) 9
(D) 15
(E) 6
Rationale: 490/70 = 7
The answer is A.
Answer: (A) 7
Question: A sum of money becomes double itself in 8 years at simple interest. How many times will it become 10 years at the same rate?
(A) 2 1/4
(B) 2 1/9
(C) 2 1/2
(D) 2 1/6
(E) 2 1/7
Rationale: P ---- 2P ---- 8 years
2 1/4 P ---- 10 years
Answer: A
Answer: (A) 2 1/4
Question: If a computer program generates three-digit odd numbers using the numbers 9, 7, 0, 2, and 1, and the digits can be repeated, what is the probability that the number formed from the program is a multiple of three?
(A) 1/3
(B) 1/4
(C) 1/5
(D) 1/6
(E) 1/7
Rationale: A
Answer: (A) 1/3
Question: If z≠y and z·y≠0, which of the following may be true?
(A) z=y
(B) (z+y)(z-y)=0
(C) z.y=0
(D) z^2=y^2
(E) z^2+y^2=0
Rationale: except B all conditions are not as per question
B
Answer: (B) (z+y)(z-y)=0
Question: Akshay buys a motorcycle for Rs.25000. If he decides to sell the motorcycle for a profit of 7%, find the selling price.
(A) 26750
(B) 26759
(C) 26757
(D) 26756
(E) 26753
Rationale: Explanation:
Profit = %profit/100 * cost price
P = 7/100 * 25000 = 1750.
Selling price = cost price + profit
= 25000 + 1750
= Rs.26750
ANSWER:A
Answer: (A) 26750
Question: If 9 engines consume 24 metric tonnes of coal, when each is working 8 hours
day, how much coal will be required for 8 engines, each running 13hours a day, it being given that 3 engines of former type consume as much as 4 engines of latter type?
(A) 23 metric tonnes
(B) 24 metric tonnes
(C) 25 metric tonnes
(D) 26 metric tonnes
(E) 27 metric tonnes
Rationale: We shall compare each item with the quantity of coal.
Less engines, less coal consumed (direct)
More working hours, more coal consumed (direct)
If 3 engines of former type consume 1 unit, then 1 engine will consume 1/3 unit.
If 4 engines of latter type consume 1 unit, then 1 engine will consume 1/4 unit.
Less rate of consumption, less coal consumed (direct).
Therefore, number of engines 9:8 :: 24:x
Working hours 8:13 :: 24:x
Rate of consumption 1/3:1/4 :: 24:x.
9*8*1/3*x= 8*13*1/4*24 or x= 26.
Therefore, required consumption of coal 26 metric tonnes.
ANSWER:D
Answer: (D) 26 metric tonnes
Question: There are two pipes A and B.If A filled 10 liters in hour B can fills 20 liters in same time.likewise B can fill 10,20,40,80,160.... if B filled in (1/16)th of a tank in 3 hours.how much time will it take to fill completely?
(A) 7 hours
(B) 6 hours
(C) 5 hours
(D) 8 hours
(E) 9 hours
Rationale: 1/16 in 3 hours
1/8 in 4 hours,as here rate of water filling is doubled
1/4 in 5 hours
1/2 in 6 hours
1 in 7 hours
ans will be 7 hours
ANSWER:A
Answer: (A) 7 hours
Question: A runs 5/3 times as fast as B. If A gives B a start of 80 m, how far must the winning post be so that A and B might reach it at the same time?
(A) 200 m
(B) 300 m
(C) 270 m
(D) 160 m
(E) 360 m
Rationale: Ratio of the speeds of A and B =	5	: 1 = 5 : 3.
3
Thus, in race of 5 m, A gains 2 m over B.
2 m are gained by A in a race of 5 m.
80 m will be gained by A in race of	5	x 80	m	= 200 m.
2
Winning post is 200 m away from the starting point.
ANSWER:A
Answer: (A) 200 m
Question: A right triangle with sides 3 cm, 4 cm and 5 cm is rotated the side of 3 cm to form a cone. The volume of the cone so formed is:
(A) 12
(B) 66
(C) 73
(D) 72
(E) 8
Rationale: Answer: A) 12 pi cub.cm
Answer: (A) 12
Question: g, b, c, and d are positive integers. If the remainder is 9 when g is divided by b, and the remainder is 5 when c is divided by d, which of the following is NOT a possible value for b + d?
(A)  20
(B)  19
(C)  18
(D)  16
(E)  15
Rationale: When g is divided by b remainder is 9 that means b is greater than or equals to 10, similarly d is greater than or equals to 6.
b + d cannot be 15, hence E is the answer.
Answer: (E)  15
Question: A and B are two partially filled buckets of water. If 3 liters are transferred from A to B, then A would contain one-third of the amount of water in B. Alternatively, if 5 liters are transferred from B to A, B would contain one-half of the amount of water in A. Bucket A contains how many liters of water?
(A) 11
(B) 13
(C) 39/5
(D) 21
(E) 23
Rationale: Let A contains A, B contains B liters
so, (A-3)/(B+3)= 1/3.......(1)
again, (B-5)/(A+5)= 1/2..........(2)
from (1)(2) we find A= 39/5
ans: (C)
Answer: (C) 39/5
Question: It takes printer A 4 more minutes than printer B to print 40 pages. Working together, the two printers can print 50 pages in 6 minutes. How long will it take printer A to print 80 pages?
(A) 12
(B) 18
(C) 20
(D) 24
(E) 30
Rationale: We need time taken by printer A to print 80 pages. (Let's say this is 'a' mins)
We know A takes 4 more mins for 40 pages so it will take 8 more minutes for 80 pages.
Together, they print 50 pages in 6 mins so they will print 80 pages in 6*50/80 = 48/5 mins
Now, make your sum of rates equation:
1/a + 1/(a - 8) = 5/48
Now look at the options and substitute here. First check out the straight forward options.
Say, a = 12
1/12 + 1/4 = 4/12 Nope
I will not try 18 and 20 because (18, 10) and (20, 12) doesn't give me 48, the denominator on right hand side.
I will try 24 instead.
1/24 + 1/16 = 5/48 Yes.
Answer is 24.
ANSWER:D
Answer: (D) 24
Question: How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 136 m length?
(A) 82.1 sec.
(B) 12.3 sec
(C) 19.1 sec.
(D) 17.1 sec.
(E) 42.1 sec.
Rationale: Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 110 + 136 = 246 m.
Required time = 246/20 = 12.3 sec.
Answer: B
Answer: (B) 12.3 sec
Question: The T train leaves station A moving at a constant speed, and passes by stations B and C, in this order. It takes the T train 7 hours to reach station B, and 5 additional hours to reach station C. The distance between stations A and B is m kilometers longer than the distance between stations B and C. What is the distance between stations A and C in terms of m?
(A) 1.8m
(B) 6m
(C) 7m
(D) 9m
(E) 12m
Rationale: The reason it is failing for you is that you chose incorrect numbers. If the question says T it took 7 hrs to reach from A to B and 5 hrs to reach from B to C at a constant speed. It shows that distance AB and BC should be in ratio of 7/5.
If you take such numbers you can solve problem.
AB = 7, BC=5
Therefore
AB-BC = 2
But from question, AB-BC =m
=> m=2
Now total distance = AB+BC= 12
Substitute 12 to get answer in terms of m
Total distance =12 =6m
Ans B
Answer: (B) 6m
Question: A and B can do a piece of work in 12 days and 16 days respectively. Both work for 3 days and then A goes away. Find how long will B take to complete the remaining work?
(A) 10 days
(B) 17 days
(C) 147 days
(D) 9 days
(E) 1478 days
Rationale: 3/12 + (3 + x)/16 = 1
x = 9 days
Answer: D
Answer: (D) 9 days
Question: A bookshop had science and art books in the ratio of 2:5. By the end of the week, 20% of both type of books were sold and 2240 books were unsold. How many art books were there at the starting?
(A) 1000
(B) 1200
(C) 1500
(D) 1600
(E) 2000
Rationale: science books sold = 2x × 0.2 = 0.4x
science books unsold = 2x – 0.4x = 1.6x
art books sold = 5x × 0.2 = x
art books unsold = 5x – x = 4x
total books unsold = 1.6x + 4x = 5.6x
5.6x = 2240
x = 400
2x science = 800
and 5x art books = 2000
E
Answer: (E) 2000
Question: The ratio of boys to girls is 6:4.60% of the boys and 40% of girls take lunch in the canteen.What % of class takes lunch?
(A) 51%
(B) 52%
(C) 53%
(D) 54%
(E) 55%
Rationale: let total no of students 100, boy 60 and girl 40, so lunch taken by boy and girl respectively 60* 60/100=36 and 40* 40/100=16
so total 52 students takes lunch out of 100 students..so required % is 52%
ANSWER:B
Answer: (B) 52%
Question: What is the smallest possible common multiple of three integers, all larger than 24?
(A) 27.
(B) 54.
(C) 25
(D) 19,656.
(E) 21,924.
Rationale: The Least common positive multiple would be for the immediate least number(s) after 24 i.e 25.
Since nowhere is it stated that the three integers must be different, the integers could be 25,25 and 25... leading to least possible positive common multiple to be 25. Answer C.
Answer: (C) 25
Question: An athlete runs 200 meters race in 48sec. His speed is?
(A) 20km/hr
(B) 15km/hr
(C) 30km/hr
(D) 25km/hr
(E) 40km/hr
Rationale: speed = 200/48 = 25/6 m/sec
= 25/6 * 18/5 km/hr = 15km/hr
Answer is B
Answer: (B) 15km/hr
Question: If the perimeter of a rectangular garden is 600 m, its length when its breadth is 100 m is?
(A) 338 m
(B) 778 m
(C) 200 m
(D) 276 m
(E) 971 m
Rationale: 2(l + 100)
= 600 => l
= 200 m
Answer:C
Answer: (C) 200 m
Question: The average of 11 results is 50, if the average of first six results is 49 and that of the last six is 52. Find the sixth result?
(A) 58
(B) 56
(C) 51
(D) 52
(E) 59
Rationale: 1 to 11 = 11 * 50 = 550
1 to 6 = 6 * 49 = 294
6 to 11 = 6 * 52 = 312
6th = 294 + 312 – 550
= 56
Answer: B
Answer: (B) 56
Question: In how many different number of ways 6 men and 3 women can sit on a shopa which can accommodate persons?
(A) 200
(B) 230
(C) 504
(D) 250
(E) 260
Rationale: 9p3 = 9 Ã— 8 Ã— 7 = 504
C
Answer: (C) 504
Question: A train passes a man standing on the platform. If the train is 210 meters long and its speed is 72 kmph, how much time it took in doing so?
(A) 10 ½ sec
(B) 4 ½ sec
(C) 9 ½ sec
(D) 8 ½ sec
(E) 2 ½ sec
Rationale: D = 210
S = 72 * 5/18 = 20 mps
T = 210/20 = 10 ½ sec
Answer: A
Answer: (A) 10 ½ sec
Question: A cricketer scored 134 runs which included 12 boundaries and 2 sixes. What percent of his total score did he make by running between the wickets.
(A) 55.22%
(B) 54.54 %
(C) 63%
(D) 70%
(E) None of these
Rationale: Explanation :
Number of runs made by running = 134 - (12 x 4 + 2 x 6)
= 134 - (60)
= 74
Now, we need to calculate 72 is what percent of 134.
=> 74/134 * 100 = 55.22 %
Answer : A
Answer: (A) 55.22%
Question: Points A, B, and C lie, in that order, on a straight railroad track. The distance from point A to point B is twice the distance from point B to point C. A train traveled from point A to point C without stopping. The train's average speed when traveling from point A to point B was 200 miles per hour and the train's average speed when traveling from point B to point C was 150 miles per hour. What was the train's average speed, in miles per hour, when traveling from point A to point C?
(A) 150
(B) 200
(C) 180
(D) 190
(E) 250
Rationale: Average speed = distance/time
Because we are looking for average speed we can pick a distance for the variable d.
Speed A-B = 200
Speed B-C = 150
Average Speed = total distance/total rate
rate = distance/time
A====================B==========C
If A-B is twice the length of B-C then let A-B = 2d and let B-C = d
Average speed = 3d/(2d/200) + (d/150)
3d/(6d/600) + (4d/600)
3d/(10d/600)
1800d/10d
Average speed = 180
ANSWER: C
Answer: (C) 180
Question: 72,90, 80,85,90,105,105,130,130,130
The list consists of the times in seconds that it took each of the 10 school children to run a distance of 400 mts . If the standard deviation of the 10 running times is 22.4, rounded to the nearest tenth of a second, how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times.
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: How many of the 10 running times are more than one SD below the meanmeans how many data points from given 10 are less thanmean-1SD.
We are given that SD=22.4, so we should find mean --> mean=100 --> there are only 1 data points below 100-22.4=77.6, namely 72 .
Answer: A.
Answer: (A) 1
Question: In a 300 m race A beats B by 22.5 m or 6 seconds. B's time over the course is:
(A) 80 sec
(B) 86 sec
(C) 76 sec
(D) 49 sec
(E) 50 sec
Rationale: B runs 300 m in(6*2/45*300)sec=80 sec
ANSWER A
Answer: (A) 80 sec
Question: 1+2+2^2+2^3+2^4+2^5+2^6=？
(A) (2^3-1)(2^3+1)
(B) 2^6+1
(C) 2^7-1
(D) 2^5+1
(E) 2^5-2
Rationale: From 1+2+2^2+2^3+2^4+2^5+2^6=1(2^7-1)/(2-1)=2^7-1, the correct answer is C.
Answer: (C) 2^7-1
Question: There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is?
(A) 60
(B) 70
(C) 80
(D) 90
(E) 100
Rationale: Let the number of students in rooms A and B be x and y respectively.
Then, x - 10 = y + 10 x - y = 20 .... (i)
and x + 20 = 2(y - 20) x - 2y = -60 .... (ii)
Solving (i) and (ii) we get: x = 100 , y = 80.
The required answer A = 100.
E)
Answer: (E) 100
Question: Mr. Babu ison tour and he has Rs. 360 for his expenses. If he exceeds his tour by 4 days. he must cut down his daily expenses by Rs. 3.For how many days is Mr. babu on tour?
(A) 20
(B) 30
(C) 40
(D) 90
(E) 20
Rationale: Suppose Mr. babu is on tour for x days . Then, 360/x-360/x+4
=1/x-1/x+4=1/120
x(x+4)=4x120=480
(x+24)(x-20)=0
x=20
ANSWER: A
Answer: (A) 20
Question: A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
(A) 615 m
(B) 240 m
(C) 168 m
(D) 197 m
(E) 691 m
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/36 = 15 => x
= 240 m
Answer: B
Answer: (B) 240 m
Question: Jonah drove the first half of a 200-mile trip in x hours and the second half in y hours. Which of the following is equal to Jonah’s average speed, in miles per hour, for the entire trip?
(A) 100/(x + y)
(B) 200/(x + y)
(C) 25/x + 25/y
(D) 50/x + 50/y
(E) 100/x + 100/y
Rationale: Time taken by Jonah to cover first half i.e 100 miles of a 200 mile trip = x
time taken by Jonah to cover the second half i.e 100 miles of a 200 mile trip = y
Total time taken by Jonah = x+y
Jonah's average speed for the entire trip =total distance /total time
=200/(x+y)
Answer B
Answer: (B) 200/(x + y)
Question: If the length & width of a rectangle is decreased by 50% & then again increase the new length & width by 40%. Calculate the percentage difference between the area of New Rectangle & Original Rectangle.
(A) 50%
(B) 51%
(C) 52%
(D) 53%
(E) 54%
Rationale: let length is l, width is w so area is wl
after decreament l is i/2 ,w is w/2
again inc by 40% so l is 7l/10 ,w is 7w/10 so area is 49wl/100
percentage change is wl-49wl/100=51wl/100
so 51%
ANSWER:B
Answer: (B) 51%
Question: 40% of a number is more than 20% of 650 by 190. Find the number?
(A) 288
(B) 278
(C) 800
(D) 267
(E) 121
Rationale: (40/100) * X – (20/100) * 650 = 190
2/5 X = 320
X = 800
Answer:C
Answer: (C) 800
Question: Sheila works 8 hours per day on Monday, Wednesday and Friday, and 6 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $360 per week. How much does she earn in dollars per hour?
(A) 2
(B) 8
(C) 9
(D) 10
(E) 2
Rationale: Explanation:
Total hours worked = 8 x 3 + 6 x 2 = 36
Total earned = 360. Hourly wage = 360 / 36 = 10
Answer: D
Answer: (D) 10
Question: The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is Rs. 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is:
(A) 4000
(B) 5000
(C) 6000
(D) 7000
(E) None of these
Rationale: Explanation:
Let P, Q and R represent their respective monthly incomes. Then, we have:
P + Q = (5050 x 2) = 10100 …. (i)
Q + R = (6250 x 2) = 12500 …. (ii)
P + R = (5200 x 2) = 10400 …. (iii)
Adding (i), (ii) and (iii), we get: 2(P + Q + R) = 33000 or P + Q + R = 16500 …. (iv)
Subtracting (ii) from (iv), we get P = 4000.
P’s monthly income = Rs. 4000.
Answer A
Answer: (A) 4000
Question: A shipment of 8 television sets contains 2 black-and-white sets and 5 color sets. If 2 television sets are to be chosen at random from this shipment, what is the probability that at least 1 of the 2 sets chosen will be a black-and-white set?
(A) 1/7
(B) 1/4
(C) 9/14
(D) 11/28
(E) 13/28
Rationale: I get 9/14, which is not in the answer choices.
the probability of getting at least one b/w TV is 1-(the probability of getting 2 color TVs)
1-C(5,2)/C(8/2)=18/28=9/14
C
Answer: (C) 9/14
Question: Raj invested an amount of Rs.17400 for two years. Find the rate of compound interest that will fetch him an amount of Rs.1783.50 at the end of two years?
(A) 9
(B) 8
(C) 7
(D) 5
(E) 3
Rationale: Let the rate of interest be R% p.a.
17400[1 + R/100]2 = 17400 + 1783.50
[1 + R/100]2 = (17400 + 1783.50)/17400
= 1 + 1025/10000 = 1 + 41/400
= 441/400 = [21/20]2
[1 + R/100] = 21/20
R/100 = 1/20
Therefore R = 5
Answer:D
Answer: (D) 5
Question: In a two digit number, the digit in the units place is six times the digit in ten's place and sum of the digits is equal to 7. What is the number?
(A) 16
(B) 28
(C) 32
(D) 36
(E) 38
Rationale: Solution
Let the ten digits be x. Then,units digit=6x
Therefore x + 6x = 7
‹=›7x = 7
‹=›x= 1.
So, ten's digit = 1, unit's digit = 6.
Hence, the required number is 16.
Answer A
Answer: (A) 16