mathewhe/aqua_rat huggingface dataset:
Question: Solve the given two equations and find the inequality of X and Y. (a) x^4- 227= 398 and (b) y^2 + 321=346
(A) If x>y
(B) If x>=y
(C) If x < y
(D) If x<=y
(E) x=y or relationship cannot be established
Rationale: Solution:-
X=+5,-5 and Y= +5,-5
Comparing, we get X=Y, XY.
Therefore, no relationship can be established between X and Y.
E
Answer: (E) x=y or relationship cannot be established
Question: In a certain sequence, the first term is 2, and each successive term is 3 more than the reciprocal of the term that immediately precedes it. What is the fifth term in this sequence?
(A) 360/109
(B) 421/113
(C) 488/135
(D) 584/189
(E) 821/165
Rationale: let five terms in the sequence be a,b,c,d,e
a=3
b= 3+1/3=10/3
c=3+3/10= 33/10
d= 3+10/33 = 109/33
e= 3+33/109 = 360/109
hence answer should be A.
Answer: (A) 360/109
Question: In how many ways can 7 different object be divided among three persons so that either one or two of them do not get any object?
(A) 351
(B) 361
(C) 371
(D) 391
(E) 381
Rationale: Case 1: Two guys don't get anything. All items go to 1 person. Hence, 3 ways.
Case 2: 1 guy doesn't get anything. Division of 7 items among 2 guys. Lets say they are called A & B.
a) A gets 6. B gets 1. 7 ways.
b) A gets 5. B gets 2. 21 ways.
c) A gets 4. B gets 3. 35 ways.
d) A gets 3. B gets 4. 35 ways.
e) A gets 2. B gets 5. 21 ways.
f) A gets 1. B gets 6. 7 ways.
Total = 126 ways to divide 7 items between A & B.
Total number of ways for case 2 = 126*3 = 378 (Either A, or B, or C don't get anything).
Answer = Case 1 + Case 2 = 3 + 378 = 381
ANSWER:E
Answer: (E) 381
Question: A man rows his boat 90 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
(A) 5 kmph
(B) 7 kmph
(C) 9 kmph
(D) 8 kmph
(E) 1 kmph
Rationale: Speed downstream = d/t = 90/(2 1/2) = 36 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (36 - 18)/2 = 9 kmph
Answer:C
Answer: (C) 9 kmph
Question: Two angles of a triangle have ratio 7:3, and their difference equals the third angle. What is the smallest angle, in degrees, of the triangle?
(A) 90/7
(B) 150/7
(C) 270/7
(D) 300/7
(E) 350/7
Rationale: The angles of the triangle are 7x, 3x, and (7x-3x)=4x for some value x (due to the ratio) [note that 3x is the smallest angle]
the angles of a triangle add up to 180, so
7x+3x+4x=180
14x=180
x=180/14
x=90/7
the smallest angle is 3x so 3*(90/7) = 270/7
C
Answer: (C) 270/7
Question: At present, the ratio between the ages of Arun and Deepak is 4 : 3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present ?
(A) 12 years
(B) 15 years
(C) 19 and half
(D) 21 years
(E) 22 years
Rationale: Let the present ages of Arun and Deepak be 4x years and 3x years respectively. Then,
4x + 6 = 26 4x = 20
x = 5.
Deepak's age = 3x = 15 years. Answer: Option B
Answer: (B) 15 years
Question: Rahul can do a work in 3 days while Rajesh can do the same work in 2days. Both of them finish the work together and get $250. What is the share of Rahul?
(A) $50
(B) $40
(C) $60
(D) $100
(E) $90
Rationale: Rahul's wages: Rajesh's wages = 1/3 : 1/2 = 2:3
Rahul's share = 250*2/5 = $100
Answer is D
Answer: (D) $100
Question: The H.C.F. of two numbers is 42 and the other two factors of their L.C.M. are 12 and 14. The larger of the two numbers is:
(A) 588
(B) 642
(C) 567
(D) 344
(E) 789
Rationale: Explanation:
Clearly, the numbers are (42 x 12) and (42 x 14).
{\color{Blue} \therefore } Larger number = (42 x 14) = 588.
Answer: A) 588
Answer: (A) 588
Question: Square OCAB has an area of 9 square units. Point O is found where the axes meet. What are the coordinates of point A?
(A) (3, 1)
(B) (3, 2)
(C) (3, 3)
(D) (3, 4)
(E) None
Rationale: Solution:
If the square has an area of 9 square units, then its side has a length of 3 units. If O is where the axes meet, then points C and B are found on the x- and y-axes and they have the coordinates (3, 0) and (0, 3). Point A is at 3 units from the x-axis and at 3 units from the y-axis and it has the coordinates (3, 3).
Answer C
Answer: (C) (3, 3)
Question: Laxmi and Prasanna set on a journey. Laxmi moves northwards at a speed of 20kmph and Prasanna moves southward at a speed of 30 kmph. How far will be Prasanna from Laxmi after 60 minutes ?
(A) 11
(B) 50
(C) 28
(D) 27
(E) 18
Rationale: Explanation:
We know 60 min = 1 hr
Total northward Laxmi's distance = 20kmph x 1hr = 20 km
Total southward Prasanna's distance = 30kmph x 1hr = 30 km
Total distance between Prasanna and Laxmi is = 20 + 30 = 50 km.
Answer: B
Answer: (B) 50
Question: If a number is formed by writing integers 1 to 150 one after another, like 12345...150. How many Q digits does this integer consists of?
(A) 150
(B) 339
(C) 342
(D) 359
(E) 362
Rationale: Number of single digit integers = 9
Number of 2 digit integers = 99 - 10 + 1 = 90
Number of 3 digit integers = 150 - 100 + 1 = 51
Number of digits in the integer Q= 1*9 + 2*90 + 3*51 = 9 + 180 + 153 = 342
Answer: C
Answer: (C) 342
Question: A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 100000. If the profit at the end of a year is Rs. 108000, then the share of B is?
(A) 40000
(B) 50000
(C) 70000
(D) 60000
(E) 80000
Rationale: Ratio of investments of A and B is (70000 * 12) : (100000 * 6) = 7 : 20
Total profit = Rs. 108000
Share of B = 20/27 (108000) = Rs. 80000
Answer: E
Answer: (E) 80000
Question: Insert the missing number.
3, 4, 6, 8, 9, 12, 12, 16, 15, (....)
(A) 18
(B) 19
(C) 20
(D) 25
(E) 22
Rationale: Explanation:
There are two series, beginning respectively with 3 and 4. In one 3 is added and in another 4 is added.
The next number is 16 +4 = 20.
Answer: C) 20
Answer: (C) 20
Question: One year ago, the ratio of Roonie’s and Ronaldo’s age was 6: 7 respectively. Four years hence, this ratio would become 7: 8. How old is Ronaldo ?
(A) 32
(B) 33
(C) 34
(D) 35
(E) 36
Rationale: 7(x-1)=6(y-1)=> 7x-6y-1=0 ----eq1
8(x+4)=7(y+4)=> 8x-7y+4=0 ----eq2
on solving eq1 n eq2
y=36
ANSWER:E
Answer: (E) 36
Question: A plane moves from a place 9N 40E to a place 9N 40W taking 8 hours to travel. If the plane had left at 10.00 a.m. then what is the local time of arrival at the destination?
(A) 11.40 p.m.
(B) 12.40 p.m.
(C) 1.40 p.m.
(D) 2.40 p.m.
(E) 4.40 p.m.
Rationale: Time difference between places will be 4*(40+40) minutes = 320 min =
5 hrs 20 min
as change of 1 degree in longitude cause change of 4 minutes in time.
and that change is 80 degrees here.
so when plane land. time will be = 10.00 + 8.00 -5.20 = 12.40 p.m.
ANSWER:B
Answer: (B) 12.40 p.m.
Question: An integer n between 1 and 99, inclusive, is to be chosen at random. What is the probability that n(n+2) will be divisible by 3 ?
(A) 1/9
(B) 1/3
(C) 1/2
(D) 2/3
(E) 5/6
Rationale: n(n+2) to be divisible by 3 either n or n+2 must be a multiples of 3.
In each following group of numbers: {1, 2, 3}, {4, 5, 6}, {7, 8, 9}, ..., {97, 98, 99} there are EXACTLY 2 numbers out of 3 satisfying the above condition. For example in {1, 2, 3} n can be: 1, or 3. Thus, the overall probability is 2/3.
Answer: D.
Answer: (D) 2/3
Question: On a certain road 12% of the motorists exceed the posted speed limit and receive speeding tickets, but 20% of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on the road exceed the posted speed limit?
(A) 10.5%
(B) 12.5%
(C) 15%
(D) 22%
(E) 30%
Rationale: Answer is C.
This question is in the OG and thus well explained by ets.
those who exceed : X
so X = 12%+0,2X
id est X = 15%
Answer: (C) 15%
Question: Set R has a mean of 9 and a standard deviation of 1.5. We are going to add two additional numbers to Set S. Which pair of numbers would decrease the standard deviation the most?
(A) {18, 20}
(B) {8, 10}
(C) {28, 38}
(D) {6, 10}
(E) {5, 10}
Rationale: The lesser the variance( values closer to mean) ,lower the standard deviation. As discussed in question the mean is 9,the values (8,10) are closer than others.
Hence Answer : B
Answer: (B) {8, 10}
Question: If a2 - b2 = 9 and a*b = 4, find a4 + b4.
(A) 32
(B) 90
(C) 113
(D) 92
(E) 81
Rationale: a2 - b2 = 9 : given
a4 + b4 - 2a2b2 = 92 : square both sides and expand.
a*b = 4 : given
a2b2 = 42 : square both sides.
a4 + b4 - 2(16) = 81 : substitute
a4 + b4 = 113
correct answer C
Answer: (C) 113
Question: If it is assumed that 60 percent of those who receive a questionnaire by mail will respond and 750 responses are needed, what is the minimum number of questionnaires that should be mailed?
(A) 1160
(B) 1190
(C) 1220
(D) 1250
(E) 1280
Rationale: Let x be the minimum number of questionnaires to be mailed.
0.6x = 750
x = 1250
The answer is D.
Answer: (D) 1250
Question: Cole drove from home to work at an average speed of 60 kmh. He then returned home at an average speed of 100 kmh. If the round trip took a total of 2 hours, how many minutes did it take Cole to drive to work?
(A) 66
(B) 70
(C) 72
(D) 75
(E) 78
Rationale: Let the distance one way be x
Time from home to work = x/60
Time from work to home = x/100
Total time = 2 hrs
(x/60) + (x/100)= 2
Solving for x, we get x = 75
Time from home to work in minutes= (75)*60/60 = 75 minutes
Ans= D
Answer: (D) 75
Question: Line J has a y-intercept of 8 and passes through point (a,b). What is the slope of Line J in terms of a and b?
(A) (a−6)/b
(B) (b-8)/a
(C) (6−a)/b
(D) (6−b)/a
(E) (b−6)/a
Rationale: You know that the line goes through point (a,b) and the y-intercept of 8 tells you that the line also goes through point (0,8).
slope m = (y-y1)/(x-x1) = (b-8)/(a-0)= (b-8)/a
B
Answer: (B) (b-8)/a
Question: Jancy had 100 currency notes in all, some of which are of Rs 70 denomination and the remaining of Rs 50 denomination. The total amount of all these currency notes was Rs. 5000. How much amount (in Rs) did she have in the denomination of Rs 50?
(A) 103
(B) 102
(C) 100
(D) 105
(E) 106
Rationale: Let the number of 50-rupee notes = x
Then, the number of 70-rupee notes = (100 – x)
50x + 70(100 – x) = 5000 : x = 100
ANSWER:C
Answer: (C) 100
Question: A reduction of 10% in the price of salt enables a lady to obtain 10kgs more for Rs.100, find the original price per kg?
(A) 1.1
(B) 2.2
(C) 2.5
(D) 2.1
(E) 2.9
Rationale: 100*(10/100) = 10 --- 10
? --- 1 => Rs.1
100 --- 90
? --- 1 => Rs.1.1
Answer: A
Answer: (A) 1.1
Question: A man whose speed is 3 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
(A) 7
(B) 4
(C) 3
(D) 9
(E) 3.6
Rationale: M = 3
S = 1.5
DS = 4.5
US = 3
AS = (2 * 4.5 * 3) /7.5 = 3.6
Answer:E
Answer: (E) 3.6
Question: A number when multiplied by 3 is odd and divisible by 9. This number when multiplied by 4 is 108. What is the original number?
(A) 10
(B) 18
(C) 13
(D) 21
(E) 27
Rationale: Working backward, 108 divided by 4 is 27.
This number fits the rules of Three and Nine, where the digits add up to a sum divisible by nine.
Answer is E.
Answer: (E) 27
Question: Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
(A) 11
(B) 18
(C) 12
(D) 99
(E) 13
Rationale: Speed of the first train = 120/10 = 12 m/sec.
Speed of the second train = 120/5 = 8 m/sec.
Relative speed = 12 + 8 = 20 m/sec.
Required time = (120 + 120)/20 = 12 sec.
Answer:C
Answer: (C) 12
Question: How many different positive integers exist between 10^4 and 10^5, the sum of whose digits is equal to 2?
(A) 6
(B) 7
(C) 5
(D) 8
(E) 18
Rationale: So, the numbers should be from 10,000 to 100,000
The following two cases are possible for the sum of the digits to be 2:
1. Two 1's and the rest are 0's:
10,001
10,010
10,100
11,000
4 numbers.
2. One 2 and the rest are 0's:
20,000
1 number.
Total = 5 numbers.
Answer: C
Answer: (C) 5
Question: A class of 60 students has an average height of 200 cm. Six students whose average height is 120 cm, left the class and six others whose average height is 134 cm, joined. Calculate the new average height of the students of the class (in cm) is?
(A) 231.4 cm
(B) 301.4 cm
(C) 201.4 cm
(D) 221.4 cm
(E) 101.4 cm
Rationale: Total height = 200 * 60 = 12000 cm.
Total height of those who left = 120 * 6 = 720
Total height of those who joined = 134 * 6 = 804
New average
= [12000 - 720 + 804 ] / 60 = 12084/60 cm.
= 201.4
Answer:C
Answer: (C) 201.4 cm
Question: A store owner estimates that the average price of type A products will increase by 35% next year and that the price of type B products will increase by 15% next year. This year, the total amount paid for type A products was $4000 and the total price paid for type B products was $5300. According to the store owner's estimate, and assuming the number of products purchased next year remains the same as that of this year, how much will be spent for both products next year?
(A) $14,755
(B) $11,495
(C) $16,000
(D) $16,225
(E) $17,155
Rationale: cost of type A products next year = 1.35 * 4000 = 5400
cost of type B products next year = 1.15* 5300 = 6095
total 5400 + 6095 = 11495
ANSWER:B
Answer: (B) $11,495
Question: If n = 3^6 – 2^8 which of the following is NOT a factor of n?
(A) 11
(B) 43
(C) 1
(D) 43
(E) 5
Rationale: 3^6 - 2^8
= (3^3)^2 - (2^4)^2
=(3^3 + 2^4)(3^3 - 2^4)
=(27+16)(27-16)
=43*11
Therefore, 5 is Not a factor of n.
E
Answer: (E) 5
Question: Company KW is being sold, and both Company A and Company B were considering the purchase. The price of Company KW is 20% more than Company A has in assets, and this same price is also 100% more than Company B has in assets. If Companies A and B were to merge and combine their assets, the price of Company KW would be approximately what percent of these combined assets?
(A) 66%
(B) 75%
(C) 86%
(D) 116%
(E) 150%
Rationale: Let the price of Company A's assets be 100
Price of assets of KW is 20% more than company A's assets which is 120
Price of assets of KW is 100% more than company B's assets which means price of Company B's assets is half the price of KW = 60
A+B = 160
KW = 120
KW/(A+B)*100 = 120/160*100 = 75% B
Answer: (B) 75%
Question: if 5 men take an hour to dig a ditch, then how long should 12 men take a dig to ditch of the same type?
(A) 25 min
(B) 30 min
(C) 28 min
(D) 20 min
(E) 10 min
Rationale: if 5 men take an hour to dig a ditch, then
12 men will take 5*60/12 = 25 mins to dig a ditch of the same type.
ANSWER:A
Answer: (A) 25 min
Question: 47% of the students in a class of 42 students has glasses or contacts. How many students in the class have either glasses or contacts?
(A) 15
(B) 16
(C) 17
(D) 18
(E) 20
Rationale: a=r⋅b
47%=0.47a
=0.47⋅42
a≈20
Option E is correct.
Answer: (E) 20
Question: A certain industrial loom weaves 0.132 meters of cloth every second. Approximately how many seconds will it take for the loom to weave 15 meters of cloth?
(A) 114
(B) 115
(C) 116
(D) 117
(E) 118
Rationale: Let the required number of seconds be x
More cloth, More time, (direct proportion)
Hence we can write as
(cloth) 0.132 : 15 :: 1 : x
=>0.132*x=15
=>x=15/0.132
=>x=114
ANSWER:A
Answer: (A) 114
Question: Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
(A) 10
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: Speed of the first train = 120/10 = 12 m/sec.
Speed of the second train = 120/5 = 8 m/sec.
Relative speed = 12 + 8 = 20 m/sec.
Required time = (120 + 120)/20 = 12 sec.
Answer: Option B
Answer: (B) 12
Question: The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 54 kmph, find the speed of the stream?
(A) 16 kmph
(B) 19 kmph
(C) 14 kmph
(D) 11 kmph
(E) 18 kmph
Rationale: The ratio of the times taken is 2:1.
The ratio of the speed of the boat in still water to the speed of the stream
= (2+1)/(2-1) = 3/1
= 3:1
Speed of the stream
= 54/3 = 18 kmph.
Answer: E
Answer: (E) 18 kmph
Question: An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 1 hours, it must travel at a speed of:
(A) 300 kmph
(B) 360 kmph
(C) 600 kmph
(D) 720 kmph
(E) 400 kmph
Rationale: Distance = (240 x 5) = 1200 km.
Speed = Distance/Time
Speed = 1200/(5/3) km/hr. [We can write 1(2/3) hours as 5/3 hours]
Required speed =1200 x3/5km/hr= 720 km/hr.
Answer:D
Answer: (D) 720 kmph
Question: Bob travels at an average speed of 12km/h, to the school and then return to the home he travels at an average speed of 10km/h. Which of the following is the closest approximation of Bob's average speed, in kilometers per hour, for the trip?
(A) 6.3
(B) 2.9
(C) 15.2
(D) 10.9
(E) 9.1
Rationale: Since we're not given a distance to work with, we can TEST any distance that we like. Here, since the speeds are 12 km/hour and 10 km/hour, using a multiple of both 12 and 10 would make the math easiest.
Let's set the Distance up the hill at 60 km.
So, going school, we have....
D = (R)(T)
60 = (5)(T)
60/12 = 5 = T
5 hours to go school
Going home, we have....
D = (R)(T)
60 = (10)(T)
60/10 = 6 = T
6 hours to go home
Total Distance = 120 km
Total Time = 5+6 = 11 hours
Average Speed = 120/11 = 10.9 km/hour
D
Answer: (D) 10.9
Question: Using all the letters of the word "NOKIA", how many words can be formed, which begin with N and end with A?
(A) 5
(B) 6
(C) 8
(D) 9
(E) 2
Rationale: There are five letters in the given word.
Consider 5 blanks ....
The first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 3! ways.
The number of words = 3! = 6.
Answer: B
Answer: (B) 6
Question: What least value must be assigned to * so that the number 197*5462 is r 9 ?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 5
Rationale: Let the missing digit be x.
Sum of digits = (1 + 9 + 7 + x + 5 + 4 + 6 +»2) = (34 + x).
For (34 + x) to be divisible by 9, x must be replaced by 2 .
Hence, the digit in place of * must be 2.
Answer is A.
Answer: (A) 2
Question: If 20 men can build a water fountain 56 metres long in 6 days, what length of a similar water fountain can be built by 35 men in 3 days?
(A) 40 m
(B) 44 m
(C) 47 m
(D) 49 m
(E) 50 m
Rationale: Explanation :
Let the required length be x metres
More men, More length built (Direct Proportion)
Less days, Less length built (Direct Proportion)
Men 20: 35
Days 6: 3 : : 56 : x
Therefore (20 x 6 x x)=(35 x 3 x 56)
x=(35 x 3 x 56)/120=49
Hence, the required length is 49 m.
Answer : D
Answer: (D) 49 m
Question: The first three terms of a proportion are 3, 9 and 12. The fourth term is?
(A) 26
(B) 87
(C) 86
(D) 36
(E) 73
Rationale: (9*12)/3
= 36
Answer: D
Answer: (D) 36
Question: Krishan and Nandan jointly started a business. Krishan invested three times as Nandan did and invested his money for double time as compared to Nandan. Nandan earned Rs. 4000. If the gain is proportional to the money invested and the time for which the money is invested then the total gain was?
(A) 28,002
(B) 28,027
(C) 28,028
(D) 28,000
(E) 28,0012
Rationale: 3:1
2:1
------
6:1
1 ----- 4000
7 ----- ? => Rs.28,000
Answer:D
Answer: (D) 28,000
Question: The LCM of two numbers is 2310 and HCF is 47. If one of the numbers is 210. Then what is the other number ?
(A) 715
(B) 825
(C) 330
(D) 582
(E) 517
Rationale: First number * Second Number = LCM * HCF
Other number = 2310 * 47 / 210 = 11*47 = 517
ANSWER :E
Answer: (E) 517
Question: In 1998 the profits of company N were 10 percent of revenues. In 1999, the revenues of company N fell by 20 percent, but profits were 16 percent of revenues. The profits in 1999 were what percent of the profits in 1998?
(A) 80%
(B) 105%
(C) 120%
(D) 124.2%
(E) 128%
Rationale: 0,128R = x/100*0.1R
Answer E
Answer: (E) 128%
Question: A 120 meter long train crosses a man standing on the platform in 6 sec. What is the speed of the train?
(A) 229
(B) 108
(C) 278
(D) 72
(E) 112
Rationale: S = 120/6 * 18/5 = 72 kmph
Answer: D
Answer: (D) 72
Question: If a 10 percent deposit that has been paid toward the purchase of a certain product is $80, how much more remains to be paid?
(A) $640
(B) $680
(C) $720
(D) $760
(E) $800
Rationale: 90% remains to be paid so the remaining amount is 9*80=$720.
The answer is C.
Answer: (C) $720
Question: If goods be purchased for Rs.840 and one-fourth be sold at a loss of 20% at what gain percent should the remainder be sold so as to gain 20% on the whole transaction?
(A) 38 1/3%
(B) 33 1/7%
(C) 33 1/3%
(D) 33 8/3%
(E) 33 1/1%
Rationale: 1/4 CP = 210 SP = 21*(80/100) = 168
SP = 840*(120/100) = 1008
1008 - 168 = 840
3/4 SP = 630
Gain = 210
630 --- 210
100 --- ? => 33 1/3%
Answer:C
Answer: (C) 33 1/3%
Question: Jane covered a distance of 320 miles between city A and city B taking a total of 5 hours. If part of the distance was covered at 60 miles per hour speed and the balance at 80 miles per hour speed, how many hours did she travel at 60 miles per hour?
(A) 2 hours 30 minutes
(B) 3 hours
(C) 2 hours
(D) 1 hour 45 minutes
(E) None of these
Rationale: Answer
Let Jane travel 'x' at 60 miles per hour.
As the total time taken to cover 340 miles is 5 hours, Jane would have traveled (5 - x) hours at 80 miles per hour.
Distance covered at 60 miles per hour = Speed * time = 60 * x = 60x miles.
Distance covered at 80 miles per hour = Speed * time = 80 (5 - x) = 400 - 80x miles.
Total distance covered = Distance covered at 60 miles per hour + Distance covered at 80 miles per hour.
Therefore, total distance = 60x + 400 - 80x.
Total distance travelled = 340 miles.
Therefore, 320 = 60x + 400 - 80x
20x = 40 or x = 2 hours.
Choice C
Answer: (C) 2 hours
Question: Helen went to the stationers and bought things worth Euro 25, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
(A) Euro 15
(B) Euro 15.7
(C) Euro 19.7
(D) Euro 20
(E) None
Rationale: Explanation: Let the amount taxable purchases be Euro x.
Then, 6% of x = 30/100
x = (30/100 x 100/6) = 5.
Cost of tax free items = Euro [25 - (5 + 0.30)] = Euro 19.70
Answer: Option C
Answer: (C) Euro 19.7
Question: (786×74) ÷ ? = 1817.6
(A) A)4.8
(B) B)48
(C) C)58
(D) D)68
(E) E)32
Rationale: Explanation:
58164/x = 1817.6 => x = 58164/1817.6 = 32
Answer: Option E
Answer: (E) E)32
Question: A train has a length of 150 meters . it is passing a man who is moving at 5 km/hr in the same direction of the train, in 3 seconds. Find out the speed of the train.
(A) 182 km/hr
(B) 180 km/hr
(C) 185 km/hr
(D) 169 km/hr
(E) 179 km/hr
Rationale: Explanation:
Length of the train, l = 150m
Speed of the man , Vm= 5 km/hr
Relative speed, Vr = total distance/time = (150/3) m/s = (150/3) × (18/5) = 180 km/hr
Relative Speed = Speed of train, Vt - Speed of man (As both are moving in the same direction)
=> 180 = Vt - 5
=> Vt = 180 + 5 = 185 km/hr
Answer: Option C
Answer: (C) 185 km/hr
Question: A set of numbers has the property that for any number t in the set, t + 2 is in the set. If -1 is in the set, which of the following must also be in the set?
I. 5
II. 1
III. -4
(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, and III
Rationale: The question is which of the following must be in the set, not could be in the set.
If -1 is in the set so must be -1+2=1, as 1 is in the set so must be 1+2=3, as 3 is in the set so must be 3+2=5 and so on. So basically knowing that -1 is in the set we can say that ALL odd numbers more than -1 are also in the set.
Answer: C.
Answer: (C) I and II only
Question: A tap can fill a tank in 12 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?
(A) 5 hr 30 mins
(B) 7 hr 30 mins
(C) 4hr 30 mins
(D) 2 hr 30 mins
(E) 3 hr 30 mins
Rationale: Explanation:
A tap can fill a tank in 12 hours.
Therefore the tap can fill half the tank in 6 hours.
One tap take time to fill half of the tank = 6 hrs
4 taps take time to fill half of the tank = 6/4 hrs = 1 hr 30 mins
Total time taken to fill the tank = 6 hr+1 hr 30 min = 7 hr 30 mins
Answer : B
Answer: (B) 7 hr 30 mins
Question: The radius of a cylindrical vessel is 7cm and height is 5cm. Find the whole surface of the cylinder?
(A) 308 sq cm
(B) 528 sq cm
(C) 440 sq cm
(D) 132 sq cm
(E) 138 sq cm
Rationale: r = 7 h = 5
2πr(h + r) = 2 * 22/7 * 7(12) = 528
ANSWER:B
Answer: (B) 528 sq cm