mathewhe/aqua_rat huggingface dataset:
Question: In the rectangular coordinate system, what is the area of triangle CDE with points
C=(3,7)
D=(4,4)
E=(1,1)
(A) 5
(B) 6
(C) 7
(D) 6.5
(E) 5.5
Rationale: Use the formula of the distance formula
square root (x2-x1)^2+(y2-y1)^2
Do this for each of the sides and then the value is given as B.
Answer: (B) 6
Question: If the true discount on a sum due 2 years hence at 14% per annum be Rs. 168, the sum due is :
(A) Rs. 768
(B) Rs. 968
(C) Rs. 1960
(D) Rs. 2400
(E) None
Rationale: Solution
P.W = 100xT.D./R x T = 100x 168/14x 2 = 600.
∴ Sum = (P.W. + TD.) = Rs. 768.
Answer A
Answer: (A) Rs. 768
Question: What is the value of 27^2 + 28^2 + 29^2 + 30^2 + 31^2 + 32^2 + 33^2 ?
(A) 6298
(B) 6308
(C) 6318
(D) 6328
(E) 6338
Rationale: the method would seem to be lengthy as it is being explained but is very short actually
second would be to take advantage of proximity to 30 and a set of two numbers giving us 60 as sum..
(27^2 + 33^2) + (29^2 + 31^2) + (32^2 + 28^2)+ 30^2
(60^2-2*27*33) +(60^2-2*29*31)+ (60^2-2*28*32)+ 30^2
3*60^2+30^2-2(27*33+29*31+28*32)
3*60^2+30^2-2((30-3)*(30+3)+(30-1)*(30+1)+(30-2)*(30+2))
3*60^2+30^2-2((30^2-3^2)+(30^2-1^2)+(30^2-2^2))
3*60^2+30^2-6(30^2)+2(3^2+1^2+2^2)
we are interested only in terms where square of multiple of 10 is not involved..
2(9+1+4)=28 so the answer should be something*100+28....this gives us the answer as 6328
ANSWER:D
Answer: (D) 6328
Question: In a rectangular coordinate system, what is the area of a rhombus whose vertices have the coordinates (0, 3.5), (6, 0), (0, -3.5), (-6, 0)?
(A) 42
(B) 56
(C) 88
(D) 112
(E) 116
Rationale: Ares of rhombus= 1/2* D1 *D2
Length of 1st diagonal = 6+6= 12
Length of 2nd diagonal= 3.5+3.5= 7
Area= 1/2*12*7= 42
A is the answer
Answer: (A) 42
Question: In a game of 80 points; A can give B 10 points and C 15 points. Then how many points B can give C in a game of 70 ?
(A) can give C 1 points
(B) can give C 4 points
(C) can give C 2 points
(D) can give C 5 points
(E) can give C 8 points
Rationale: A: B = 80 : 70, A : C = 80 : 65.
B/C = ( B/ A * A/C) = (70/ 80 * 80 / 65) = 14/13 = 70 /65
Therefore ,In a game of 70, B can give C 5 points.
Answer is D.
Answer: (D) can give C 5 points
Question: Rose is thrice as good as workman as Jerry and therefore is able to finish a job in 60 days less than Jerry. if theu work together in how many days they will complete?
(A) 21 3/4
(B) 22 1/2
(C) 23 4/5
(D) 25 1/6
(E) 27 3/5
Rationale: Ratio of times taken by A and B = 1 : 3.
The time difference is (3 - 1) 2 days while B take 3 days and A takes 1 day.
If difference of time is 2 days, B takes 3 days.
If difference of time is 60 days, B takes 3	x 60 = 90 days.
2
So, A takes 30 days to do the work.
A's 1 day's work =	1
30
B's 1 day's work =	1
90
(A + B)'s 1 day's work = 1	+	1 =	4	=	2
30	90	90	45
A and B together can do the work in	45	= 22	1/2 days.
2	2
B
Answer: (B) 22 1/2
Question: In a certain company 20% of the men and 40% of the women attended the annual company picnic.If 50% of all the employees are men .What % of all the employee went to the picnic?
(A) 30%
(B) 34%
(C) 35%
(D) 36%
(E) 37%
Rationale: total men in company 50% means total women in company 50%(assume total people in company 100%)
no of men employees attended picnic=50x(20/100)=10
no of women employees attend picnic=50x(40/100)=20
total percentage of employees attend the picnic=10+20=30%
ANSWER:A
Answer: (A) 30%
Question: TIM has 13 ten-dollar bills, 11 five-dollar bills, and 17 one-dollar bills. If TIM needs to pay exactly $128, what is the least number of bills he will need to use?
(A) 68
(B) 66
(C) 565
(D) 16
(E) 35
Rationale: 128 is the total sum of money.
as we have 13 10 dollar bills so the closest we can get to 128 using the 10 dollar bills is by using 12 * 10 dollar bils
128-120 = 8
so now we need to get 8 from either 5 dollar bills or 1 dollar bills
8 - 5 (use only 1 5 dollar bill) = 3
so we can get 3 from using 3 $1 bills.
Hence 16 ( 12+1+3 )
ANSWER IS D
Answer: (D) 16
Question: A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 20%?
(A) 600
(B) 882
(C) 772
(D) 662
(E) 521
Rationale: Cost price = Rs.500
profit = 20% of 500 = Rs.100
Selling price = Cost price + Profit
= 500 + 100 = 600
Answer: A
Answer: (A) 600
Question: Professor absentminded has a very peculiar problem, in that he cannot remember numbers larger than 15. However, he tells his wife, I can remember any number up to 100 by remembering the three numbers obtained as remainders when the number is divided by 3, 5 and 7 respectively. For example (2,2,3) is 17. Professor remembers that he had (1,1,6) rupees in the purse, and he paid (2,0,6) rupees to the servant. How much money is left in the purse?
(A) 56
(B) 57
(C) 58
(D) 59
(E) 60
Rationale: Let the money with the professor = N
Then N = 3a +1 = 5b + 1 = 7c + 6.
Solving the above we get N = 181
(Explanation: See LCM formula 1 and 2: Click here)
When a number is divided by several numbers and we got same remainder in each case, then the general format of the number is LCM (divisors).x + remainder.
In this case 3, 5 are divisors. So N = 15x + 1. Now we will find the number which satisfies 15x + 1 and 7c + 6.
⇒ 15x + 1 = 7c + 6 ⇒ c = 15x−5715x−57 ⇒ c = 2x+x−572x+x−57
Here x = 5 satisfies. So least number satisfies the condition is 5(15)+1 = 76.
(x = 12 also satisfies condition. So substituting in 15x + 1 we get, 181 which satisfies all the three equations but this is greater than 100)
Similarly Money given to servant = M = 3x + 2 = 5y = 7z + 6
Solving we get M = 25.
(125 also satisfies but this is next number)
Now N - M = 56
Answer:	A
Answer: (A) 56
Question: Sanoop bought 8 t-shirts at an average price (arithmetic mean) of Rs.526. If Sanoop returned 4 t-shirts to the retailer, and the average price of the remaining t-shirts was Rs.505, then what is the average price, of the three returned t-shirts?
(A) 560
(B) 561
(C) 562
(D) 563
(E) 547
Rationale: Total price of 8 t-shirts= 8*526=4208
Total price of 5 t-shirts=4*505=2020
Total price of 4 t-shirts=4208-2020=2188
Average price of 3 t-shirts=2188/4=547
Correct option Answer:E
Answer: (E) 547
Question: In a group of 60 people, 35 have visited Iceland and 23 have visited Norway. If 31 people have visited both Iceland and Norway, how many people have visited neither country?
(A) 30
(B) 31
(C) 32
(D) 33
(E) 34
Rationale: This is an example of a standard Overlapping Sets question. It has no 'twists' to it, so you'll likely find using the Overlapping Sets Formula to be a fairly easy approach. If you're not familiar with it, then here is the Formula:
60= 35 + 23 - 31 + (# in Neither Group)
=33
The prompt gives you all of the numbers you need to get to the correct answer. Just plug in and solve.
D
Answer: (D) 33
Question: The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ Rs. 26.50 per metre is Rs. 5565, what is the length of the plot in metres?
(A) 333
(B) 200
(C) 288
(D) 210
(E) 1999
Rationale: Let length of plot = L meters, then breadth = L - 20 meters
and perimeter = 2[L + L - 20] = [4L - 40] meters
[4L - 40] * 26.50 = 5565
[4L - 40] = 5565 / 26.50 = 210
4L = 250
L = 250/4= 62.5 meters.
Answer: D
Answer: (D) 210
Question: A, B and C can do a piece of work in 24 days, 30 days and 40 days respectively. They began the work together but C left 12 days before the completion of the work. In how many days was the work completed?
(A) 13 days
(B) 16 days
(C) 18 days
(D) 11 days
(E) 38 days
Rationale: One day work of A, B and C = 1/24 + 1/30 + 1/40 = 1/10 Work done by A and B together in the last 12 days = 12*(1/24 + 1/30) = 9/10
Remaining work = 1/10
The number of days required for this initial work = 1 days.
The total number of days required = 12 + 1 = 13 days.
Answer: A
Answer: (A) 13 days
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 245
(B) 726
(C) 566
(D) 268
(E) 261
Rationale: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30
= 25/2 => 2(130 + x) = 750 => x
= 245 m.
Answer: A
Answer: (A) 245
Question: What is the cost painting the two adjacent walls of a hall at Rs. 5 per m2 which has no windows or doors?
I.	The area of the hall is 24 sq. m.
II.	The breadth, length and height of the hall are in the ratio of 4 : 6 : 5 respectively.
III.	Area of one wall is 30 sq. m.
(A) I only
(B) II only
(C) III only
(D) Either I or III
(E) All I, II and III are required.
Rationale: EXPLANATION
From II, let l = 4x, b = 6x and h = 5x.
Then, area of the hall = (24x2) m2.
From I. Area of the hall = 24 m2.
From II and I, we get 24x2 = 24 x = 1.
l = 4 m, b = 6 and h = 5 m.
Thus, area of two adjacent walls = [(l x h) + (b x h)] m2 can be found out and so the cost of painting two adjacent walls may be found out.
Thus, III is redundant.
answer is (C).
Answer: (C) III only
Question: Man, woman and a boy finish work together in 6 days. Man alone takes 10 days; woman alone takes 24 days then how many days boy alone will take to do that work?
(A) 20 days
(B) 30 days
(C) 40 days
(D) 50 days
(E) 60 days
Rationale: Let M, W , B be man, women, nd boy
M + W + B 's 1 day work = 1/6
M's 1 day work = 1/10
W's 1 day work = 1/24
M + W's 1 day work = 1/10 + 1/24 ==> 34/240 = 17/120
B's 1 day work = (M + W + B) - (M + W)
==========> 1/6 - 17/120 ==> 120 - 102/720
==========>18/720 = 1/40
So boy alone ll finish d work in 40 days
ANSWER:C
Answer: (C) 40 days
Question: The length of the bridge, which a train 160 m long and traveling at 45 km/hr can cross in 30 sec is?
(A) 377
(B) 367
(C) 237
(D) 215
(E) 267
Rationale: Speed = 45 * 5/18 = 25/2 m/sec.
Time = 30 sec
Let the length of bridge be x meters.
Then, (160 + x)/30 = 25/2
x = 215 m.
Answer: D
Answer: (D) 215
Question: The areas, in kilometers squared, of some countries are given below. USA: 9,629,091, Russia: 17,098,242, China: 9,598,094, Canada: 9,984,670, the UK: 242,400 and India: 3,287,263.
What is the difference between the areas of Russia and China?
(A) 5,476,811 kilometers squared
(B) 7,500,148 kilometers squared
(C) 9,843,123 kilometers squared
(D) 1,878,965 kilometers squared
(E) 4,787,900 kilometers squared
Rationale: he difference between the areas of Russia and China is given by
17,098,242 - 9,598,094 = 7,500,148 kilometers squared
correct answer B
Answer: (B) 7,500,148 kilometers squared
Question: The greatest possible length which can be used to measure exactly the length 3m, 5m 30cm, 4 m is
(A) 10
(B) 27
(C) 35
(D) 87
(E) 98
Rationale: Explanation:
Required Length = H.C.F of 300 cm, 530 cm and 400 c
= 10 cm.
Answer: A) 10 cm
Answer: (A) 10
Question: Each week, Harry is paid x dollars per hour for the first 21 hours and 1.5x dollars for each additional hour worked that week. Each week, James is paid x dollars per per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week James worked a total of 41 hours If Harry and James were paid the same amount last week, how many hours did Harry work last week ?
(A) 35
(B) 36
(C) 37
(D) 38
(E) 39
Rationale: 42x=21x+1.5x(H-21)
==> 42=21+1.5(H-21)
==> H-21 = 21/1.5=14=> H = 35
Answer is A
Answer: (A) 35
Question: s is a positive integer and multiple of 2; p = 4^s, what is the remainder when p is divided by 10?
(A) 10
(B) 6
(C) 4
(D) 0
(E) It Cannot Be Determined
Rationale: It is essential to recognize that the remainder when an integer is divided by 10 is simply the units digit of that integer. To help see this, consider the following examples:
4/10 is 0 with a remainder of 4
14/10 is 1 with a remainder of 4
5/10 is 0 with a remainder of 5
105/10 is 10 with a remainder of 5
It is also essential to remember that the s is a positive integer and multiple of 2. Any integer that is a multiple of 2 is an even number. So, s must be a positive even integer.
With these two observations, the question can be simplified to:what is the units digit of 4 raised to an even positive integer?
The units digit of 4 raised to an integer follows a specific repeating pattern:
4^1 = 4
4^2 = 16
4^3 = 64
4^4 = 256
4^(odd number) --> units digit of 4
4^(even number) --> units digit of 6
There is a clear pattern regarding the units digit. 4 raised to any odd integer has a units digit of 4 while 4 raised to any even integer has a units digit of 6.
Since s must be an even integer, the units digit of p=4^s will always be 6. Consequently, the remainder when p=4^s is divided by 10 will always be 6.
In case this is too theoretical, consider the following examples:
s=2 --> p=4^z=16 --> s/10 = 1 with a remainder of 6
s=4 --> p=4^z=256 --> s/10 = 25 with a remainder of 6
s=6 --> p=4^z=4096 --> s/10 = 409 with a remainder of 6
s=8 --> p=4^z=65536 --> s/10 = 6553 with a remainder of 6
Answer: B.
Answer: (B) 6
Question: If a survey shows that 28 citizens out of a sample of 200 support a particular Senate bill, what percent of the sample does not support the bill?
(A) 56%
(B) 64%
(C) 72%
(D) 82%
(E) 86%
Rationale: Those who support = 28.
% of those who don't support it is (200-28)/ 200 = 86%
Answer E
Answer: (E) 86%
Question: A company consists of 5 senior and 3 junior staff officers. If a committee is created with 2 senior and 2 junior staff officers, in how many ways can the committee be formed?
(A)  12
(B)  30
(C)  45
(D)  80
(E)  200
Rationale: Choose 2 senior from 5 senior and choose 2 junior from 3 junior:
5C2 * 3C2 = 10*3 = 30
Ans: B
Answer: (B)  30
Question: A briefcase has a number-lock system containing a combination of 3 digits (Each digit can be of numbers 0 to 8). If the correct combination is unknown, how much maximum time would be required to open the bag if each “trial” of combination takes 3 seconds?
(A) 36.45 minutes
(B) 36.47 minutes
(C) 36.41 minutes
(D) 36.42 minutes
(E) 36.65 minutes
Rationale: Explanation:
Maximum number of trials required = 9 * 9 * 9 = 729. Since for each combination trial, 3 seconds are required to open the briefcase is given as 3 * 729 = 2187 seconds = 36.45 minutes.
ANSWER: A
Answer: (A) 36.45 minutes
Question: Shyam walks 5 km towards East and then turns left and walks 6 km. Again he turns right and walks 9 km. Finally he turns to his right and walks 6 km. How far is he from the starting point?
(A) 26 km
(B) 21 km
(C) 14 km
(D) 9 km
(E) 19 km
Rationale: he is 14 km towards East from starting point.
ANSWER:C
Answer: (C) 14 km
Question: Lalasa, Bhavani and Geetha has bought items of Rs. 4000, Rs. 12000 and Rs. 6000 respectively. Addition to it, Bhavani has spent Rs. 2000 to buy sunglasses. The difference between the money spent by A and C is?
(A) 800
(B) 650
(C) 450
(D) 400
(E) 680
Rationale: Ratio of cost of items bought by Lalasa, Bhavani and Geetha is 4000 : 10000 : 6000 = 2 : 5 : 3
And also given that, additional items bought by Bhavani is Rs. 2000
=> 5 parts out of 10 parts is Rs. 2000
Now, required difference is 3 - 2 = 1 part
Required difference = 1/5 (2000) = Rs. 400.Answer: D
Answer: (D) 400
Question: The probability that A speaks truth is 4/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?
(A) 19/35
(B) 19/37
(C) 19/39
(D) 19/33
(E) 19/31
Rationale: If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 4/5 * 4/7 + 1/5 * 3/7
= 19/35
Answer:A
Answer: (A) 19/35
Question: 1/(2-√3)=?
(A) 9+4√5
(B) 9-4√5
(C) 9+2√5
(D) 2+√3
(E) 4+9√5
Rationale: This question requires us to rationalize (fix) the denominator.
For more on this technique, seehttps://www.gmatprepnow.com/module/gmat ... video/1044
Given: 1/(2-√3)
Multiply top and bottom by the CONJUGATE of 2-√3, which is 2+√3
So, 1/(9-4√5) = (1)(9+4√5)/(9-4√5)(9+4√5)
D
Answer: (D) 2+√3
Question: If the area of a circle is 36pi square feet, find its circumference.
(A) 65 pi feet
(B) 43 pi feet
(C) 12 pi feet
(D) 18 pi feet
(E) 64 pi feet
Rationale: The area is given by pi * r * r. Hence
pi * r *r = 81 pi
r *r = 36 ; hence r = 36 feet
The circumference is given by
2 *pi *r = 2 * pi * 6 = 128 pi feet
correct answer C
Answer: (C) 12 pi feet
Question: A can do a job in 45 days and B can do it in 30 days. A and B working together will finish four times the amount of work in ------- days?
(A) 30days
(B) 45 days
(C) 80 days
(D) 72 1/2 days
(E) 72 days
Rationale: 1/45+ 1/30 = 5/90 = 1/18
18/1 = 18*4 = 72 days
Answer:E
Answer: (E) 72 days
Question: What is the smallest number by which 2880 must be divided in order to make it into a perfect square ?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: 880/3=960 is not a perfect square
2880/4=720 is not a perfect square
2880/5=576 which is perfect square of 24
ANSWER:C
Answer: (C) 5
Question: An art gallery has only paintings and sculptures. Currently, 1/3 of the pieces of art are displayed, and 1/6 of the pieces on display are sculptures. If 1/3 of the pieces not on display are paintings, and 1200 sculptures are not on display, how many pieces of art does the gallery have?
(A) 360
(B) 2700
(C) 540
(D) 640
(E) 720
Rationale: Too many words and redundant info there.
(i) 1/3 of the pieces of art are displayed, hence2/3 of the pieces of art are NOT displayed.
(ii) 1/6 of the pieces on display are sculptures, hence 5/6 of the pieces on display are paintings.
(iii) 1/3 of the pieces NOT on display are paintings, hence2/3 of the pieces NOT on display are sculptures.
1200 sculptures are not on display, so according to (iii) 2/3*{not on display} = 1200 --> {not on display} = 1800.
According to (i) 2/3*{total} = 1800 --> {total} = 2700.
Answer: B.
Answer: (B) 2700
Question: What will come in place of the x in the following Number series? 279936, 46656, 7776, 1296, 216, x
(A) 2
(B) 3
(C) 5
(D) 6
(E) 8
Rationale: Go on dividing by 6 to the next number
C)
Answer: (C) 5
Question: In a group of 90 students, 36 are taking History, and 32 are taking Statistics. If 57 students are taking History or Statistics or both, then how many students are taking History but not Statistics?
(A) 9
(B) 19
(C) 25
(D) 27
(E) 31
Rationale: Number of students taking history =H=36
Number of students taking statistics =S= 32
Total number of students =T= 90
Number of students taking History or Statistics or both =B= 57
Number of students taking neither history nor statistics =N= 90-57=33
LetXbe the number of students taking both history and statistics.
Then
T = H + S + N - X
or 90 = 36 + 32 +33 - X
or X = 11
Now,
Number of students taking only history will be
H-X
or 36-11 = 25
Answer:- C
Answer: (C) 25
Question: A and B began business with Rs.7000 and Rs.15000 after 6 months, A advances Rs.3000 and B withdraws Rs.5000. At the end of the year, their profits amounted to Rs.2940 find the share of A and B respectively.
(A) 1100, 1750
(B) 1140, 1800
(C) 940, 2000
(D) 1190, 1750
(E) 1000: 1690
Rationale: 7*6 + 10*6):(15*6 + 10*6) =102 : 150 = 51 : 75 = 17 : 25
17 : 25
A's Share = 17/42 * 2940 = 1190.
B's Share = 25/42 * 2940 = 1750.
A and B shares respectively 1190 and 1750 . Answer: D
Answer: (D) 1190, 1750
Question: All the milk in container A which was filled to its brim was poured into two containers B and C. The quantity of milk in container B was 62.5% less than the capacity of container A. If 150 liters was now transferred from C to B, then both the containers would have equal quantities of milk. What was the initial quantity of milk in container A?
(A) 1200
(B) 1723
(C) 1129
(D) 2613
(E) 1372
Rationale: A
B has 62.5% or (5/8) of the milk in A. Therefore, let the quantity of milk in container A(initially) be 8k.
Quantity of milk in B = 8k - 5k = 3k.
Quantity of milk in container C = 8k - 3k = 5k
Container: A B C
Quantity of milk: 8k 3k 5k
It is given that if 150 liters was transferred from container C to container B, then both the containers would have equal quantities of milk.
5k - 150= 3k + 150 => 2k = 300 => k = 150
The initial quantity of milk in A = 8k = 8 * 150= 1200 liters.
Answer: (A) 1200
Question: Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 80 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work?
(A) 20
(B) 34
(C) 58
(D) 40
(E) 46
Rationale: Nice question +1
We have that X/24 - (60-X)/2R = 40
Also X/R - (60-X)/2R = 120
So we get that 2x - 60 = 80R
3x - 60 = 240R
Get rid of R
120 = 3x
x = 58
Hence answer is C
Answer: (C) 58
Question: Which of the following numbers is the biggest => [-3/7 , -7/8 , -9/10 , -12/13 , -34/35]
(A) A)-3/7
(B) B)-7/8
(C) C)-9/10
(D) D)-12/13
(E) E)-34/35
Rationale: If we observe all the fractions just differ by one i.e denominator vs numerate.. in such case the biggest will be with large values... here all values are with -ve value...the least value is biggest. i.e. -3/7..
Hence A is correct answer...
Answer: (A) A)-3/7
Question: If 15 students in a class average 75% on an exam and 10 students average 90% on the same exam, what is the average in percent for all 25 students?
(A) 80%
(B) 81%
(C) 82%
(D) 83%
(E) 84%
Rationale: (15*75 + 10*90) / 25 = 81%
The answer is B.
Answer: (B) 81%
Question: The bus that travels from St. Louis to Chicago and back comes to St. Louis every 2 hours while the bus that travels from St. Louis to Springfield and back comes to St. Louis every 3 hours. If at 12:00 o'clock both bused arrived at St. Louis, at what time will they meet in St. Louis again?
(A) 16:00.
(B) 18:00.
(C) 20:00.
(D) 22:00.
(E) 24:00.
Rationale: Time taken by bus to travel from St. Louis to Chicago and back comes to St. Louis = 2 hours
Time taken by bus to travel from St. Louis to Springfield and back comes to St. Louis = 3 hours
Time taken by both buses to meet again in St. Louis will be LCM of 2 and 3 = 6
If the buses start at 12:00 o'clock from St. Louis , they will meet again in St. Louis at 18:00 hours
Answer B
Answer: (B) 18:00.
Question: If a is Negative integers and b is positive integers and a ≠ 0 which of the following equal 0 ?
(A) a-b
(B) a^2+b^2
(C) a*b
(D) a/b
(E) a^2-b^2
Rationale: All options Except E gives Non-zero answer.
a should be negative integers and b should be an positive integers.
(E)a^2-b^2
If b=0,a^2-b^2=a^2.
a is negative integers. Any square of the negative integers gives us a positive numbers.
So The option E is answer
Answer: (E) a^2-b^2
Question: The sum of three consecutive even numbers is 63, Find the last one ?
(A) 26
(B) 24
(C) 21
(D) 23
(E) 19
Rationale: Let the first number be n
Let the second number be n + 2
Let the third number be n + 4
n + n + 2 + n + 4 = 63
Combine like terms:
3n + 6 = 63
3n = 63 - 6
3n = 57
n = 19
n + 2 = 21
n + 4 = 23
The last number is 23
Answer: D
Answer: (D) 23
Question: If difference between compound interest and simple interest on a sum at 5% P.a. for 2 years is Rs.60, then what is the sum?
(A) Rs.8000
(B) Rs.4000
(C) Rs.5000
(D) Rs.6000
(E) Rs.24000
Rationale: C.I-S.I=60
SI=(x*2*5)/100=x/10
CI={x*(1+5/100)^2-x} = 41x/400
CI-SI= 41x/400 - x/10 =60
x=24000
ANSWER:E
Answer: (E) Rs.24000
Question: In how many no. between 10 and 20 exactly Two of the digits is 1?
(A) 25
(B) 35
(C) 10
(D) 1
(E) 15
Rationale: It's simple can be solved by elimination of answer choices.
Option A and B are too large, not possible. Even CE are large to have correct choice.
Ans : D
Answer: (D) 1
Question: The sum of the two numbers is 11 and their product is 24. What is the sum of the reciprocals of these numbers ?
(A) 11/24
(B) 11/25
(C) 13
(D) 13/15
(E) None
Rationale: Let the numbers be
x
x and
y
y Then
x
+
y
=
11
x
y
=
24
x+y=11xy=24
Hence,
x
+
y
x
y
=
11
24
x+yxy=1124
⇒
1
y
+
1
x
=
11
24
Answer is A
Answer: (A) 11/24
Question: A car covers a distance of 1932 km in 7 hours. Find its speed?
(A) 104
(B) 288
(C) 271
(D) 276
(E) 128
Rationale: 1932/7 = 276 kmph
Answer: D
Answer: (D) 276