mathewhe/aqua_rat huggingface dataset:
Question: Betty took out a charge account at the General Store and agreed to pay 4% simple annual interest. If she charges $50 on her account in January, how much will she owe a year later, assuming she does not make any additional charges or payments?
(A) $51.50
(B) $52.00
(C) $52.50
(D) $53.00
(E) $53.50
Rationale: 1.04*$50=$52.00
The answer is B.
Answer: (B) $52.00
Question: A train 110 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
(A) 5
(B) 6
(C) 4
(D) 9
(E) 8
Rationale: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr
[66 * 5/18] m/sec = [55/3] m/sec.
Time taken to pass the man = [110 * 3/55] sec = 6 sec
Answer: Option B
Answer: (B) 6
Question: A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 4 m, the volume of the box (in m3) is:
(A) 4480
(B) 5120
(C) 6420
(D) 8960
(E) 7960
Rationale: Clearly, l = (48 - 8)m = 40 m,
b = (36 -8)m = 28 m,
h = 8 m.
Volume of the box = (40 x 28 x 4) m3 = 4480 m3. Answer: Option A
Answer: (A) 4480
Question: A 180 meter long train crosses a man standing on the platform in 6 sec. What is the speed of the train?
(A) 108 kmp
(B) 188 kmp
(C) 299 kmp
(D) 278 kmp
(E) 288 kmp
Rationale: S = 180/6 * 18/5
= 108 kmp
Answer: B
Answer: (B) 188 kmp
Question: If you are given $5, and the amount doubles every day, how much money will you have after 4 days?
(A) $256
(B) $512
(C) $1024
(D) $625
(E) $720
Rationale: 5^4=625
The answer is D
Answer: (D) $625
Question: The difference b/w the compound interest payble half yearly and the simple interest on a certain sum lent out at 10% p.a for 1 year is Rs 25. What is the sum?
(A) Rs. 15000
(B) Rs. 12000
(C) Rs. 10000
(D) Rs. 20000
(E) none of these
Rationale: in simple words S.I= PTR/100=(P*1*10)/100 P/10
HERE AMOUNT A= p+ S.I= P+ P/10=11P/10....
NOW FOR COMPOUND INTEREST WHEN CALCULATED HALF YEARLY AMOUNT=P[1+R/200]^2T=P[1+10/200]^2*1=441P/400
here its given in the question dat diff btwn simple interest and compound interest half yearly ... is 25
=> 441p/400-11p/10= 25 =>p/400=25 =>p= 400*25=10000 so sum = 10000
ANSWER:C
Answer: (C) Rs. 10000
Question: How many different subsets of the set {0, 1, 2, 3, 4} do not contain 0?
(A) A.16
(B) B.27
(C) C.31
(D) D.32
(E) E.64
Rationale: Number of subset
Since we have 4 digits other than 0, we can take any numbers from the set of 4 to make a subset. Also it is a matter of selection and not arrangement.So we will consider combinations.
4c1+4c2+4c3+4c4=15
And one set is the NULL set having no elements in it so
15+1=16.
ANSWER A.
Answer: (A) A.16
Question: What number should replace the question mark?
105, 87, 70, ?, 35
(A) 52
(B) 37
(C) 70
(D) 55
(E) 83
Rationale: A
52
The sequence progresses -18, -17, -18, -17.
Answer: (A) 52
Question: An accurate clock shows 8 o'clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 10 o'clock in the morning?
(A) 30
(B) 60
(C) 90
(D) 120
(E) 150
Rationale: The hour hand will move 2/12 of a circle.
(2/12)*360 = 60 degrees.
The answer is B.
Answer: (B) 60
Question: One root of the quadratic equation x2 - 12x + a = 0, is thrice the other. Find the value of a?
(A) 21
(B) 25
(C) 27
(D) 29
(E) 31
Rationale: Let the roots of the quadratic equation be x and 3x.
Sum of roots = -(-12) = 12
a + 3a = 4a = 12 => a = 3
Product of the roots = 3a2 = 3(3)2 = 27.
C)
Answer: (C) 27
Question: If 12/x is an integer and 3/x is an integer, which of the following must be true? I. 6/x is an integer II. 18/x is an integer III. 3/x is an integer
(A) II only
(B) II, III only
(C) III only
(D) I,III only
(E) II only
Rationale: The question asks which of the following MUST be true, not COULD be true. The largest possible value of x is 3, GCD of 12 and 3, and if x=3 then ONLY III is true.
Answer: C
Answer: (C) III only
Question: You have a six-sided cube and six cans of paint, each a different color. You may not mix colors of paint. How many distinct ways can you paint the cube using a different color for each side? (If you can reorient a cube to look like another cube, then the two cubes are not distinct.)
(A) 24
(B) 30
(C) 48
(D) 60
(E) 120
Rationale: Paint one of the faces red and make it the top face.
5 options for the bottom face.
Now, four side faces can be painted in (4-1)! = 3! = 6 ways (circular arrangements of 4 colors).
Total = 5*6 = 30.
Answer: B.
Answer: (B) 30
Question: 6 dogs and 8 cats do a work in 12 days, while 5 dogs and 8 cats finish it in 16days, 4dogs and 8 cats will finish it in.
(A) 14 days
(B) 20 days
(C) 24 days
(D) 12 days
(E) 28 days
Rationale: Explanation:
(6dogs+8cats) 1 day work = 1/12
(5dogs+8cats) 1 day work = 1/16
substract 1 and 2
i.e 1/12 – 1/16= 1/48
i.e 1 dog 1 day work is 1/48
4dogs + 8cats 1day work is 1/16 – 1/48 = 1/24
thus 4 dogs and 8 cats will finish it in 24 days
Answer: Option C
Answer: (C) 24 days
Question: If w, x, and y are consecutive odd positive integers and w < x < y, which of the following could be equal to y - w - x ?
(A) -4
(B) -2
(C) -1
(D) 0
(E) -5
Rationale: Since W, X and Y are CONSECUTIVE ODD POSITIVE INTEGERS and W < X < Y, we can start with the easiest set of values that comes to mind:
W = 7
X = 9
Y = 11
Here, Y - W - X is....
11 - 7 - 9 = -5
-5 IS among the answer choices, so we're done.
E
Answer: (E) -5
Question: list of salaries of 8 employees are listed below. What is the median salary?
$40,000, $29,000, $35,500, $31,700, $43,000, $30,000, $27,000, $32,700
(A) $28,000
(B) $32,200
(C) $30,200
(D) $30,800
(E) $31,500
Rationale: Ordering the data from least to greatest, we get:
$27,000, $29,000, $30,000, $31,700, $32,700, $35,500, $40,000, $43,000
Since there is an even number of items in the data set, we compute the median by taking the mean of the two middlemost numbers.
$31,700 + $32,700 = $64,400
The median salary is $32,200.
Answer : B
Answer: (B) $32,200
Question: The distance traveled by train in one year approximately 50,000,000 miles.The distance traveled by Train in 25 years?
(A) 10<9>
(B) 10<8>
(C) 10<11>
(D) 10<17>
(E) 10<7>
Rationale: The distance traveled by train in one year = 50,000,000 miles
The distance traveled by Train in 25 years = 50,000,000 miles*25 years =1,250,000,000
= 125*10<7> Answer = E
Answer: (E) 10<7>
Question: Rahul's shop runs a sale on goldfish and platys. If one customer buys 13 goldfish and 12 platys for $5.60, and another buys 14 goldfish and 21 platys for $8.05, what is the ratio of the price of goldfish to platys?
(A) 0.8
(B) 0.75
(C) c) 8/9
(D) 5/7
(E) 6/8
Rationale: The approach of plugging in the numbers is a fine approach. But, in this case, the answer was the first option and thus, by plugging in a number in the ration given, we arrived at the answer quickly!
However, what if the correct ratio was option D or C?
In any case, the algebraic solution isn't that complex if you realize a key concept:
The number 7 can be factored out of the second equation!
Here's the working:Rahul's shop runs a sale on goldfish and platys.
13x + 12y = 5.60 <<<<< Equation 1
14x + 21y = 8.05 <<<<< Equation 2
2x + 3y = 1.15 [Factor Out 7 from equation 2] <<<<< Equation 3
8x + 12y = 4.6 [Multiply Equation 3 with 4]
5x = 1.0 [Equation 1 - Equation 2]
x = 0.2
3y = 1.15 - 0.4 = 0.75 [Substitute for x in Equation 1]
y = 0.25
x/y = 0.2/0.25 = 20/25 = 4/5 = 0.8 [Answer A]
The whole thing must have taken me about 45 s :D
Answer: (D) 5/7
Question: A sum of money place at compound interest doubles itself in 6 years. In how many years will it amount to eight times itself?
(A) 15 years
(B) 11 years
(C) 12 years
(D) 18 years
(E) 19 years
Rationale: 100 ---- 200 ---- 6
400 ---- 6
800 ---- 6
------
18 years
Answer: D
Answer: (D) 18 years
Question: lets say that the average (arithmetic mean) of seven numbers is 12.2
If the sum of four of these numbers is 42.8, what is the average of the other 3 numbers?
(A) (a) 12.4
(B) (b) 14.2
(C) (c) 16.8
(D) (d) 18.6
(E) (e) 19.2
Rationale: We're told that the average of 7 numbers is 12.2
(Sum of numbers)/7 = 12.2
Sum of numbers = (12.2)(7) = 85.4
Next, we're told that the sum of 4 (of the 7) numbers is 42.8
From this information, we can calculate the sum of the OTHER 3 numbers:
85.4 - 42.8 = 42.6
The question asks for the AVERAGE of the OTHER 3 numbers....
42.6/3 = 14.2
B
Answer: (B) (b) 14.2
Question: There are 680 students in a school. The ratio of boys and girls in this school is 3:5. Find the total of girls & boys are there in this school?
(A) 425
(B) 345
(C) 375
(D) 380
(E) 400
Rationale: In order to obtain a ratio of boys to girls equal to 3:5, the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys. The total number of boys and girls is 680. Hence
3x + 5x = 680
Solve for x
8x = 680
x = 85
Number of boys
3x = 3 × 85 = 255
Number of girls
5x = 5 × 85 = 425
A
Answer: (A) 425
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue?
(A) fraction of 1/455
(B) 1/451
(C) 1/457
(D) 1/459
(E) 1/452
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that all the three marbles picked at random are blue = 3C3/15C3
= (1 * 3 * 2 * 1)/(15 * 14 * 13)
= 1/455
Answer: A
Answer: (A) fraction of 1/455
Question: If each side of a square is increased by 25%, find the percentage change in its area?
(A) 52.25%
(B) 42.55%
(C) 56.25%
(D) 36.55%
(E) 26.55%
Rationale: let each side of the square be a , then area = a x a
New side = 125a / 100 = 5a / 4
New area =(5a x 5a) / (4 x 4) = (25a²/16)
increased area== (25a²/16) - a²
Increase %= [(9a²/16 ) x (1/a² ) x 100]% = 56.25%
ANSWER : C
Answer: (C) 56.25%
Question: A sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 45 paisa and Z gets 50 paisa. If the share of Y is RS. 27, what is the total amount?
(A) 115
(B) 116
(C) 117
(D) 118
(E) 119
Rationale: x:y:z = 100:45:50
20:9:10
9 --- 27
39 --- ? => 117
ANSWER:C
Answer: (C) 117
Question: Two trains of length 100 meters and 200 meters are 660 meters apart. They are moving towards each other on parallel tracks, at speeds of 90 km/h and 108 km/h. After how many seconds will the trains meet?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
Rationale: The speeds are 90000/3600 = 25 m/s and 108000/3600 = 30 m/s
The relative speed is 55 m/s.
time = 660 / 55 = 12 seconds
The answer is A.
Answer: (A) 12
Question: In a mixture 60 litres, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then the quanity of water to be further added is:
(A) 20 litres
(B) 30 litres
(C) 40 litres
(D) 60 litres
(E) none
Rationale: Quantity of milk = (60 * 2/3)litres = 40 litres.
Quantity of water in it = (60- 40) litres = 20 litres.
New ratio = 1 : 2
Let quantity of water to be added further be x litres.
Then, milk : water = (40 / (20+x))
Now, (40 / (20+x)) = 1/2
20 + x = 80
x = 60.
Quantity of water to be added = 60 litres.
Answer = D
Answer: (D) 60 litres
Question: How many integers between 324,805 and 458,705 have tens digit 2 and units digit 3?
(A) 1,352
(B) 1,359
(C) 1,329
(D) 1,349
(E) 1,348
Rationale: There is one number in hundred with 2 in the tens digit and 3 in the units digit: 23, 123, 223, 323, ...
The difference between 324,700 and 458,600 is 458,600-324,700=134,900 - one number per each hundred gives 133,900/100=1,349 numbers.
Answer: D.
Answer: (D) 1,349
Question: A certain list consists of 21 different numbers. If n is in the list and n is 3 times the average (arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list?
(A) 1/20
(B) 1/6
(C) 1/5
(D) 4/21
(E) 3/23
Rationale: series : a1, a2....a20,n
sum of a1+a2+...+a20 = 20*x (x = average)
so, n = 3*x
Hence, a1+a2+..+a20+n = 23x
So, the fraction asked = 3x/23x =3/23
Answer E
Answer: (E) 3/23
Question: Two trains 121 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?
(A) 7.16
(B) 7.16
(C) 7.12
(D) 7.15
(E) 7.11
Rationale: T = (121 + 165)/ (80 + 65) * 18/5
T = 7.15
Answer: D
Answer: (D) 7.15
Question: The H.C.F. of two numbers is 15 and the other two factors of their L.C.M. are 11 and 15. The larger of the two numbers is:
(A) 225
(B) 300
(C) 299
(D) 322
(E) 345
Rationale: the numbers are (15 x 11) and (15 x 15).
Larger number = (15 x 15) = 225.
ANSWER :A
Answer: (A) 225
Question: Computer completes the first iteration in 10 seconds and then the following iterations are completed in 7 seconds as constants are already loaded. What is the maximum number of completed iterations under 5 minutes?
(A) 41
(B) 42
(C) 43
(D) 44
(E) 45
Rationale: b must be an integer as it is the number of completed iterations at a rate of 7sec/iteration
10 + 7b =5*60
7b = 290
b= 41
The total number of iterations --> 41+1 = 42 and
43rd iteration will be completed at 304seconds which is above 5 minutes
ANSWER: B
Answer: (B) 42
Question: Mr. Karan borrowed a certain amount at 6% per annum simple interest for 9 years. After 9 years, he returned Rs. 8110/-. Find out the amount that he borrowed.
(A) Rs. 5266
(B) Rs. 5269
(C) Rs. 5228
(D) Rs. 5218
(E) Rs. 52192
Rationale: Explanation:
Let us assume Mr. Karan borrowed amount is Rs. A. (the principal)
By formula of simple interest, S.I. = PRT / 100
Where P = The principal, R = Rate of interest as a %, T = Time in years
S.I. = (P * 6 * 9)/100 = 54 P/100
Amount = Principal + S.I.
8110 = P + (54P/100)
8110 = (100P + 54P)/100
8110 = 154P/100
P = (8110 * 100)/154 = Rs. 5266.233
ANSWER: A
Answer: (A) Rs. 5266
Question: In a class of 54 students, 12 enrolled for both English and German. 22 enrolled for German. If the students of the class enrolled for at least one of the two subjects, then how many students enrolled for only English and not German?
(A) 30
(B) 10
(C) 18
(D) 28
(E) 32
Rationale: Total=English+German-Both+Neither --> 54=English+22-12+0 --> English=44 --> Only English=English-Both=44-12=32.
Answer: E.
Answer: (E) 32
Question: A boat can travel 1.5 times the distance down the stream than up the stream in the same time. If the speed of the current is 2 KMPH, Find the speed of the boat in still water
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25
Rationale: Simple question, messy language.
Lets say boat's speed is B and current's speed is C.
Upstream speed : B - C
Downstream speed : B + C
Distance will be the same both times. lets say D.
given : time it takes upstream = 1.5 times time it takes downstream
D/(B + C) = 1.5 * [D/(B - C)]
Solving B = 5 C
given : C is 2 KMPH
So B is 10 KMPH
B
Answer: (B) 10
Question: What profit percent is made by selling an article at a certain price, if by selling at 3/4rd of that price, there would be a loss of 20%?
(A) 20%
(B) 29%
(C) 7%
(D) 27%
(E) 28%
Rationale: SP2 = 3/4 SP1
CP = 100
SP2 = 80
3/4 SP1 = 80
SP1 = 107
100 --- 107 => 7%
Answer: C
Answer: (C) 7%
Question: Mary passed a certain gas station on a highway while traveling west at a constant speed of 40 miles per hour. Then, 15 minutes later, Paul passed the same gas station while traveling west at a constant speed of 50 miles per hour. If both drivers maintained their speeds and both remained on the highway for at least 2 hours, how long after he passed the gas station did Paul catch up with Mary?
(A) 1/2
(B) 1
(C) 3/4
(D) 2
(E) 3
Rationale: d = rt
M: r = 40mph, t = t + 1/4hr
d = 40 (t + 1/4)
P: r = 50, t = t
d = 50t
since they went the same distance:
40t + 40/4 = 50t
10t = 10
t = 1 hr,
B
Answer: (B) 1
Question: A courtyard is 18 meter long and 16 meter board is to be paved with bricks of dimensions 20 cm by 10 cm. The total number of bricks required is?
(A) 22877
(B) 27778
(C) 20000
(D) 27999
(E) 14400
Rationale: Number of bricks =Courtyard area/1 brick area
=(1800×1600/20×10)=14400
Answer: E
Answer: (E) 14400
Question: 1.A committee that includes 6 members is about to be divided into 2 subcommittees with 3 members each. On what percent of the possible subcommittees that Michael is a member of is David also a member
(A) A.10%
(B) B.20%
(C) C.25%
(D) D.46%
(E) E.50%
Rationale: A,B, C is too low so I eliminated those answers, E was too high of a number, so I chose D as my final answer.D
Answer: (D) D.46%
Question: A train running at the speed of 60 km/hr crosses a pole in 6 seconds. What is the length of the train?
(A) 187 m
(B) 278 m
(C) 876 m
(D) 150 m
(E) 100 m
Rationale: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train
= (Speed x Time)
= (50/3 * 6) m
= 100 m.
Answer: E
Answer: (E) 100 m
Question: What is the greatest integer that will always evenly divide the sum of seven consecutive integers?
(A) 2
(B) 3
(C) 4
(D) 7
(E) 12
Rationale: Let the three consecutive even integers be x , x + 7 , x+14 , x+21 , x+28 , x+35, x+42
Sum = x + x + 7 + x + 14 + x + 21 + x + 28 + x + 35 + x + 42
= 7x+147 = 7(x+21)
Therefore , 7 will always be a factor .
Answer D
Answer: (D) 7
Question: If the sides of a cube are in the ratio 7:3. What is the ratio of their diagonals?
(A) 9:4
(B) 8:4
(C) 7:4
(D) 7:3
(E) 6:4
Rationale: Explanation:
Diagonal of a Cube=a√3 where a is side
a1:a2 = 7:3
d1:d2 = 7:3 where√3 cancelled both side
ANSWER:D
Answer: (D) 7:3
Question: If the LCM and HCF of 12 and another number is 60 and 3 respectively. Find the other number ?
(A) 17
(B) 12
(C) 15
(D) 13
(E) 11
Rationale: HCF x LCM = Product of Numbers
3 x 60 = 12 x the other number
other number = (3 x 60) / 12
other number = 15
ANSWER : C
Answer: (C) 15
Question: A train running at the speed of 180 km/hr crosses a pole in 36 seconds. What is the length of the train?
(A) 450 m
(B) 500 m
(C) 550 m
(D) 600 m
(E) 650 m
Rationale: Speed=(180 * 5/18) m/sec
= (50/3) m/sec Length of the train
= (Speed x Time)
= (50/3 * 36) m = 600 m.
Answer:D
Answer: (D) 600 m
Question: Alok ordered 16 chapatis, 5 plates of rice, 7 plates of mixed vegetable and 6 ice-cream cups. The cost of each chapati is Rs.6, that of each plate of rice is Rs.45 and that of mixed vegetable is Rs.70. The amount that Alok paid the cashier was Rs.961. Find the cost of each ice-cream cup?
(A) 25
(B) 76
(C) 29
(D) 12
(E) 20
Rationale: Explanation:
Let the cost of each ice-cream cup be Rs.x
16(6) + 5(45) + 7(70) + 6(x) = 961
96 + 225 + 490 + 6x = 961
6x = 150 => x = 25.
Answer:A
Answer: (A) 25
Question: x, y and z are consecutive positive integers such that x < y < z; which of the following must be true?
1. yz is even
2. (z-x)(y-x+1) = 4
3. xy is odd
(A) I only
(B) I , II only
(C) III only
(D) I and II only
(E) I, II, and III
Rationale: Since x, y and z are consecutive integers such that x < y < z, we can say x = y-1 and Z = y+1
Statement 1 yz =y*(y+1) ..if one is odd then other will be even and vice versa ..true
Statement 2 can be simplified if we write everything in terms of y as ((y+1)-(y-1))*(y-(y-1)+1) = 2*2 = 4 So, always true
Statement 3 talks about xy Since x and y are consecutive integers one of them is odd and other is even so product would always be even and hence not true.
So, I and II are always true and hence answer is
B
Answer: (B) I , II only
Question: A producer of tea blends two varieties of tea from two tea gardens one costing Rs 18 per kg and another Rs 20 per kg in the ratio 5 : 3. If he sells the blended variety at Rs 26 per kg, then his gain percent is
(A) 12%
(B) 39%
(C) 14%
(D) 15%
(E) 16%
Rationale: Explanation:
Suppose he bought 5 kg and 3 kg of tea.
Cost Price = Rs. (5 x 18 + 3 x 20) = Rs. 150.
Selling price = Rs. (8 x 26) = Rs. 208.
Profit = 208 - 150 = 58
So, Profit % = (58/150) * 100 = 39%
Option B
Answer: (B) 39%
Question: The ratio of the volumes of two cubes is 125 : 512. What is the ratio of their total surface areas?
(A) 81 : 121
(B) 25 : 64
(C) 729 : 1331
(D) 27 : 121
(E) None of these
Rationale: Ratio of the sides = Â³âˆš125 : Â³âˆš512 = 5 : 8
Ratio of surface areas = 5^2 : 8^2 = 25 : 64
ANSWER: B
Answer: (B) 25 : 64
Question: If â€˜MADURAIâ€™ is coded as â€˜DADCIAIâ€™, then â€˜DELHIâ€™ is coded as
(A) DEHIE
(B) DDEHI
(C) EDDIH
(D) DECHI
(E) CHIDE
Rationale: M=13,1+3=4=D
A=1=A
SIMILARLY,
M=13=1+3=4=D
D=4=D
E=5=E
L=12=1+2=C
H=8=H
I=9=I
SO ANS IS
DECHI
ANSWER:D
Answer: (D) DECHI
Question: Find the circumference and area of radius 7 cm.
(A) 124 cm²
(B) 144 cm²
(C) 154 cm²
(D) 184 cm²
(E) 194 cm²
Rationale: Area of circle = πr²
= 22/7 × 7 × 7 cm²
= 154 cm²
ANSWER:C
Answer: (C) 154 cm²
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 12 sec, then the speed of each train is?
(A) 22
(B) 88
(C) 36
(D) 77
(E) 81
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (120 + 120)/12 => x = 10
Speed of each train = 10 m/sec.
= 10 * 18/5 =- 36 km/hr.
Answer:C
Answer: (C) 36
Question: If x^2+(1/x^2)=2, x^4+(1/x^4)=?
(A) 10
(B) 2
(C) 12
(D) 14
(E) 15
Rationale: -> x^4+(1/x^4)=(x^2)^2+(1/x^2)^2=(x^2+1/x^2)^2-2x^2(1/x^2)=2^2-2=2.
Thus, the answer is B.
Answer: (B) 2
Question: How many integers between 2000 and 3000 that have distinct digits and increase from left to right ?
(A) 10
(B) 20
(C) 60
(D) 120
(E) 600
Rationale: Since the numbers must be distinct and increasing from left to right,
The only arrangements we could come-up with are:
245_ --> 4
246_ --> 3
247_ --> 2
248_ --> 1
256_ --> 3
257_ --> 2
258_ --> 1
267_ --> 2
268_ --> 1
Number of integers =20
B
Answer: (B) 20
Question: How many positive integers less than 600 can be formed using the numbers 1, 2, 3, 5 and 6 for the digits?
(A)  48
(B)  130
(C)  66
(D)  68
(E)  84
Rationale: Notice that we can find the number of 2 and 3 digit numbers by just assuming the first digit can also be zero:
0 1 1
1 2 2
2 3 3
3 5 5
5 6 6
Number of possibilities = 5*5*5 = 125.
Then, just add up the number of 1 digits numbers = 5, so total is 125+5 = 130.
Answer: B
Answer: (B)  130
Question: After an ice began to melt out from the freezer, in the first hour lost 3/4, in the second hour lost 3/4 of its remaining. If after two hours, the volume is 0.25 cubic inches, what is the original volume of the cubic ice, in cubic inches?
(A) 2.5
(B) 3.0
(C) 4.0
(D) 6.5
(E) 8.0
Rationale: Let initial volume of ice be = x
Ice Remaining after 1 hour = x - 0.75x = 0.25x
Ice Remaining after 2 hour = (1/4)x - (3/4 * 1/4 * x) = (1/16)x
(1/16)x = 0.25
x = 4
Alternate solution: Try to backsolve.
Initial volume = 4
After one hour --> (1/4)4 = 1
After two hours --> (1/4)1 = 0.25
Answer: C
Answer: (C) 4.0
Question: The speed of a boat in still water is 55kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
(A) 80,70 kmph
(B) 80,40 kmph
(C) 75,35 kmph
(D) 80,80 kmph
(E) 84,40 kmph
Rationale: Speed downstream = 55 + 20
= 75 kmph
Speed upstream = 55 - 20
= 35 kmph
Answer: C
Answer: (C) 75,35 kmph
Question: If y ≠ 3 and 2r/y is a prime integer greater than 2, which of the following must be true?
I. r = y
II. y = 1
III. r and y are prime integers.
(A)  None
(B)  I only
(C)  II only
(D)  III only
(E)  I and II
Rationale: Note that we are asked which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.
So we should try to make the listed statements not true for some r and y (which satisfy y≠3 and 2r/y=prime>2).
I. r = y --> not necessarily true: r=3 and y=2 (2r/y=3=prime>2);
II. y=1 --> not necessarily true: r=3 and y=2 (2r/y=3=prime>2);
III. r and y are prime integers --> not necessarily true: r=10 and y=4 (2r/y=5=prime>2).
Answer: A.
Answer: (A)  None
Question: ABCD is a square. E,F,G,H is the midpoint of the sides of square. J and K is the midpoint of the sides HG and FG . L is a point on sides EF such that LF= 1/3 EF. Find the ratio of area of triangle JKL to the area of square ABCD.
(A) 5: 46
(B) 5: 44
(C) 4: 48
(D) 5: 48
(E) 5: 4
Rationale: ratio = 5: 48
ANSWER:D
Answer: (D) 5: 48