mathewhe/aqua_rat huggingface dataset:
Question: A man spends 10% of his income in house rent, 20% of the rest on his children’s education, 25% of the rest miscellaneous causes. If he now posses Rs. 1944 then his income is?
(A) 3600
(B) 5280
(C) 3400
(D) 5380
(E) 3400
Rationale: Explanation:
X * (90/100) * (80/100) * (75/100) = 1944
X * 0.9 * 0.8 * 0.75
X = 1944/0.54
X = 3600
Answer: Option A
Answer: (A) 3600
Question: A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 256 sq. feet, how many feet of fencing will be required?
(A) 45.6
(B) 40
(C) 68
(D) 88
(E) 92
Rationale: Given that length and area, so we can find the breadth.
Length x Breadth = Area
20 x Breadth = 256
Breadth = 12.8 feet
Area to be fenced = 2B + L = 2 (12.8) + 20 = 45.6 feet answer : A
Answer: (A) 45.6
Question: The length of the bridge, which a train 110 m long and traveling at 45 km/hr can cross in 30 sec is?
(A) 377
(B) 367
(C) 237
(D) 245
(E) 265
Rationale: Speed = 45 * 5/18 = 25/2 m/sec.
Time = 30 sec
Let the length of bridge be x meters.
Then, (110 + x)/30 = 25/2
x = 265 m.
Answer: E
Answer: (E) 265
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
(A) 63kmph
(B) 63kmph
(C) 20kmph
(D) 62kmph
(E) 74kmph
Rationale: Explanation:
M = 15
S = 5
DS = 15 + 5 = 20
Answer: Option C
Answer: (C) 20kmph
Question: The avg weight of A,B & C is 84 kg. If D joins the group, the avg weight of the group becomes 80 kg.If another man E who weights is 3 kg more than D Replaces A, Then the avgof B,C,D&E becomes 79 kg. What is the weight of A?
(A) 60
(B) 34
(C) 75
(D) 87
(E) 94
Rationale: A + B + C = 3 *84 = 252
A + B + C + D = 4 * 80 = 320 ---- (i)
So, D = 68& E = 68 + 3 = 71
B + C + D +E = 79 * 4 = 316 --- (ii)
From Eq. (i) & (ii)
A-E = 320 – 316 = 4
A = E +4 = 71 + 4 = 75
C
Answer: (C) 75
Question: From a seven-member dance group, five will be chosen at random to volunteer at a youth dance event. If Kori and Jason are two of the seven members, what is the probability that both will be chosen to volunteer?
(A) a) 1/21
(B) b) 1/7
(C) c) 40/7
(D) d) 2/7
(E) e) 3/7
Rationale: Total number of ways to choose 5 out of 7 = 7C5 = 7/4.
Number of ways to choose 2 (any but Kori and Jason) out of 5 (excluding Kori and Jason) = 5C2 = 10.
P = favorable/total = 10/(7/4) = 40/7.
Answer: C.
Answer: (C) c) 40/7
Question: A 100-litre mixture of milk and water contains 30.25 litres of milk. 'x' litres of this mixture is removed and replaced with an equal quantum of water. If the process is repeated once, then the concentration of the milk stands reduced at 25%. What is the value of x?
(A) 9.1 litres
(B) 10 litres
(C) 8 litres
(D) 12 litres
(E) 6 litres
Rationale: Working formula ...
Initial Concentration*Initial Volume=Final Concentration*Final Volume.
Let X is the part removed from 100 lts.
30.25%(1-X/100)^2 = 25% * 100%
(1-x/100)^2=25/30.25------>(1-x/100)^2=(5/5.5)^2
100-X=500/5.5
x=9.1...
Ans A
Answer: (A) 9.1 litres
Question: What least number must be added to 1100, so that the sum is completely divisible by 23 ?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: 48*23 = 1104
1104 - 1100 = 4
Answer : C
Answer: (C) 4
Question: the age difference between two brothers is 3 years. After 6 years the ratio between the age is 9:8
What are their ages?
(A) 21 and 18
(B) 21 and 19
(C) 21 and 17
(D) 20 and 18
(E) 22 and 18
Rationale: x-y=3
x+6/y+6=9/8
solving this we get y=18 and x=21
21 and 18
ANSWER:A
Answer: (A) 21 and 18
Question: A man whose speed is 5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
(A) 7
(B) 4
(C) 6
(D) 9
(E) 4.55
Rationale: M = 5.0
S = 1.5
DS = 6.5
US = 3.5
AS = (2 * 6 * 3) /10 = 4.55
Answer:E
Answer: (E) 4.55
Question: The average of 6 no.'s is 3.95. The average of 2of them is 3.4, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's?
(A) 3.4
(B) 3.9
(C) 4.1
(D) 4.2
(E) 4.6
Rationale: Sum of the remaining two numbers = (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)]
= 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20.
Required average = (9.2 / 2) = 4.6.
E
Answer: (E) 4.6
Question: A and B started business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in the total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?
(A) 7500
(B) 7389
(C) 7379
(D) 7453
(E) 7637
Rationale: A:B:C = (20000 * 24) : (15000 * 24) : (20000 * 18) = 4:3:3
B's share = 25000 * 3/10 = Rs.7500.
Answer: A
Answer: (A) 7500
Question: P, Q and R have $7000 among themselves. R has two-thirds of the total amount with P and Q. Find the amount with R?
(A) 2800
(B) 2403
(C) 3998
(D) 2539
(E) 1930
Rationale: A
2800
Let the amount with R be $ r
r = 2/3 (total amount with P and Q)
r = 2/3(7000 - r) => 3r = 14000 - 2r
=> 5r = 14000 => r = 2800.
Answer: (A) 2800
Question: A school’s annual budget for the purchase of student computers increased by 75% this year over last year. If the price of student computers increased by 50% this year, then the number of computers it can purchase this year is what percent greater than the number of computers it purchased last year?
(A) 15.5%
(B) 12%
(C) 14%
(D) 15%
(E) 16.67%
Rationale: Pick numbers.
Lats year: budget = $100, price = $1 --> the number of computers purchased = 100/1 = 100;
This year: budget = $175, price = $1.5 --> the number of computers purchased = 175/1.5 = ~116.67
Increase in the number of computers purchased = 16.67%
Answer: E.
Answer: (E) 16.67%
Question: A certain debt will be paid in 52 installments from January 1 to December 31 of a certain year. Each of the first 8 payments is to be $410; each of the remaining payments is to be $65 more than each of the first 8 payments. What is the average (arithmetic mean) payment that will be made on the debt for the year?
(A) 443
(B) 450
(C) 465
(D) 468
(E) 475
Rationale: Total number of installments = 52
Payment per installment for the first 8 installments = 410
Payment per installment for the remaining 32 installments = 410+65=475
Average = (8*410 + 44*475)/52 = 465
Answer C
Answer: (C) 465
Question: Working at constant rate, pump X pumped out half of the water in a flooded basement in 7 hours. The pump Y was started and the two pumps, working independently at their respective constant rates, pumped out rest of the water in 3 hours. How many hours would it have taken pump Y , operating alone at its own constant rate, to pump out all of the water that was pumped out of the basement?
(A) a. 10
(B) b. 12
(C) c. 34
(D) d. 18
(E) e. 24
Rationale: rate of x=1/8
rate of x+y=1/6
rate of y=1/6-1/8=1/24
34 hours
C
Answer: (C) c. 34
Question: If a, b, and c are three different positive integers whose sum is prime, which of the following statements could be true?
(A) Each of a, b, and c is prime.
(B) Each of a + 3, b + 3, and c + 3 is prime
(C) Each of a + b, a + c, and b + c is prime
(D) The average (arithmetic mean) of a, b, and c is prime
(E) a + b = c
Rationale: 3 different +ve integers (assume a, b, c) – sum is a prime number
All prime numbers except 2 are odd.
Consider 2 -> There is no combination of a, b & c to get a sum of 2. (a, b and c have to be different and positive integers)
Now for a, b and c to add up to a prime number (>2) the possibilities are
2 numbers are even positive integers and 1 is an odd positive integer ( E, E, O – i.e. assume a & b are even and c is odd)
OR
All 3 are odd positive integers (O, O, O – a, b & c are odd)
(A)	E, E, O (even if 1 of the even numbers is 2 there is another number which cannot be prime) combination not true
but O, O, O combination could be true.
(B)	E+3 could be prime but O+3 is an even integer >2 so cannot be prime
So E,E,O combination not true (a+3 OK, b+3 OK but c+3 – cannot be prime ) and O,O,O (a/b/c+3 cannot be prime)combination is also not true.
(C)	E+O could be prime but O+O cannot be So E,E,O (a+b cannot be prime) combination and O,O,O (a+b, b+c and c+a cannot be prime) combination not true
(D)	If the average of 3 numbers is a prime number then the sum of the 3 numbers is a multiple of 3 and the arithmetic mean. So the sum cannot be even – therefore this option is also not possible.
(E)	If a+b=c then a+b+c = 2c which is an even no and hence this option is not possible
Answer (A)
Answer: (A) Each of a, b, and c is prime.
Question: The distance from City A to City B is 240 miles. While driving from City A to City B, Jim drives at a constant speed of 40 miles per hour. Kerri leaves City A 60 minutes after Jim. What is the minimum constant speed in miles per hour that Kerri must exceed in order to arrive in City B before Jim?
(A) 42
(B) 44
(C) 46
(D) 48
(E) 50
Rationale: The time it takes Jim to drive to City B is 240 / 40 = 6 hours.
Hannah needs to take less than 5 hours for the trip.
Hannah needs to exceed a constant speed of 240 / 5 = 48 miles per hour.
The answer is D.
Answer: (D) 48
Question: A cistern is normally filled in 10 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in?
(A) 33
(B) 88
(C) 60
(D) 99
(E) 11
Rationale: 1/10 - 1/x = 1/12
x = 60
Answer: C
Answer: (C) 60
Question: A person purchased a TV set for Rs. 1800 and a DVD player for Rs. 300. He sold both the items together for Rs. 3129. What percentage of profit did he make?
(A) 20%
(B) 96%
(C) 40%
(D) 49%
(E) 23%
Rationale: The total CP = Rs. 1800 + Rs. 300
= Rs. 2100 and SP = Rs. 3129
Profit(%)
= (3129 - 2100)/2100 * 100
= 49%
Answer: D
Answer: (D) 49%
Question: A cube is painted red on all faces. It is then cut into 27 equal smaller cubes. How many H cubes are painted on only 2 faces?
(A) 12
(B) 8
(C) 6
(D) 10
(E) 16
Rationale: 1) Draw a simple cube
2) Draw 9 squares on each face of the cube (so that it looks like a Rubik's Cube) - this is what the cube will look like when it's cut into 27 equal smaller cubes.
3) Remember that the OUTSIDE of the cube is the part that's painted....
The mini-cubes with 2 painted sides are ALL on the edge of the cube, in themiddleof the edge. There are 4 in front, 4 in back and 4 more on thestripthat runs around the left/top/right/bottom of the cube. H=4 + 4 + 4 = 12. Answer A
Answer: (A) 12
Question: there are 41 students in a class, number of girls is one more than number of guys. we need to form a team of four students. all four in the team cannot be from same gender. number of girls and guys in the team should NOT be equal. How many ways can such a team be made?
(A) 50540 ways
(B) 60540 ways
(C) 50840 ways
(D) 40540 ways
(E) 51540 ways
Rationale: boys=20 and girls=21 now the combinations are {girl,girl,girl,boy} or {boy,boy,boy,girl}
so 21c3*20c1+20c3*21c1=50540 ways
ANSWER:A
Answer: (A) 50540 ways
Question: How many combinations of three letters taken from letters (a, a, b, b, c, c ) are possible?
(A) 12
(B) 13
(C) 5
(D) 7
(E) 6
Rationale: So 3C3 for abc - 1 choice
2 more for aa(b,c )
2 more for bb(a,c )
2 more for cc(a,b )
total 7
Ans :D
Answer: (D) 7
Question: A Lady has given one-fourth part of her property to her daughter, half part to her sons and one-fifth part given as charity. How much part of hier property she has given?
(A) 1/20
(B) 19/20
(C) 1/10
(D) 9/10
(E) None
Rationale: Answer
Total share given by a person
= (1/4) + (1/2) + (1/5)
= (5 + 10 + 4)/20
= 19/20
Option: B
Answer: (B) 19/20
Question: Find the amount on Rs.8000 in 9 months at 20% per annum, if the interest being compounded quarterly?
(A) 9261
(B) 1261
(C) 9621
(D) 9162
(E) 5000
Rationale: A = 8000(21/20)3 = 9261
ANSWER A
Answer: (A) 9261
Question: Mark and Ann together were allocated n boxes of cookies to sell for a club project. Mark sold 9 boxes less than n and Ann sold 2 boxes less than n. If Mark and Ann have each sold at least one box of cookies, but together they have sold less than n boxes, what is the value of n?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 13
Rationale: if n =10
mark sold 1 box
and Ann sold 8 boxes
total 9 < 10
Answer:B
Answer: (B) 10
Question: Two pipes A and B can fill a cistern in 10 and 30 minutes respectively, and a third pipe C can empty it in 50 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
(A) 19 1/7 min
(B) 15 1/7 min
(C) 17 1/7 min
(D) 8.8 min
(E) 7 2/7 min
Rationale: 1/10 + 1/30 - 1/50 = 17/150
150/17 = 8.8
ANSWER:D
Answer: (D) 8.8 min
Question: What is the twenty-fourth decimal to the right in the fraction 47/48?
(A) 1
(B) 2
(C) 4
(D) 6
(E) 8
Rationale: 47/48 = 0.979166666666666....
The answer is D.
Answer: (D) 6
Question: In the equation a = 36.12b, b and a are integers. If a/b leaves a remainder of r, which of the following must divide into r?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 12
Rationale: 1) It says it is a equation, so a=36.12b should be 36.12 * b..
2) It says b is an integer, again it means 36.12 * b..
Otherwise b would be just a digit and it would be mentioned..
Although not clearly mentioned that 36.12b is actually 36.12 * b, BUT entire info points towards that..
and that is why I have taken a/b = 36.12
Answer: (B) 3
Question: A flagpole 18 meters high casts a shadow of length 45 meters. If a building under similar conditions casts a shadow of length 55 meters, what is the height of the building (in meters)?
(A) 20
(B) 22
(C) 24
(D) 26
(E) 28
Rationale: The height:length ratio will be equal in both cases.
18 / 45 = x / 55
x = 22
The answer is B.
Answer: (B) 22
Question: Five friends go to a city where they can stay in 10 different hotels. In how many ways can they stay in these hotels if at least two of them stay together?
(A) 5^10−10C5∗5!
(B) 5^10−10C5
(C) 5^10−5!
(D) 10^5−10C5∗5!
(E) 10^5−10C5
Rationale: There are 10 hotels and each person can stay in 10 hotels
Total = 10 * 10 * 10 * 10 * 10 --> 10^5 --> Notice that there is no restriction to avoid a hotel.
Number of ways so that no person stays together with another friend = 10 * 9 * 8 * 7 * 6 = 10P5 = 10C5 * 5!
Number of ways can 5 friends stay in these hotels if at least two of them stay together = 10^5 - (10C5 * 5!)
Answer: D
Answer: (D) 10^5−10C5∗5!
Question: If nn is a positive integer and (n+1)(n+3)(n+1)(n+3) is odd, then (n+2)(n+4)(n+2)(n+4) must be a multiple of which one of the following?
(A) 5
(B) 7
(C) 6
(D) 8
(E) 9
Rationale: (n+1)(n+3)(n+1)(n+3) is odd only when both (n+1)(n+1) and (n+3)(n+3) are odd. This is possible only when nn is even.
Hence, n=2mn=2m, where mm is a positive integer. Then,
(n+2)(n+4)=(2m+2)(2m+4)=2(m+1)2(m+2)=4(m+1)(m+2)(n+2)(n+4)=(2m+2)(2m+4)=2(m+1)2(m+2)=4(m+1)(m+2)
=4 * (product of two consecutive positive integers, one which must be even)=4 * (product of two consecutive positive integers, one which must be even) =4 * (an even number), and this equals a number that is at least a multiple of 8=4 * (an even number), and this equals a number that is at least a multiple of 8
Hence, the answer is (D).
Answer: (D) 8
Question: Simple interest on a certain sum is 16 over 25 of the sum. Find the rate per cent and time, if both are equal.
(A) 8% and 8 years
(B) 6% and 6 years
(C) 10% and 10 years
(D) 12 % and 12 years
(E) None of these
Rationale: 16⁄25P = P×R×R/100
⇒ R2 = 1600⁄25 ⇒ R = 40⁄5 = 8%
Also, time = 8 years
Answer A
Answer: (A) 8% and 8 years
Question: Ajay marked the price of his goods 30% more than his C.P. He then sells 1/4th of his stock at a discount of 15%, and half of the stock at the marked price, and the rest at a discount of 30%. Find his gain percentage.
(A) 16.5%
(B) 15.375%
(C) 14.20%
(D) 13.37%
(E) None of these
Rationale: If C.P = 100, M.P = 130
S.P = (1/4) x 110.5 + (1/2) x 130 + (1/4) x 91
S.P = 27.625 + 65 + 22.75 = 115.375
Hence , Profit = 15.375%
ANSWER:B
Answer: (B) 15.375%
Question: At a certain school, the ratio of the number of English majors to the number of Sociology majors is 5 to 2, and the ratio of the number of Psychology majors to the number of Sociology majors is 3 to 4. If the ratio of the number of History majors to the number of English majors is 5 to 3, what is the ratio of the number of Psychology majors to the number of History majors
(A) 25 to 3
(B) 20 to 9
(C) 9 to 50
(D) 6 to 25
(E) 3 to 10
Rationale: Correct B
Answer: (B) 20 to 9
Question: John can do a piece of work in 30 days while michael can do it in 40 days. In how many days will they finish it together?
(A) 17 1/7 days
(B) 27 1/7 days
(C) 23 2/7 days
(D) 16 4/11 days
(E) 17 5/11 days
Rationale: Explanation:
1/30 + 1/40 = 7/120
120/7 = 17 1/7 days
Answer: A
Answer: (A) 17 1/7 days
Question: A and B can finish a piece of work in 30 days. They worked at it for 20 days and then B left. The remaining work was done by A alone in 20 more days. A alone can finish the work in
(A) 48 days
(B) 50 days
(C) 54 days
(D) 60 days
(E) 65 days
Rationale: Explanation:
(A + B)’s 1 day’s work = 1/30
Their 20day’s work = 1/30 × 20 = 2/3
Remaining 1/3 work is done by A in 20 days
Therefore, A alone can finish the work in 3 × 20 = 60 days.
Answer: Option D
Answer: (D) 60 days
Question: A and B undertake to do a piece of work for $120. A alone can do it in 4days while B alone can do it in 6days. With the help of C, they finish it in 2days. Find the share of B?
(A) $150
(B) $100
(C) $200
(D) $50
(E) $40
Rationale: C's 1day work = (1/2)-(1/4 + 1/6) = 1/12
A:B:C= 1/4 : 1/6: 1/12 = 3:2:1
B's share = 120*2/6 = $40
Answer is E
Answer: (E) $40
Question: A and B can finish a work in 10 days while A alone can do the same work in 20 days. In how many days B alone will complete the work?
(A) 20 days
(B) 48 days
(C) 98 days
(D) 31 days
(E) 22 days
Rationale: B = 1/10 – 1/20 = 1/20 => 20 days
Answer: A
Answer: (A) 20 days
Question: It takes ten minutes to fry a steak (five minutes for each side). You are frying the steaks in a pan that can accommodate only two steaks at one time. What is the least amount of time by which you can fry all the three steaks you have?
(A) 14 Minutes
(B) 15 Minutes
(C) 16 Minutes
(D) 17 Minutes
(E) 19 Minutes
Rationale: Solution:
Fifteen Minutes.
After frying for five minutes, you can take out one steak and put the third one inside while turning the other one inside. After five more minutes, one steak is fried from both sides and you can take it out. Now put in the steak that we removed and turn the other one inside. After five more minutes, they both will also be fried from both sides.
Answer B
Answer: (B) 15 Minutes
Question: A rectangular plot measuring 40 meters by 50 meters is to be enclosed by wire fencing. If the poles of the fence are kept 5 meters apart. How many poles will be needed?
(A) 46m
(B) 36m
(C) 26m
(D) 56m
(E) 25m
Rationale: Perimeter of the plot = 2(40+50) = 180m
no of poles =180/5 =36m
Answer: B
Answer: (B) 36m
Question: There are two circles of different radii. The are of a square is 784 sq cm and its side is twice the radius of the larger circle. The radius of the larger circle is seven - third that of the smaller circle. Find the circumference of the smaller circle.
(A) 19∏ cm
(B) 10∏ cm
(C) 12∏ cm
(D) 11∏ cm
(E) 13∏ cm
Rationale: Explanation:
Let the radii of the larger and the smaller circles be l cm and s cm respectively. Let the side of the square be a cm.
a2 = 784 = (4)(196) = (22).(142)
a = (2)(14) = 28
a = 2l, l = a/2 = 14
l = (7/3)s
Therefore s = (3/7)(l) = 6 Circumference of the smaller circle = 2∏s = 12∏ cm.
Answer: Option C
Answer: (C) 12∏ cm
Question: In a camp, there is a meal for 120 men or 200 children. If 150 children have taken the meal, how many men will be catered to with remaining meal?
(A) 50
(B) 30
(C) 40
(D) 10
(E) 20
Rationale: Explanation :
Meal for 200 children = Meal for 120 men
Meal for 1 child = Meal for 120/200 men
Meal for 150 children = Meal for (120×150)/200 men=Meal for 90 men
Total mean available = Meal for 120 men
Renaming meal = Meal for 120 men - Meal for 90 men = Meal for 30 men . Answer : Option B
Answer: (B) 30
Question: Four extra-large sandwiches of exactly the same size were ordered for m students, where m > 7. Three of the sandwiches were evenly divided among the students. Since 4 students did not want any of the fourth sandwich, it was evenly divided among the remaining students. If Carol ate one piece from each of the four sandwiches, the amount of sandwich that she ate would be what fraction of a whole extra-large sandwich?
(A) (6m-21)/[m(m-7)]
(B) (4m-21)/[m(m-7)]
(C) (8m-21)/[m(m-5)]
(D) (10m-21)/[m(m-5)]
(E) (4m-15)/[m(m-5)]
Rationale: Three of the sandwiches were evenly divided among the students
i.e. Amount of Sandwiches with each students = 3/m
Amount of 4th Sandwich with remaining (m-7) students = 1/(m-7)
The amount of Sandwich that carol ate = 3/m + 1/(m-7) = (3m-21+m)/[m(m-7)] = (4m-21)/[m(m-7)]
Answer: B
Answer: (B) (4m-21)/[m(m-7)]
Question: If 2|2 –f| = 5, what is the sum of all the possible values for f ?
(A) 1/2
(B) 2
(C) 5/2
(D) 4
(E) 5
Rationale: if f<2, then 2-f=5/2; f=-1/2
if f>2 , then f-2=5/2; f=9/2
9/2-1/2=8/2=4=D
Answer: (D) 4
Question: Enrollment in City College in 1980 was 42 percent of enrollment in 1990. What was the percent increase in the college’s enrollment from 1980 to 1990?
(A) 10%
(B) 138.09 %
(C) 20%
(D) 25%
(E) 183 1/3%
Rationale: Assume 100 enrollments present in 1990
42 % of 1990 = enrollments on 1980
enrollments on 1980 = 42
% change = (enrollment in 1990 - enrollment in 1980)*100/(enrollment in 1980)
=(100 - 42) *100 / 42
= 5800 / 42
= 138.09 %
Ans - B
Answer: (B) 138.09 %
Question: Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 2/3 were basic and the rest were deluxe. If it takes 1.1 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?
(A) 7/17
(B) 14/31
(C) 7/15
(D) 11/31
(E) 1/2
Rationale: The easiest way for me is to plug in numbers.
Let the number of basic stereos produced be 40, and number of delux stereos produced be 20. Total of 60 stereos.
If it takes an hour to produce a basic stereo then it will take 1.4 hours to produce a deluxe stereo.
40 basic stereos = 40 hours.
20 delux stereos = 22 hours.
Total hours = 62.
Then the fraction would be 22/62 = 11/31. Therefore answer
D.
Answer: (D) 11/31
Question: Two pumps are connected to an empty tank. Pump X fills the tank with water at a constant rate, while pump Y drains water out of the tank at a constant rate. The two pumps finish filling the tank in six times the duration it would take pump X alone to fill the tank. If pump Y alone can empty a whole tank in 48 minutes, then how many minutes does it take pump X alone to fill the tank?
(A) 32
(B) 34
(C) 36
(D) 38
(E) 40
Rationale: Let V be the volume of the tank.
Let R be the rate per minute that pump X fills the tank.
Let T be the time it takes pump X to fill the tank.
The rate at which pump Y empties the tank is V/48 per minute.
(R - V/48)*6T=V=RT.
(R-V/48)*6=R
5R=V/8.
R=V/40.
It takes pump X 40 minutes to fill the tank.
The answer is E.
Answer: (E) 40
Question: A garrison of 400 men had a provision for 31 days. After 28 days 280 persons re-enforcement leave the garrison. Find the number of days for which the remaining ration will be sufficient?
(A) 22
(B) 28
(C) 10
(D) 66
(E) 23
Rationale: 400 --- 31
400 --- 3
120 --- ?
400*3 = 120*x => x =10 days
Answer: C
Answer: (C) 10
Question: Of 32 applicants for a job, 14 had at least 4 years' experience, 18 had degrees, and 7 had less than 4 years' experience and did not have a degree. How many of the applicants had at least 4 years' experience and a degree?
(A)  14
(B)  13
(C)  9
(D)  7
(E)  5
Rationale: set A : people with more than 4 years exp
set B : people with degree
AUB = total - (less than 4 exp and no degree)
AUB = 32-7=25
AUB = A + B - AiB
AiB = 18+14-25
=7
Answer D
Answer: (D)  7
Question: A car covers a certain distance at aspeed of 60 kmph in 5 hours. To cover the same distance in 4 hrs, it must travel at a speed of?
(A) 567 km/hr
(B) 75 km/hr
(C) 782 km/hr
(D) 789 km/hr
(E) 720 km/hr
Rationale: Distance = (60 x 5) = 300 km.
Speed = Distance/Time
Speed = 300/4 = 75 kmph
Answer : B
Answer: (B) 75 km/hr