mathewhe/aqua_rat huggingface dataset:
Question: A, B and C rents a pasture for Rs.870. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should B pay?
(A) 360
(B) 227
(C) 268
(D) 198
(E) 176
Rationale: 12*8 :16*9 = 18*6
8: 12: 9
12/29 * 870 = 360
Answer:A
Answer: (A) 360
Question: The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 867 sq m, then what is the breadth of the rectangular plot?
(A) 16
(B) 17
(C) 18
(D) 19
(E) 14
Rationale: Let the breadth of the plot be b m.
Length of the plot = 3 b m
(3b)(b) = 867
3b2 = 867
b2 = 289 = 172 (b > 0)
b = 17 m.
Answer: Option B
Answer: (B) 17
Question: In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?
(A) 175
(B) 195
(C) 180
(D) 160
(E) 140
Rationale: Suppose the man works overtime for x hours.
Now, working hours in 4 weeks = (5 x 8 x 4) = 160.
160 x 2.40 + x * 3.20 = 432
3.20x = 432 - 384 = 48
x = 15.
Hence, total hours of work = (160 + 15) = 175.
Answer is A.
Answer: (A) 175
Question: A shipment of 220 smartphones contains 84 that are defective. If a customer buys two smartphones at random from the shipment, what is the approximate probability that both phones are defective?
(A) 1/250
(B) 1/84
(C) 11/76
(D) 1/9
(E) 1/3
Rationale: Probability of chosing one defective phone from a lot of 220 which ontains 84 defective phones is = (84/220)
Probability of chosing one defective phone from a lot of 219(we already picked one) which ontains 83(we already picked one) defective phones is = (83/219)
Combined probability of series of events = product of the probabilities = (84/220)*(83/219)
84/220 is close to (21/55) and (83/219)= (36/95)
so answer is (21/55)*(36/95) = (11/76)
So, answer will be C
Answer: (C) 11/76
Question: A man sells a horse for Rs.800 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse?
(A) 277
(B) 277
(C) 261
(D) 860
(E) 267
Rationale: CP = SP + 1CP = SP - g
800 + x = 980 - 2x
3x = 180 => x = 60
CP = 800 + 60 = 860
Answer: D
Answer: (D) 860
Question: Integer n is a four digit number such that it is made exactly of 2 distinct digits. If n is divisible by 9, how many possible values does n have?
(A) 59
(B) 60
(C) 61
(D) 68
(E) 69
Rationale: Then the additional combinations would be, 9000(1), 8883(4), 7776(4), 6669(4), 6660(3), 5553(4), 4446(4), 3339(4), 3330(3), 2221(4), 1116(4), 9990(3).
8*4 = 32
3*3 = 9
1*1 = 1
total = 42
Previous was 27. So total 27+42 = 69.
ANSWER:E
Answer: (E) 69
Question: In a certain town, the ratio of NY Yankees fans to NY Mets fans is 3:2, and the ratio of NY Mets fans to Boston Red Sox fans is 4:5. If there are 330 baseball fans in the town, each of whom is a fan of exactly one of those three teams, how many NY Mets fans are there in this town?
(A) 72
(B) 88
(C) 95
(D) 120
(E) 135
Rationale: The ratio of Yankees:Mets:Red Sox = 6:4:5
The Mets fans are 4/15 of the population.
(4/15)*330 = 88
The answer is B.
Answer: (B) 88
Question: pqrs is a rectangle having area 50. rx=1/4sr.what is the area of pqxs?
(A) 41.75
(B) 42.75
(C) 43.75
(D) 44.75
(E) 45.75
Rationale: given pqrs is a rectangle and x located on sr whivh is having length rx=1/4sr.
from this we get right angle traingle qrx.
area of qrx=1/2*l/4*b=lb/8= 50/8 =6.25.
therefore area of pqxs= 50-6.25 = 42.75
ANSWER:B
Answer: (B) 42.75
Question: A runs 1 2⁄3 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) 250 m
(C) 450 m
(D) 350 m
(E) 270 m
Rationale: Speed of A : Speed of B = 5⁄3 : 1 = 5 : 3
i.e., In a race of 5 m, A runs 5 m and B runs 3 m
i.e., A gains 2 m over B in a race of 5 m
=> A gains 80 m over B in a race of 52×80 = 200 m
Hence, winning point should be 200 m away from the starting point.
ANSWER:A
Answer: (A) 200 m
Question: Johnny bought six peanut butter cans at an average price (arithmetic mean) of 35¢. If Johnny returned two cans to the retailer, and the average price of the remaining cans was 31¢, then what is the average price, in cents, of the two returned peanut butter cans?
(A) 5.5
(B) 43
(C) 47.5
(D) 66
(E) 67.5
Rationale: Total price of six cans = 6*35 = 210
Total price of 4 cans = 4*31 = 124
Total rice of two cans = 210 - 124 = 86
Average price of two cans = 86/2 = 43 c
Another way to do it is this:
Assume that the four leftover cans were of 31c each. The avg was 35c initially because the two cans were 35c each and were providing another 4c of cost to other 4 cans.
So cost of the two cans = 2*35 + 4*4 = 86
Avg cost of the two cans = 86/2 = 43c
Answer (B)
Answer: (B) 43
Question: A rope of which a calf is tied is increased from 5m to 9 m, how much additional grassy ground shall it graze?
(A) 1218
(B) 180
(C) 176
(D) 200
(E) 291
Rationale: π (92 – 52) = 176
Answer: C
Answer: (C) 176
Question: 5% of a number is more than 20% of 650 by 190. Find the number?
(A) 288
(B) 278
(C) 800
(D) 267
(E) 6400
Rationale: (5/100) * X â€“ (20/100) * 650 = 190
1/20 X = 320
X = 6400
Answer:E
Answer: (E) 6400
Question: For all numbers a and b, the operation is defined by ab = (a + 2)(b – 3).
If 3x = –20, then x =
(A)  –15
(B)  –6
(C)  3
(D)  6
(E)  -1
Rationale: (3+2)(x-3)=-20..
x-3=-4..
x=-1
E
Answer: (E)  -1
Question: (7 + 7 + 7 ÷ 7) / (5 + 5 + 5 ÷ 5) = ?
(A) 1
(B) 1 / 5
(C) 15 / 11
(D) 3 / 11
(E) None
Rationale: Answer
Given expression = (7 + 7 + 7 ÷ 7) / (5 + 5 + 5 ÷ 5)
= (14 + 1) / (10 + 1)
=15 / 11
Option: C
Answer: (C) 15 / 11
Question: Three investors, A, B, and C, divide the profits from a business enterprise in the ratio of 5 : 7 : 8, respectively. If investor A earned $ 3,500, how much money did investors B and C earn in total?
(A) $4,000
(B) $4,900
(C) $5,600
(D) $9,500
(E) $10,500
Rationale: Let profit for A = 5x
profit for B = 7x
profit for C = 8x
Investor A earned = 3500
5x = 3500
Total profit for B and C = 7x+ 8x = 15x
Therefore , 15x = 5x * 3 = 3500 * 3 = 10,500
Answer E
Answer: (E) $10,500
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train.
(A) 150
(B) 776
(C) 555
(D) 257
(E) 812
Rationale: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train(Distance) = Speed * Time
=50/3∗9=150meter
Answer: A
Answer: (A) 150
Question: In a certain province in France there are 15 cities. If a single road segment connects only two cities, how many road segments are required in order to connect the cities so that each city is connected to all other cities with a single road segment?
(A) 30
(B) 105
(C) 330
(D) 14!
(E) 15!
Rationale: 1 city needs 14 roads to connect directly to the rest => 15 city needs 15*14 roads.
One road is counted twice => the number of road needed is 15*14/2 = 105
Answer B
Answer: (B) 105
Question: The value of (8x10^7)(8x10^8) is closest to which of the following?
(A) 10^17
(B) 10^14
(C) 10^18
(D) 10^19
(E) 10^20
Rationale: multiplying these we get,
64 x 10^7 x 10^8
= 6.4 x 10^16
which is closer to 10^17
Answer: A
Answer: (A) 10^17
Question: If the number65947*8 is completely divisible by 8, then the smallest whole number in place of * will be?
(A) 1
(B) 2
(C) 3
(D) 4
(E) None of these
Rationale: The number 7x8 must be divisible by 8.
x=2 as 728 is divisible by 8.
Correct Option : B
Answer: (B) 2
Question: A sum of money place at compound interest doubles itself in 7 years. In how many years will it amount to eight times itself?
(A) 21
(B) 25
(C) 31
(D) 35
(E) 41
Rationale: 100 ---- 200 ---- 7
400 ---- 7
800 ---- 7
------
21 years
Answer: A
Answer: (A) 21
Question: A dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent?
(A) 180%
(B) 189%
(C) 100%
(D) 109%
(E) 120%
Rationale: MP = 100
CP = 75
SP = 150
------
75 ---- 75
100 ---- ? => 100%
Answer: C
Answer: (C) 100%
Question: The division of a whole number N by 13 gives a quotient of 15 and a remainder of 2. Find N.
(A) 195
(B) 196
(C) 197
(D) 198
(E) 199
Rationale: According to the division process of whole numbers, N can be written, using multiplication, as follows
N = quotient × divisor + remainder = 15 × 13 + 2 = 197
correct answer is C)197
Answer: (C) 197
Question: Solution A is 30% salt and Solution B is 80% salt. If you have 30 ounces of solution A and 60 ounces of solution B, in what ratio could you mix Solution A with Solution B to produce 50 ounces of a 50% salt solution?
(A) 6:4
(B) 6:14
(C) 4:4
(D) 4:6
(E) 3:2
Rationale: Forget the volumes for the time being.
You have to mix 30% and 80% solutions to get 50%. This is very straight forward since 50 is int he middle of 20 and 80 so we need both solutions in equal quantities. If this doesn't strike, use
w1/w2 = (A2 - Aavg)/(Aavg - A1)
w1/w2 = (80 - 50)/(50 - 30) = 3/2
So the volume of the two solutions will be equal. Answer has to be 3:2
E
Answer: (E) 3:2
Question: A train running at the speed of 36 km/hr crosses a pole in 9 seconds. Find the length of the train?
(A) 150 meter
(B) 299 meter
(C) 666 meter
(D) 90 meter
(E) 144 meter
Rationale: Speed = 36*(5/18) m/sec = 10 m/sec
Length of Train (Distance) = Speed * Time
(10) * 9
= 90 meter
Answer: D
Answer: (D) 90 meter
Question: Which of the following best approximates the value of q if 6^44+3^11=6^q ?
(A) 55
(B) 50
(C) 45
(D) 44
(E) 43
Rationale: We have: 6^44+3^11=6^q
==> because 3^11 > 0 --> 6^q MUST be equal or greater than 6^44 ==>q MUST be equal or greater than 44
==> Option E is out immediately.
Divide both sides by 6^q and q >= 44
We have:
6^(44-q) + 3^11/6^q = 1
Because q >= 44 ==>3^11/6^q = 0.0000xyz, that is very small,we can ignore it.
Thus, 6^(44-q) must be approximately 1
==> 44-q = 0 ==> q is approximately 44
D is the answer.
Answer: (D) 44
Question: A worker is paid x rupees for painting every 10 metres of a wall and y rupees for painting every extra metre. During one week, he painted 10 metres on Monday, 13 metres on Tuesday, 12 metres on Wednesday, 11 metres on Thursday and 12 metres on Friday. What is his average daily earning rupees for the five day week?
(A) x + (8/5)y
(B) (5x + 9y)/5
(C) 10x + (8/5)y
(D) None of these
(E) Cannot be determined
Rationale: Explanation :
On Monday, the payment = Rs x
On Tuesday, the payment = Rs (x + 3y)
On Wednesday, the payment = Rs (x + 2y)
On Thursday, the payment = Rs (x + y)
On Friday, the payment = Rs (x + 2y)
Average daily earning during the five-day week = (5x + 8y)/5
= x + (8/5)y
Answer : A
Answer: (A) x + (8/5)y
Question: A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
(A) 298 m
(B) 188 m
(C) 120 m
(D) 178 m
(E) 189 m
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec
= 20 m/sec.
Length of the train = 20 * 6
= 120 m.
Answer:C
Answer: (C) 120 m
Question: A distributor sells a product through an online store, which take a commission of 20% of the price set by the distributor. The distributor obtains the product from a producer at the price of $20 per item. What is the price that the buyer observers online if the distributor wants to maintain a 20% profit on the cost of the item?
(A) $30
(B) $31
(C) $32
(D) $33
(E) $34
Rationale: Let x be the price that buyers see online.
The distributor wants to receive 1.2(original price) which should be 80% of x.
1.2(20) = 0.8x
x = 1.2(20) / 0.8 = 1.5(20) = $30
The answer is A.
Answer: (A) $30
Question: In a Basket there are 10 apples. Jack wants only 5 apples to eat. How many Possible Combinations that he have?
(A) 60
(B) 720
(C) 84
(D) 100
(E) 120
Rationale: Jack Wants only 5 apples. so the combination comes under 10C5.
10C5= 10!/(10-5)!*5!=10!/5!*5!
10!=10*9*8*7*6*5!
5!=5*4*3*2*1
10C5=10*9*8*7*6/5*4*3*2=84
There are 84 possible ways to choose apples in a basket
Answer: (C) 84
Question: A town consists of only one street in the form of a circle. The town authorities give out four licenses for a particular kind of business. The inhabitants of the town live in equal density along the circle and will always go to the closest business for what they need. Business A gets to choose a location first, then business B, then C, and finally D. Each business desires to carve out as much business for themselves as possible but each knows the others all have the same motive. Assume that if a business is indifferent between locating in two different sections of the circle it will choose a section at random. Also assume that the business that goes last will choose a location in the middle of the largest (or one of the largest) sections. Where should business B choose relative to the location of A?
(A) more then 1/3
(B) barely less then 1/3
(C) less then 2/3
(D) more then 2/3
(E) more then 3/3
Rationale: The answer is just barely less then 1/3 of the circumference of the circle away from A.
This is only a quick overview of the solution, the details are left up to you. Let the circumference of the circle be 1 and that A chooses a location at point 0. Business D will choose a location in the middle of the largest section.
Business C will also choose the midpoint of the larger of the two gaps between the first two businesses.
If business B chooses a point before 1/3 then C will choose a point halfway between B and 1. Business D will choose randomly between the halfway point between A and C or B and C. If x is the location of business B then the area which B will carve out of the circle will be either (1+3x)/8 if D goes between B and C or (1+x)/4 if D goes between A and C. The average of these is (3+5x)/16. The same logic applies if B chooses a point after 2/3.
If business B chooses a point after 1/3 (but before 1/2) then C will choose a point halfway between A and B going the long way and D will choose the halfway point between A and B the short way. This will leave B exactly a 1/4 share of the business. The same logic applies if A chooses a point between 1/2 and just before 2/3.
If B should choose a location at exactly 1/3 then C would choose at 2/3 and D would be indifferent between 1/6, 1/2, and 5/6. B would have a 2/3 chance of having 1/4 of the business share and 1/3 chance of having 1/3, the average being 5/18 =~ 0.27778 .
Thus B should try to maximize (3+5x)/16 without choosing x equal or greater to 1/3. The optimal choice of location would be just a hair short of 1/3 (or just a hair after 2/3). At this point B will have a 50/50 chance at having either 1/4 or 1/3 of the market share for an average of 7/24=~ 0.29166667 of the market share.
correct answer B
Answer: (B) barely less then 1/3
Question: Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 sec. What is the length of the fast train?
(A) 27 7/7 m
(B) 27 8/9 m
(C) 29 7/9 m
(D) 27 7/9 m
(E) 27 7/2m
Rationale: Relative speed = (40 - 20) = 20 km/hr.
= 20 * 5/ 18 = 50/9 m/sec.
Length of faster train = 50/9 * 5
= 250/9
= 27 7/9 m.
Answer:D:
Answer: (D) 27 7/9 m
Question: |13 - 3| - |4 - 10| = ?
(A) 3
(B) 2
(C) 1
(D) 0
(E) 4
Rationale: |13 - 3| - |4 - 10| = | 10 | - | -6 | = 10 - 6 = 4
correct answer E
Answer: (E) 4
Question: If 3 people can do 3 times of a particular work in 3 days, then how many days would it take 4 people to do 4 times of that particular work?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 7
Rationale: 3 people can do the work one time in one day.
1 person can do 1/3 of the work in one day.
4 people can do 4/3 of the work in one day.
4 people can do 4 times the work in 3 days.
The answer is C.
Answer: (C) 3
Question: There are 12 stamps from which two stamps will be selected. We have five stamps which are the same as five of the stamps which could be selected. What is the probability that the two stamps selected will be different from the stamps that we have?
(A) 3/14
(B) 5/19
(C) 7/22
(D) 9/23
(E) 11/28
Rationale: P(first stamp is different) = 7/12
P(second stamp is different) = 6/11
P(both stamps are different) = 7/12*6/11 = 7/22
The answer is C.
Answer: (C) 7/22
Question: Certain sum becomes 3 times it self at compound interest in 10 years. In how many years it becomes 9 times?
(A) 24
(B) 20
(C) 22
(D) 28
(E) 25
Rationale: P(1 + R/100)(power10) = 3P
=> P(1 + R/100)(power10) = 3
Let P(1 + R/100)(power n) = 9P
=> (1 + R/100)(power n) = 9
=> 3(power 2) = [(1 + R/100)(power10)](power2)
=> (1 + R/100)(power n) => (1 + R/100)(power 20)
=> n = 20 Years.
Answer is B.
Answer: (B) 20
Question: 5 years ago Kate was 5 times as old as her Son. 5 years hence her age will be 8 less than three times the corresponding age of her Son. Find the age of kate?
(A) 33
(B) 34
(C) 35
(D) 36
(E) 37
Rationale: let x be the mother's age and y be the son's age
x-5=5(y-5)
x+5=3(y+5)-8
by solving this we get x=35
ANSWER:C
Answer: (C) 35
Question: The last day of a century cannot be
(A) Monday
(B) Wednesday
(C) Tuesday
(D) Friday
(E) 3922
Rationale: Answer: C) Tuesday
Answer: (C) Tuesday
Question: What is the ratio between perimeters of two squares one having 3 times the diagonal then the other?
(A) 32.5
(B) 32.4
(C) 32.9
(D) 32.3
(E) 32.1
Rationale: 36/7 r = 6.3
= 32.4
Answer:B
Answer: (B) 32.4
Question: If x is the interest on y and y is the interest on z, the rate and time is the same on both the cases. What is the relation between x, y and z?
(A) Y2 = XY
(B) Y2 = XZ
(C) Y2 = XZ
(D) X2 = XZ
(E) Y2 = ZY
Rationale: X = (Y*NR)/100 Y = (Z*NR)/100
X/Y = NR/100 Y/Z = NR/100
X/Y = Y/Z
Y2 = XZ
Answer: C:
Answer: (C) Y2 = XZ
Question: A gas station sold 50 000 liters of petrol at $1.50 per liter, 40 000 liters of diesel at $2.20 per liter and 100 000 liters of bio diesel at $1.10 per liter. what % of its total revenue is from bio diesel?
(A) 45.3%
(B) 40.3%
(C) 41.3%
(D) 42.3%
(E) 46.3%
Rationale: Correct Answer:B
The company's total revenue from petrol=50000*$1.50=$75000
The company's total revenue from diesel=40000*$2.20=$88000
The company's total revenue from bio diesel =100000*$1.10=$110000
The combined total of all sales=$273000
Therefore % of bio diesel sales=110000/273000*100= 40.3%
Answer: (B) 40.3%
Question: How many multiples of 7 are there between 10 and 100 (both are inclusive)?
(A) 11
(B) 13
(C) 15
(D) 17
(E) 21
Rationale: 7 multiples are 14,21,28,---------,98
It should be mentioned whether 10 and 100 are inclusive.
the answer is (98-14)/7+1=13
Answer is B
Answer: (B) 13
Question: if a men rows at the rate of 5 kmph in still water and his rate against the current is 3.5 kmph, then the man’s rate along the current is :
(A) 4.25 kmhr
(B) 6 kmph
(C) 6.5 kmph
(D) 8.5 kmph
(E) None of these
Rationale: Solution
Let the rate along the current be x kmph.
Then,1/2(x +3.5)= 5 or x= 6.5 kmph. Answer C
Answer: (C) 6.5 kmph
Question: between 100 to 200 how many no are divisible by both 3 and 2 and 100,200 are inclusive?
(A) 77
(B) 78
(C) 79
(D) 80
(E) 81
Rationale: Prime numbers are 21
So 100-21=79
ANSWER:C
Answer: (C) 79
Question: Suppose that another fresh fruit contains 40% water and dry fruit contains 25% water. How much dry fruit can be obtained from 100kg of fresh fruit?
(A) A)32kg
(B) B)40kg
(C) C)80kg
(D) D)85kg
(E) E)100kg
Rationale: Quantity of pulp in 100kg of fresh fruits = (100-40)% of 100kg = 60kg
Let the quantity of dry fruit obtained be x kg
then, (100-25)% of x = 60
(75/100)*x = 60
x = 80
correct option is C
Answer: (C) C)80kg
Question: How many seconds will a 500 meter 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) 25 sec
(B) 40 sec
(C) 30 sec
(D) 60 sec
(E) 50 sec
Rationale: Let length of tunnel is x meter
Distance = 800+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
800+x = (65/3) * 60
800+x = 20 * 65 = 1300
x = 1300 - 800 = 500 meters
ANSWER C
Answer: (C) 30 sec
Question: Cheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 5 to 7 to 8. If a total of 360 sandwiches were made, how many Cheese sandwiches
were made?
(A) 15
(B) 30
(C) 90
(D) 42
(E) 48
Rationale: For deciding such task we should calculate all parts 5 + 7 + 8 = 20 parts
and we should calculate how many sandwiches holds 1 part:
360 / 20 = 18 sandwiches in one part
For cheese we have 5 parts so:
5 * 18 = 90
Answer is C
Answer: (C) 90
Question: If |20x-10| = 130, then find the product of the values of x?
(A) -45
(B) 50
(C) -42
(D) 35
(E) -30
Rationale: |20x-10| = 130
20x-10 = 130 or 20x-10 = -130
20x = 140 or 20x = -120
x = 7 or x = -6
product = -6*7 = -42
Answer is C
Answer: (C) -42
Question: One side of a rectangular field is 4 m and its length along diagonal is 5 m. What is the area of the field?
(A) 3
(B) 4
(C) 6
(D) 8
(E) 9
Rationale: M = 4
S = 2
US = 4 - 2 = 2
D = 6
T = 6/2 = 3
Answer: A
Answer: (A) 3
Question: Together, 15 type A machines and 7 type B machines can complete a certain job in 4 hours. Together 8 type B machines and 15 type C machines can complete the same job in 11 hours. How many hours E would it take one type A machine, one type B machine, and one type C machine working together to complete the job (assuming constant rates for each machine)?
(A)  22 hours
(B)  30 hours
(C)  44 hours
(D)  60 hours
(E)  It cannot be determined from the information above.
Rationale: Say the rates of machines A, B and C are a, b, and c, respectively.
Together 15 type A machines and 7 type B machines can complete a certain job in 4 hours --> 15a + 7b = 1/4;
Together 8 type B machines and 15 type C machines can complete the same job in 11 hours --> 8b + 15c = 1/11.
Sum the above: 15a + 15b + 15c = 1/4 + 1/11 = 15/44 --> reduce by 15: a + b + c = 1/44 --> so, the combined rate of the three machines is 1/44 job/hour --> time is reciprocal of the rate, thus machines A, B and C can do the job E in 44 hours.
Answer: C.
Answer: (C)  44 hours
Question: What percent is 10 gm of 1 kg?
(A) 0.5 %
(B) 1%
(C) 1.5%
(D) 2%
(E) 3%
Rationale: 1 kg = 1000 gm
10/1000 × 100 = 1000/1000
=1 %
B)
Answer: (B) 1%
Question: Jerry’s average (arithmetic mean) score on the first 3 of 4 tests is 94. If Jerry wants to raise his average by 2 points, what score must he earn on the fourth test?
(A) 87
(B) 89
(C) 90
(D) 93
(E) 102
Rationale: Total score on 3 tests = 94*3 = 282
Jerry wants the average to be = 96
Hence total score on 4 tests should be = 96*4 = 384
Score required on the fourth test = 384 - 282 = 102
Option E
Answer: (E) 102
Question: At a certain food stand, the price of each apple is 40¢ and the price of each orange is 60¢. Mary selects a total of 10 apples and oranges from the food stand, and the average (arithmetic mean) price of the 10 pieces of fruit is 52¢. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is 44¢?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: If the average price is 52, then Mary has 6 oranges and 4 apples (a ratio of 3:2).
For the average price to be 44, the ratio should be 1:4.
Mary must put back 5 oranges.
The answer is E.
Answer: (E) 5
Question: The total price of a basic computer and printer are $2,500. If the same printer had been purchased with an enhanced computer whose price was $500 more than the price of the basic computer, then the price of the printer would have been 1/3 of that total. What was the price of the basic computer?
(A) 1500
(B) 1600
(C) 1750
(D) 1900
(E) 2000
Rationale: Let the price of basic computer be C and the price of the printer be P: C+P=$2,500.
The price of the enhanced computer will be C+500 and total price for that computer and the printer will be 2,500+500=$3,000. Now, we are told that the price of the printer is 1/3 of that new total price: P=1/3*$3,000=$1000
Plug this value in the first equation: C+1000=$2,500 --> C=$1,500.
Answer: A.
Answer: (A) 1500
Question: The number of girls in a class is 5 times the number of boys. Which one of the following numbers cannot represent the total number of children in the class
(A) 27`
(B) 28
(C) 277
(D) 198
(E) 171
Rationale: Answer:B
Answer: (B) 28
Question: The number of girls in a class is 5 times the number of boys. Which one of the following numbers cannot represent the total number of children in the class.
(A) 36
(B) 41
(C) 48
(D) 72
(E) 11
Rationale: Answer:A
Answer: (A) 36