mathewhe/aqua_rat huggingface dataset:
Question: It takes 2 workers a total of 12 hours to build a giant machine with each worker working at the same rate. If 3 workers start to build the machine at 11:00 AM, and one extra worker per hour is added beginning at 2:00 PM, at what time will the machine be complete?
(A) 4:30
(B) 4:45
(C) 5:00
(D) 5:15
(E) 5:30
Rationale: 2 workers build 1/12 of a machine in one hour.
1 worker builds 1/24 of a machine in one hour.
In the first 3 hours, 3 workers build 3*(1/24)*3=9/24 of a machine
From 2:00 to 3:00, 4 workers build another 4/24. The total is 13/24.
From 3:00 to 4:00, 5 workers build another 5/24. The total is 18/24.
From 4:00 to 5:00, 6 workers build another 6/24. The total is 24/24.
The machine is complete at 5:00.
The answer is C.
Answer: (C) 5:00
Question: Train X crosses a stationary train Y in 60 seconds and a pole in 25 seconds with the same speed. The length of the train X is 300 m. What is the length of the stationary train Y?
(A) 420
(B) 776
(C) 288
(D) 268
(E) 198
Rationale: Let the length of the stationary train Y be LY
Given that length of train X, LX = 300 m
Let the speed of Train X be V.
Since the train X crosses train Y and a pole in 60 seconds and 25 seconds respectively.
=> 300/V = 25 ---> ( 1 )
(300 + LY) / V = 60 ---> ( 2 )
From (1) V = 300/25 = 12 m/sec.
From (2) (300 + LY)/12 = 60
=> 300 + LY = 60 (12) = 720
=> LY = 720 - 300 = 420 m
Length of the stationary train = 420 m
Answer:B
Answer: (B) 776
Question: The distance between West-Town to East-Town is 10 kilometers. Two birds start flying simultaneously towards one another, the first leaving from West-Town at a speed of 4 kilometers per minute and the second bird, leaving from East-Town, at a speed of 1 kilometers per minute. What will be the distance, in kilometers, between the meeting point and West-Town?
(A) 3.
(B) 8.
(C) 10.
(D) 12.
(E) 15.
Rationale: Time taken by the birds to meet = 10/(4 + 1) = 2 mins
Distance traveled by the bird traveling from West-Town = 4 * 2 = 8
Answer: B
Answer: (B) 8.
Question: A vessel of capacity 2 litre has 16% of alcohol and another vessel of capacity 6 litre had 40% alcohol. The total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water. What is the new concentration of Mixture?
(A) 31%.
(B) 71%.
(C) 49%.
(D) 27.2%.
(E) 51%.
Rationale: 16% of 2 litres = 0.32 litres
40% of 6 litres = 2.4 litres
Therefore, total quantity of alcohol is 2.72 litres.
This mixture is in a 10 litre vessel. Hence, the concentration of alcohol in this 10 litre vessel is 27.2%
ANSWER:D
Answer: (D) 27.2%.
Question: 5 men and 2 boys working together can do four times as much work as a man and a boy. Working capacity of man and boy is in the ratio
(A) 1:2
(B) 1:3
(C) 2:1
(D) 2:3
(E) None of these
Rationale: Explanation:
Let 1 man 1 day work = x
1 boy 1 day work = y
then 5x + 2y = 4(x+y)
=> x = 2y
=> x/y = 2/1
=> x:y = 2:1
Option C
Answer: (C) 2:1
Question: A and B start a business with Rs.6000 and Rs.8000 respectively. Hoe should they share their profits at the end of one year?
(A) 3:5
(B) 3:4
(C) 3:1
(D) 3:2
(E) 3:9
Rationale: They should share the profits in the ratio of their investments.
The ratio of the investments made by A and B =
6000 : 8000 => 3:4
Answer:B
Answer: (B) 3:4
Question: A group of ants, each 1/3 centimeters in length, crosses a sidewalk in single file, each right behind the next, at a speed of 30 cm/min. If the sidewalk is 1.5 meters wide, how long does it take for 30 ants to all make it across?
(A) 2 min
(B) 3 min
(C) 4 min
(D) 5 min
(E) 6 min
Rationale: E
6 min
d = 30 * 1/3 cm + 150 cm = 180 cm
T = 180 cm / 30 cm/min = 6 min
Answer: (E) 6 min
Question: In a certain match all the teams were to play with each other. If there are 7 teams, how many matches will have to be played?
(A) 40
(B) 21
(C) 24
(D) 25
(E) None of the above
Rationale: 7c2
=21
ANSWER:B
Answer: (B) 21
Question: How many possible integer values are there for x if |5x - 3| < 6 ?
(A) One
(B) Two
(C) Three
(D) Four
(E) Five
Rationale: Solution: |5x-3| < 6
let 5x=a therefore we have |a-3| < 6 ==> read this as origin is at +3 and we have to move +6 to the right and -6 to the left
(the less than sign represents that the a must be within boundaries )
(3-6)----------3----------(3+6)
now, we have -3<a<9
but a =5x ==> -3<5x<9
dividing all values by +4 we have -0.6<x < 1.8
Now question says Integer values (not rational ) therefore we have 0,1
Hence 2 B
Answer: (B) Two
Question: The number 523dbc is divisible by 7,8,9. Then what is the value of d*b*c
(A) 504
(B) 532
(C) 210
(D) 180
(E) 280
Rationale: LCM of 7, 8 and 9 is 504, thus 523dbc must be divisible by 504.
523dbc=523000+dbc
523000 divided by 504 gives a remainder of 352.
Hence, 352+dbc=k*504.
k=1 dbc=152 --> d*b*c=10
k=2 dbc=656 --> d*b*c=180
As dbc is three digit number k can not be more than 2.
Two answers? Well only one is listed in answer choices, so D.
Answer: D.
Answer: (D) 180
Question: A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.200 when the rate to profit rises from 5 to 7 percent. Find the Capital of B?
(A) 2655
(B) 3527
(C) 2500
(D) 2567
(E) 2571
Rationale: A:B:C = 2/3:1/6:1/6
= 4:1:1
x * 2/100 * 2/3
= 200
B capital = 15000*1/6
= 2500
Answer: C
Answer: (C) 2500
Question: A company D has 15 percent of the employees are secretaries and 45 percent are salespeople. If there are 50 other employees of Company D, how many employees does Company D have?
(A) 200
(B) 125
(C) 180
(D) 152
(E) 250
Rationale: Let the total number of employees in the company be x
% of secretaries = 15%
% of salespeople = 45%
% of of employees other than secretaries and salespeople = 100 - 60 = 40%
But this number is given as 50
so 40% of x = 50
x = 125
Therefore there a total of 125 employees in the company D
Correct answer - B
Answer: (B) 125
Question: If m is a positive integer and m^2 is divisible by 33, then the largest positive integer that must divide m is?
(A)  3
(B)  6
(C)  8
(D)  11
(E)  16
Rationale: M^2 is divisible by 33 so M^2 must be multiple of 48.
If the value of M is Multiples of 11 then it will satisfy the condition. If we If M is 12 or 24 or 36 then it ans is D but if M = 33 then answer should be 16.
Is the question right? Or am i missing some thing?
D
Answer: (D)  11
Question: In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is 2/3 of the number of students of 8 years of age which is 48. What is the total number of students in the school?
(A) 72
(B) 80
(C) 120
(D) 150
(E) 100
Rationale: Let the number of students be x.
Then, Number of students above 8 years of age = (100 - 20)% of x = 80% of x.
80% of x = 48 + 2/3 of 48
80/100x = 80
x = 100.
Answer: Option E
Answer: (E) 100
Question: In what ratio should a mixture of milk and water in the ratio of 3:4 be mixed with another mixture of milk and water in the ratio 5:2 so that the resultant mixture contains equal quantities of milk and water?
(A) 3:1
(B) 3:5
(C) 7:8
(D) 7:9
(E) 9:11
Rationale: First mixture: milk and water in the ratio of 3x:4x.
Second mixture: milk and water in the ratio 5y:2y.
We want their mixture to have equal quantities of milk and water: 3x + 5y = 4x + 2y --> x/y = 3.
Answer: A.
Answer: (A) 3:1
Question: A man takes 3 hours 45 minutes to row a boat 15 km downstream of a river and 2hours30minutes to cover a distance of 5km upstream. find the speed of the river current in km/hr.
(A) 1 km/hr
(B) 2 km/hr
(C) 3 km/hr
(D) 4 km/hr
(E) 5 km/hr
Rationale: rate downstream=(15/3 Â¾)km/hr=(15*4/15)km/hr=4km/hr.
Rate upstream=(5/2 Â½)km/hr=(5*2/5)km/hr=2km/hr.
Speed of current=1/2(4-2)km/hr=1km/hr
ANSWER A
Answer: (A) 1 km/hr
Question: Two numbers are respectively 17% and 30% more than a third number. The percentage that is first of the second is?
(A) 75%
(B) 80%
(C) 85%
(D) 70%
(E) 90%
Rationale: I II III
117 130 100
130----------117
100-----------? => 90%
Answer:E
Answer: (E) 90%
Question: In a bag, there are coins of 25 p, 10 p and 5 p in the ratio of 1:2:3. If there are Rs. 30 in all, how many 5 p coins are there?
(A) 176
(B) 167
(C) 150
(D) 717
(E) 154
Rationale: Let the number of 25 p, 10 p and 5 p coins be x, 2x and 3x respectively.
Then, sum of their values
= [25x/100 + (10 * 2x)/100 + (5 * 3x)/100]
= Rs. 60x/100
60x/100 = 30 => x = 50.
Hence, the number of 5 p coins = 3 * 50 = 150.
Answer:C
Answer: (C) 150
Question: In one hour, a boat goes 8 km/hr along the stream and 2 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
(A) 3 km/hr
(B) 4 km/hr
(C) 5 km/hr
(D) 6 km/hr
(E) 8 km/hr
Rationale: Upstream relative speed is u + v=8km/hr
Downstream speed is u-v = 2
Where u = speed of boat in still water and v is speed of stream
Then adding two equations u+v + u-v =8+2
2u=10
Finally, u=5.
ANSWER : C
Answer: (C) 5 km/hr
Question: Find the value of b from (15)^2 x 9^2 Ã· 356 = b.
(A) 53.2
(B) 52.2
(C) 51.2
(D) 8.2
(E) 54.2
Rationale: Given Exp. =(15)^2 x 9^2 Ã· 356= b
= 225 x 81 Ã· 356
= 51.2
C
Answer: (C) 51.2
Question: In a bag there are coins of 50 paisa, 25 paisa and one rupee in the proportion 4:3:2. If there are in all Rs.42, the number of one rupee coins is?
(A) 22
(B) 26
(C) 18
(D) 16
(E) 24
Rationale: 4x 3x 2x
50 25 100
200x + 75x + 200x = 3800
475x = 3800
x = 8 => 2x = 16
Answer: D
Answer: (D) 16
Question: A sum of money is divided among A, B, C & D in the ratio 3:5:8:9 respectively. If the share of D Rs.1872 more than the share of A, then what is the total amount of money of B & C together?
(A) 3000
(B) Rs. 4056
(C) 5000
(D) 5400
(E) 5600
Rationale: Sol. Share of B + C = -3 x (5 + 8) = Rs. 4056
B
Answer: (B) Rs. 4056
Question: The diagonals of a rhombus are 15 cm and 20 cm. Find its area?
(A) 176
(B) 186
(C) 150
(D) 179
(E) 172
Rationale: 1/2 * 15 * 20
= 150
Answer:C
Answer: (C) 150
Question: Which of the following is divisible by the first ten positive integer multiples of 11?
(i) 18810
(ii) 263640
(iii) 3011010
(A) None
(B) ii only
(C) i and ii only
(D) i and iii only
(E) ii and iii only
Rationale: A positive integer x is divisible by the first five integer multiples of 23 if and only if it is divisible by their least common multiple, 8*9*5*7*11.
8*9*5*7*11 is less than 70*30*10=21000, (i) cannot possibly be divisible by 8*9*5*7*11.
The integers of 3011010 sum to 6, so 3011010 is divisible by 3, but not 9, so (iii) is not divisible by 8*9*5*7*11.
If (ii) is divisible by 8*9*5*7*11 then 26364 is divisible by 11. So 26364=11y=10y+y for some positive integer y. y must have initial digit 2 and final digit 4. Final and third digit of y must add to 6, so third digit of y is 2. Then similarly, second and third digit add to three, so second digit is 1. But then second and first digit must sum to 6, but first digit is 2, second is 1, so (ii) cannot be divisible by 11.
Answer A
Answer: (A) None
Question: Maxwell leaves his home and walks toward Brad's house at the same time that Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 70 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 6 km/h, what is the distance traveled by Brad?
(A) 42
(B) 18
(C) 20
(D) 24
(E) 30
Rationale: Time taken = Total Distance / Relative Speed
Total Distance = 70 kms
Relative Speed (Opposite side) (As they are moving towards each other speed would be added ) = 6+ 4 = 10 kms/hr
Time taken = 70 / 10 = 7 hrs
Distance traveled by Brad = Brad's speed * time taken = 6 * 7 = 42 kms... Answer - A
Answer: (A) 42
Question: A train 100 meters long completely crosses a 300 meters long bridge in 15 seconds. What is the speed of the train is?
(A) 32 kmph
(B) 96 kmph
(C) 34 kmph
(D) 43 kmph
(E) 40 kmph
Rationale: S = (100 + 300)/45
= 400/15 * 18/5
= 96
Answer:B
Answer: (B) 96 kmph
Question: The value of x + x(xx) when x = 6 is:
(A) 8
(B) 10
(C) 12
(D) 14
(E) 222
Rationale: x + x(xx)
Put the value of x = 6 in the above expression we get,
6 + 6(6*6)
= 222
ANSWER : E
Answer: (E) 222
Question: Dan's age after 16 years will be 6 times his age 4 years ago. What is the present age of Dan?
(A) 8
(B) 10
(C) 12
(D) 14
(E) 16
Rationale: Let Dan's present age be x.
x+16 = 6(x-4)
5x = 40
x = 8
The answer is A.
Answer: (A) 8
Question: If e = 20! + 17, then e is divisible by which of the following?
I. 15
II. 17
III. 19
(A)  None
(B)  I only
(C)  II only
(D)  I and II
(E)  II and II
Rationale: Another crude way to answer this, if you did not know the properties above would be to consider that that 20! will have the number ending in 00 due to 10 and 20 being included.
So e!+17 = xxxx00 +17 = xxxx17 which is only possibly divisible by 17. Hence Option C is the answer.
Answer: (C)  II only
Question: A man can row 7.8 kmph in still water and he finds that it takes him twice as long to row up as to row down the river. Find the rate of stream.
(A) 2.6 km/hr
(B) 12.5 km/hr
(C) 1 2.6 km/hr
(D) 22.5 km/hr
(E) 22.6 km/hr
Rationale: Given that, time taken to travel upstream = 2 × time taken to travel downstream
When distance is constant, speed is inversely proportional to the time
Hence, 2 × speed upstream = speed downstream
Let speed upstream = x
Then speed downstream = 2x
we have, 1/2(x+2x) = speed in still water
⇒1/2(3x)=7.8
3x = 15.6
x = 5.2
i.e., speed upstream = 5.2 km/hr
Rate of stream = 1/2(2x−x)=x/2=5.2/2=2.6 km/hr
Answer is A
Answer: (A) 2.6 km/hr
Question: What is the value of (P + Q)/(P - Q) if P/Q is 5?
(A) 4/3
(B) 3/2
(C) 2/6
(D) 7/8
(E) 8/7
Rationale: (P + Q)/(P - Q) = [(P/Q) + 1]/[(P/Q) - 1]
= (5 + 1)/(5 - 1)
= 6/4
= 3/2
ANSWER:B
Answer: (B) 3/2
Question: If population of certain city increases at the rate of 5%. If population in 1981 was 324135, then population in 1978 was?
(A) 120000
(B) 228788
(C) 280000
(D) 267689
(E) 127791
Rationale: X * (105/100) * (105/100) * (105/100) = 324135
X = 324135/1.157625
X = 280000
Answer C
Answer: (C) 280000
Question: The value of (0.137+0.098)²-(0.137 - 0.098)² / 0.137×0.098 is
(A) 0.039
(B) 0.235
(C) 0.25
(D) 4
(E) 5
Rationale: Solution
Given expression	= (a+b)² - (a-b)²/ab
= 4ab/ab
= 4.
Answer D
Answer: (D) 4
Question: Joe has candys on his pocket, 4 of those candies have lemon flavor, and 3 have caramel flavor. If Joe take one, what is the probability that he picks one caramel flavor?
(A) 1
(B) 2
(C) none
(D) 3/7
(E) 3/4
Rationale: the total number of candies is 7
and the number of candies with lemon flavor is 3
then, in one chance the probability to pick one candie with lemon flavor is
3/7
Answer D
Answer: (D) 3/7
Question: ♠n denotes the number obtained when n is rounded to the nearest tenth. For example ♠4.31 = 4.3
♠0.089 - ♠1.235 =
(A) 1.05
(B) 1.04
(C) -1.05
(D) -1.0
(E) -1.1
Rationale: ♠0.089 - ♠1.135 =
0.1 - 1.2 = -1.1
Answer : E
Answer: (E) -1.1
Question: Find the sum lend at C.I. at 5 p.c per annum will amount to Rs.441 in 2 years?
(A) 227
(B) 400
(C) 277
(D) 686
(E) 120
Rationale: 441 = P(21/20)2
P = 400
Answer: B
Answer: (B) 400
Question: It takes Joey the postman 1 hours to run a 3 mile long route every day. He delivers packages and then returns to the post office along the same path. If the average speed of the round trip is 6 mile/hour, what is the speed with which Joey returns?
(A) 11
(B) 12
(C) 13
(D) 14
(E) 18
Rationale: let his speed for one half of the journey be 3 miles an hour
let the other half be x miles an hour
now,
avg speed =6 mile an hour
2*3*x/3+x=6
6x=6x+18=>x=18
E
Answer: (E) 18
Question: My grandson is about as many days as my son in weeks, and my grandson is as many months as I am in years. My grandson, my son and I together are 140 years. Can you tell me my age in years?
(A) 80
(B) 90
(C) 85
(D) 84
(E) 89
Rationale: let the age of the man = x years
so according to the given condition
age of my grandson = x/12 years
and age of my son = x30/52 = 15x/26
and x + (x/12) + (15x/26) = 140
or (156x+13x+90x)/156 = 140
or 259x = 156*140
or x = 156*140/259 = 84
ANSWER:D
Answer: (D) 84
Question: A man buys an article for $100. and sells it for $110. Find the gain percent?
(A) 10%
(B) 15%
(C) 25%
(D) 20%
(E) 30%
Rationale: C.P. = $100
S.P. = $110
Gain = $10
Gain% = 10/100 *100 = 10%
Answer is A
Answer: (A) 10%
Question: A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is :
(A) 45.30 km/hr
(B) 55.15 km/hr
(C) 70.15 km/hr
(D) 71.11 km/hr
(E) None
Rationale: Sol.
Total time taken = [160/64 + 160/8] hrs = 9/2 hrs.
∴ Average speed = [320*2/9] km/hr = 71.11 km/hr.
Answer D
Answer: (D) 71.11 km/hr
Question: Ram, who is half as efficient as Krish, will take 18 days to complete a task if he worked alone. If Ram and Krish worked together, how long will they take to complete the task?
(A) 16 days
(B) 12 days
(C) 8 days
(D) 6 days
(E) 18 days
Rationale: Number of days taken by Ram to complete task = 18
Since Ram is half as efficient as Krish , Amount of work done by Krish in 1 day = Amount of work done by Ram in 2 days
If total work done by Ram in 18 days is 18w
Amount of work done by Ram in 1 day = w
Amount of work done by Krish in 1 day = 2w
Total amount of work done by Krish and Ram in a day = 3w
Total amount of time needed by Krish and Ram to complete task = 18w/3w = 6 days
Answer D
Answer: (D) 6 days
Question: If x is a positive odd number, then each of the following is odd EXCEPT
(A) (x + 3)(x + 5)
(B) x^2 + 5
(C) x^2 + 6x + 9
(D) 3x^2 + 4
(E) 5(x + 3)
Rationale: Since it is given tht x is even number, so any integer multiplied with x will also be even..
so, we should concentrate only on other terms..
lets see the choices..
A. (x + 3)(x + 5)
We have two terms with x and each is added with a odd number..
each bracket becomes odd and Odd*Odd=Odd
B. x^2 + 5
here we are adding an Odd number to even.. so E + O=O
C. x^2 + 6x + 9
here we are again adding an Odd number to even.. so E +E + O=O
D. 3x^2 + 4
here we are adding an Even number to even.. so E + E=E..
so tjis is our answer
E. 5(x + 3)
again O*O=O
B
Answer: (B) x^2 + 5
Question: A man gave 1/8 of his property to his wife and 1/4 of the remaining to his daughter. What fraction of his property is he left with after giving to his wife and his daughter?
(A) 5/16
(B) 2/8
(C) 21/32
(D) 4/8
(E) 12/15
Rationale: A man gave 1/8 of his property to his wife, so remaining is 7/8
He gave 1/4 of the remaining property to his daughter, 1/4*7/8=7/32
Total property given to his wife and daughter is 1/8+7/32
To make the denominator common, we use 32=4/32
4/32+7/32=11/32 is given to his wife and daughter
Remaining property left with him is 21/32
Answer is C
Answer: (C) 21/32
Question: The average of 4,8,12 and x is 10. Find the value of x?
(A) 10
(B) 16
(C) 15
(D) 24
(E) 12
Rationale: average = (4+8+12+x)/4 = 10
x = 16
Answer is B
Answer: (B) 16
Question: If a man lost 4% by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44%?
(A) 2
(B) 8
(C) 6
(D) 4
(E) 2
Rationale: 96% ---- 12
144% ---- ?
96/144 * 12 = 8
Answer: B
Answer: (B) 8
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 four times the duration it would take pump X alone to fill the tank. If pump Y alone can empty a whole tank in 44 minutes, then how many minutes does it take pump X alone to fill the tank?
(A) 27
(B) 30
(C) 33
(D) 36
(E) 39
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/44 per minute.
(R - V/44)*4T=V=RT.
(R-V/44)*4=R
3R=V/11.
R=V/33.
It takes pump X 33 minutes to fill the tank.
The answer is C.
Answer: (C) 33
Question: 12.1212+17.0005 - 9.1105 = ?
(A) 20.0015
(B) 20.0105
(C) 20.0115
(D) 20.1015
(E) 20.0112
Rationale: Solution
Given expression
=(12.1212+17.0005)-9.1105
= (29.1217 - 9.1105)
=20.0112.
Answer E
Answer: (E) 20.0112
Question: If a and b are nonzero integers such that 4a = 10b, then each of the following must be true EXCEPT
(A) 0 < b/a < 1
(B) ab is positive.
(C) On the number line, b lies between 0 and a.
(D) The ratio of a to b is equivalent to 10/4.
(E) a – b is positive.
Rationale: This question can be solved by TESTing VALUES. Based on its wording, you would likely need to do 2 TESTs to get to the correct answer though.
We're told that A and B are NONZERO INTEGERS and that 4a = 10b or 2A = 5b. We're told that each of the answer is always true EXCEPT for one of them...
Before we get to the actual work, it's important to note a few details:
1) We are NOT told that A and B are positive - we're just told that they're NONZERO - that's interesting - it means that we have to consider the possibility that they're both NEGATIVE...
2) 4 of the answers will always be true, while one of them will EITHER be sometimes true OR never true. We'll have to keep working until we find 1 answer that is not true (for whatever reason) - that will be the solution to this question.
Since 2A = 5B, I'm going to run 2 pairs of TESTs at the same time...
A = 5
B = 2
AND
A = -5
B = -2
Answer A: 0 < B/A < 1
2/5 and -2/-5 both = 2/5. Answer A appears true.
Answer B: AB is positive
(2)(5) and (-2)(-5) both = +10. Answer B appears true.
Answer C: B is between 0 and A on the number line
0....2....5
-5....-2....0
Answer C appears true.
Answer D: A/B = 10/4
5/2 = -5/-2
10/4 = 5/2
Answer D appears true.
Answer E: A - B is positive
5 - 2 = 3
-5 - (-2) = -3 *****This is NOT always true.
Final Answer:
E
Answer: (E) a – b is positive.
Question: Cars emerging from a motorway arrive at a junction that splits the road into two separate lanes. The number of cars per hour that continue in either lane is constant. If 7 cars per hour were diverted from the left lane to the right lane, the number of cars entering the right lane per hour would be twice as big as the number of cars entering the left lane per hour. Alternatively, if 7 cars per hour were diverted from the right lane to the left lane, the number of cars entering the left lane per hour would be four times as great as the number of cars entering the right lane per hour. How many cars enter the left lane per hour?
(A) 21
(B) 18
(C) 17
(D) 19
(E) 28
Rationale: as per question 7 cars diverted from left lane to right lane. Thus we get equation R+7=2(L-7)
as per question 7 cars diverted from right lane to left lane .thus we get equation L+7=4(R-7)
by solving two equation i.e R +7 =2L-14 OR. R =2L -21 AND L+7= 4R -28 OR L= 4R -35
BY SOLVING WE GET L= 4( 2L -21) -35 OR L= 8L -84-35 OR 119 =7L THUS L =17
C
Answer: (C) 17
Question: Find the unit's digit from the given 264^102+264^103?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: Required unit's digit = unit's digit in 4102+4103.4102+4103.
Now, 4242 gives unit digit 6.
⇒ 41024102 gives unit digit 6.
⇒ 41034103 gives unit digit of the product 6×46×4 i.e., 4.
Hence, unit's digit in 264102+264103264102+264103
= unit's digit in (6+4)=0
A
Answer: (A) 0
Question: On the first of the year, James invested x dollars at Proudstar bank in an account that yields 2.2% in interest every quarter year. At the end of the year, during which he made no additional deposits or withdrawals, he had y dollars in the account. If James had invested the same amount in an account which pays interest on a yearly basis, what must the interest rate be for James to have y dollars at the end of the year?
(A) 2.04%
(B) 6.12%
(C) 8%
(D) 8.25%
(E) 9%
Rationale: If the interest were compounded annually instead of quarterly then in one year the interest would be 2.2*4=8.8%. Now, since the interest is compounded quarterly then there would be interest earned on interest (very small amount) thus the actual interest would be a little bit more than 8.8%
Answer: E.
Answer: (E) 9%
Question: Indu gave Bindu Rs.1250 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
(A) 7
(B) 2
(C) 9
(D) 5
(E) 4
Rationale: 1250
= D(100/4)2
D = 2
Answer: B
Answer: (B) 2
Question: How long does a train 110 m long traveling at 90 kmph takes to cross a bridge of 170 m in length?
(A) 16.5
(B) 16.0
(C) 16.4
(D) 16.8
(E) 11.2
Rationale: D = 110 + 170 = 280 m
S = 90 * 5/18 = 25
T = 280 * 1/25 = 11.2 sec
Answer: E
Answer: (E) 11.2