divelab/Sys2Bench huggingface dataset:
Question: P can do a work in 36 days. Q can do the same work in 9 days and R can do the same in 12 days. Q and R start the work and leave after 3 days. P finishes the remaining work in --- days.
Options:
A)7
B)8
C)9
D)10
E)15
Rationale: Work done by P in 1 day = 1/36
Work done by Q in 1 day = 1/9
Work done by R in 1 day = 1/12
Work done by Q and R in 1 day = 1/9 + 1/12 = 7/36
Work done by Q and R in 3 days = 3Ã—7/36 = 7/12
Remaining work = 1 â€“ 7/12 = 5/12
Number of days in which P can finish the remaining work = (5/12) / (1/36) = 15
Option E
Answer: E
Question: A certain car averages 25 miles per gallon when driving in the city and 40 miles per gallon when driving on the highway. According to these rates, which of the following is closest to the number of miles per gallon that the car averages when it is driven 15 miles in the city and then 50 miles on the highway?
Options:
A)28
B)30
C)35
D)36
E)38
Rationale: Answer C
No of Miles per Gallon = Total no of miles/Total no of Gallons
=15+50/(15/25+50/40) ~ 35.13
Answer: C
Question: P and Q be centers of two circle having radius 200cms. These circle intersect each other at some point A and B. Length of PQ is 250 cms. What will the angle AQP be?
Options:
A)between 0 to 45
B)between 0 to 30
C)between 0 to 60
D)between 0 to 75
E)between 0 to 95
Rationale: raw the diagram, in triangle AQP, AP = 200 , AQ = 200 and PQ = 250
cos(AQP)= (200^2+250^2-200^2)/(2*200*250)= 5/8 = .625 [using cal, cos(AQP)= 51]
or,
as cos45=.7 & cos60=.5 so, cos(AQP)=.625 lies betn angles 45 & 60
between 0 to 60
ANSWER:C
Answer: C
Question: 306 Ã· ? Ã— 15 + 270 = 405
Options:
A)24
B)25
C)34
D)39
E)43
Rationale: Explanation:
306 Ã· ? Ã— 15 = 405 - 270 = 135
(306 Ã— 15)/? = 135
? = (306Ã— 15)/135 = 34
Answer: Option C
Answer: C
Question: A man leaves a point P at 6 a.m. and reaches the point Q at 10 a.m. another man leaves the point give at 8 a.m. and reaches the point P at 12 noon. At what time do they meet?
Options:
A)6
B)7
C)9
D)8
E)5
Rationale: 9 a.m.
Answer: C
Answer: C
Question: A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?
Options:
A)67 seconds
B)32 seconds
C)40 seconds
D)87 seconds
E)12 seconds
Rationale: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (2/25) = 40 seconds
Answer:C
Answer: C
Question: The ratio between the present ages of P and Q is 6:7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years
Options:
A)7:8
B)7:9
C)3:8
D)5:8
E)None of these
Rationale: Explanation:
Let P age and Q age is 6x years and 7x years.
Then 7x - 6x = 4 <=> x = 4
So required ratio will be (6x+4): (7x+4) => 28:32 => 7:8
Option A
Answer: A
Question: In a class of 250 students, 150 study Spanish and 100 study French. If a student must study at least one of these two languages, what percent of the students study French but NOT Spanish?
Options:
A)80%
B)40%
C)30%
D)20%
E)10%
Rationale: No of students study french= 250- No of students study spanish = 250-150=100
% of the students study french but not spanish = (100/250)*100 % = 40 %
Answer:B
Answer: B
Question: A total of $20,000 was invested in two certificates of deposit at simple annual interest rates of 4 percent and 8 percent, respectively. If the total interest on the two certificates was $1,440 at the end of one year, what fractional part of the $20.000 was invested at the higher rate?
Options:
A) 3/8
B) 4/5
C) 1/2
D) 3/5
E) 3/4
Rationale: x * 4/100 * 1 + (20000 - x) * 8/100 * 1 = 1440
4x - 8x = 144000 - 160000
=> -4x = -16000
=> x = 4000/4
So 16000/20000 = 4/5
Answer - B
Answer: B
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 240 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is:
Options:
A)68 km/hr.
B)32 km/hr.
C)34 km/hr.
D)35 km/hr.
E)72 km/hr.
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (240 + 240 )/12
2x = 40
x = 20.
Speed of each train = 10 m/sec = 20 x 18/5 km/hr = 72 km/hr.
answer :E
Answer: E
Question: Kelly rows her canoe 2 miles downstream in 15 minutes. It takes her 60 minutes to row it back upstream the same 2 miles. What was the speed of the water current in mph?
Options:
A)3 mph
B)4 mph
C)5 mph
D)6 mph
E)7 mph
Rationale: Explanation:
Speed of boat Downstream: (2/15) X 60 = 8 mph
Speed of boat Upstream: (2/60) X 60 = 2 mph
Speed of current: 1/2 (8-2) = 6/2 = 3 mph
Answer: Option A
Answer: A
Question: If an average hard drive had a capacity of 0.6 TB in 2000, and average hard drive capacities double every 5 years, what will be the average hard drive capacity in 2050?
Options:
A)256
B)512
C)768
D)6144
E)1536
Rationale: 0.6*2^10=0.6*1024=614.4
The answer is D.
Answer: D
Question: In a sequence, each term starting with the third onward is defined by the following formula an=an−1−an−2an=an−1−an−2, where n is an integer greater than 2. If the first term of that sequence is 3 and the second term is 4, what is the value of the 70th of that sequence?
Options:
A)−4
B)−3
C)−1
D)3
E)4
Rationale: Given an=an−1−an−2an=an−1−an−2
a3 = a2 - a1 => 4-3 = 1.
a4 = -3
a5 = -4
a6 = -1
a7 = 3
a8 = 4
a9 = 1
a10 = -3
So pattern is 3,4 ,1,-3,-4,-1,3,4,1 and -3 - first term terms...
70th term is -3.
Answer :option B
Answer: B
Question: Choose the missing terms out of the given alternatives.
AZ, BY, CX, ?
Options:
A)EF
B)GH
C)ED
D)DW
E)KN
Rationale: D
DW
The first letter moves one step forward. The second letter moves one step backward.
Answer: D
Question: The length of a rectangular plot is 10mtr more than its width. The cost of fencing the plot along its perimeter at the rate of Rs. 6.5mtr is Rs.1690. The perimeter of the plot is?
Options:
A)126
B)156
C)190
D)321
E)260
Rationale: Sol. Let width = x, Length = (10+x)
Perimeter = 2(x+(10+x))
= 2(2x=10)
& 2(2x+10)*6.5 = 1650
X = 60
Required perimeter = 2(60+70) = 260
E
Answer: E
Question: A can do a piece of work in 16 days. When he had worked for 2 days B joins him. If the complete work was finished in 8 days. In how many days B alone can finish the work?
Options:
A)18
B)77
C)66
D)55
E)12
Rationale: 8/16 + 6/x = 1
X = 12 days
Answer:E
Answer: E
Question: A certain company retirement plan has arule of 70provision that allows an employee to retire when the employee's age plus years of employment with the company total at least 70. In what year could a female employee hired in 1988 on her 32nd birthday first be eligible to retire under this provision?
Options:
A)2003
B)2004
C)2005
D)2006
E)2007
Rationale: She must gain at least 70 points, now she has 32 and every year gives her two more points: one for age and one for additional year of employment, so 32 + 2*(# of years) = 70 --> (# of years) = 19 --> 1988+19=2007.
Answer: E.
Answer: E
Question: A baker filled with a measuring cup with 3/4 cup water. He poured 1/2 of the water into the batter, and then spilled 1/8 of the water on the floor. How much water will the baker needed to add what is left in the cup to have 50% more than what he started with?
Options:
A)1/8 cup
B)3/8 cup
C)1/4 cup
D)1/2 cup
E)7/8 cup
Rationale: 3/4 is the original water in cup .half in batter.So left is 3/8 out which 1/8 is spilled out.So again left with 2/8.
so 50% more than what he started was = 3/4+1/2*(3/4)=9/8
Amount of water needed to add = 9/8 - 2/8=7/8
ANSWER:E
Answer: E
Question: Adding 30% of x to x is equivalent to multiplying x by which of the following?
Options:
A)12.5
B)1.05
C)1.15
D)1.3
E)1.25
Rationale: 130x/100= 1.3*x
ANSWER:D
Answer: D
Question: 1/2 + [(2/3 * 3/8)/6] - 9/16 =
Options:
A) 29/16
B) 19/16
C) 15/16
D) 7/16
E) 0
Rationale: We need to simplify the expression using PEMDAS.
Parentheses
Exponents
Multiplication andDivision
Addition andSubtraction
The calculation of an equation or expression must be carried out in the following order:
1) Operations within parentheses (or absolute value bars or radicals)
2) Exponents
3) Multiplication and division from left to right
4) Addition and subtraction from left to right
The answer is D.
Answer: D
Question: A waitress's income consists of her salary and tips.During one week ,her tips were 9/4 of her salary.What fraction of her income for the week came from tips?
Options:
A)9/13
B)1/6
C)1/3
D)4/9
E)5/9
Rationale: Her tips were 9/4 of her salary.
Let's say her salary =$4
This mean her tips = (9/4)($4) =$9
So, her TOTAL INCOME =$4+$9=$13
What fraction of her income for the week came from tips
$9$13=9/13
=A
Answer: A
Question: A person lent a certain sum of money at 4% per annum at simple interest and in 8 years the interest amounted to Rs.340 less than the sum lent. What was the sum lent?
Options:
A)232
B)287
C)269
D)500
E)181
Rationale: P - 340 = (P*4*8)/100
P = 500
Answer: D
Answer: D
Question: If y is 80 percent greater than x, then x is what percent less than y ?
Options:
A)20
B)25
C)33 1/3
D)44 4/9
E)80
Rationale: y is 80 percent greater than x
Therefore,
y= (180/100) x
Let x be z percent of y.
So, x = (z/100) y
x = (z/100)(180/100) x
Solving, z = 55.55%
Therefore, x is (100 - 55.55 = 44.45) %
ANSWER:D
Answer: D
Question: Two numbers are in the ratio 3 : 4. If their L.C.M. is 60. what is sum of the numbers?
Options:
A)35
B)56
C)76
D)84
E)85
Rationale: Explanation:
Let the numbers be 3x and 4x
LCM of 3x and 4x = 12x (Since LCM of 3 and 4 is 12. Hence LCM of 3x and 4x is 12x)
Given that LCM of 3x and 4x is 60
=> 12x = 60
=> x = 60/12 = 5
Sum of the numbers
= 3x + 4x
= 7x
= 7 x 5 = 35
Answer: Option A
Answer: A
Question: In how many different ways can the letters of the word 'RETAIL' be arranged such that the vowels must occupy only the even positions?
Options:
A)None of these
B)64
C)120
D)36
E)360
Rationale: OEOEOE
3 vowels EAI can be arranged on even places in 3!=6 ways. Similarly 3 consonants can be arranged on odd places in 3!=6 ways.
Total = 6*6 = 36.
Answer: D.
Answer: D
Question: What is the present worth of Rs. 66 due in 2 years at 5% simple interest per annum?
Options:
A)60
B)277
C)120
D)888
E)171
Rationale: Let the present worth be Rs. x. Then,
S.I. = (66 - x)
(x * 5 * 2) / 100 = (66 - x)
10x = 6600 - 100x
110x = 6600 => x = 60.
Answer: A
Answer: A
Question: When n is divided by 5 the remainder is 3. What is the remainder when (n-1)^2 is divided by 5?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: n = 5x+3, for some integer x
(n-1)^2=(5x+2)^2=5y+4, for some integer y
When we divide this by 5, the remainder is 4.
The answer is E.
Answer: E
Question: The speed of a boat in still water is 60kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
Options:
A)80, 49
B)80, 40
C)80, 48
D)80, 46
E)82, 41
Rationale: Speed downstream = 60 + 20 = 80 kmph
Speed upstream = 60 - 20 = 40 kmph Answer: B
Answer: B
Question: Suresh and Ramesh started a business investing Rs. 24,000 and Rs. 40,000 respectively. Out of total profit of Rs. 19,000, what is Ramesh's share?
Options:
A)s. 7375
B)s. 8379
C)s. 9875
D)s. 10875
E)s. 11875
Rationale: Explanation:
Ratio of Suresh and Ramesh's share = 24,000 : 40,000 = 3 : 5
Ramesh's share = Rs. (19000 x 5 / 8) = Rs. 11875
ANSWER: E
Answer: E
Question: If John takes 4 minutes to eat x raisins, how many seconds will it take him to eat z raisins, assuming he continues to eat at the same rate?
Options:
A)240z/x
B)4xz
C)240x/z
D)240xz
E)4z/x
Rationale: It will take (z/x)(4) minutes which is (z/x)(4)(60) seconds = 240z/x seconds.
The answer is A.
Answer: A
Question: A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?
Options:
A)10/21
B)11/21
C)5/20
D)9/20
E)5/21
Rationale: Total number of balls = (2 + 3 + 2) = 7.
Let S be the sample space.
Then, n(S)	= Number of ways of drawing 2 balls out of 7
= 7C2
=(7*6)/(2*1)
=42/2
=21
Let E = Event of drawing 2 balls, none of which is blue.
n(E)	= Number of ways of drawing 2 balls out of (2 + 3) balls.
=5C2
=(5*4)/(2*1)
=20/2
=10
P(E)=n(E)/n(s)
=10/21
The answer should be A
Answer: A
Question: On a certain scale of intensity, each increment of 10 in magnitude represents a tenfold increase in intensity. On this scale, an intensity corresponding to a magnitude of 155 is how many times an intensity corresponding to a magnitude of 125?
Options:
A)40
B)100
C)400
D)1000
E)10 000
Rationale: Increase of 40 in magnitude corresponds to 10^4 increase in intensity:
If intensity for 125 is x then for 135 it'll be 10*x, for 145 it'll be 10*10*x=10^2*x, for 155 it'll be 10*10*10*x=10^3*x and for 165 it'll be 10*10*10*10*x=10^3*x.
Answer: D.
Answer: D
Question: A candidate got 35% of the votes polled and he lost to his rival by 2250 votes. How many votes were cast?
Options:
A)7500
B)8500
C)6500
D)5500
E)9500
Rationale: 35%-----------L
65%-----------W
------------------
30%----------2250
100%---------? => 7500
ANSWER:A
Answer: A
Question: A meeting has to be conducted with 5 managers. Find the number of ways in which the managers may be selected from among 7 managers, if there are 2 managers who refuse to attend the meeting together.
Options:
A)6
B)8
C)10
D)11
E)15
Rationale: The total number of ways to choose 5 managers is 7C5 = 21
We need to subtract the number of groups which include the two managers, which is 5C3 = 10.
21 - 10 = 11
The answer is D.
Answer: D
Question: A photographer will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row. The heights of the people within each row must increase from left to right, and each person in the second row must be taller than the person standing in front of him or her. How many such arrangements of the 6 people are possible?
Options:
A)5
B)6
C)9
D)24
E)26
Rationale: Lets give some identification to the persons
A,B,C,D,E,F
They are arrang in decreasing order of their height
A being tallest and F being smallest
To satisfy both the conditions
A should be in the right most position of the second row (A is the tallest in order to satisfy the condition increasing height from left to right A should be the right most and the back person should be taller then the front so A should be in the second row)
similarly F should be in the left most positon of first row
lets see the combinations
CBA--------second row
FED---------First row
DCA
FEB
DBA
FEC
ECA
FDB
EBA
FDC
these are the combinations which satisfy both the conditions
so the answer is 5 A
Answer: A
Question: In a bag of small balls 1/4 are green, 1/8 are blue, 1/12 are yellow and the remaining 26 white. How many balls are blue?
Options:
A)6 balls
B)7 balls
C)8 balls
D)9 balls
E)10 balls
Rationale: Let us first find the fraction of green, blue and yellow balls
1/4 + 1/8 + 1/12 = 6 / 24 + 3 / 24 + 2 / 24 , common denominator
= 11 / 24 , add numerators
The fraction of white balls is given by
24 / 24 - 11 / 24 = 13 / 24
So the fraction 13 / 24 corresponds to 26 balls. If x is the total number of balls then
(13 / 24) of x = 26 balls
or (13 / 24) × x = 26
x = 26 × (24 / 13) = 48 , total number of balls
The fraction of blue balls is 1 / 8 of x. The number of blue balls is given by (1 / 8) of 48 = 6 balls.
ANSWER IS A
Answer: A
Question: Lagaan is levied on the 60 percent of the cultivated land. The revenue department collected total Rs. 3,84,000 through the lagaan from the village of Mettur. Mettur, a very rich farmer , paid only Rs.480 as lagaan. The percentage of total land of Mettur over the total taxable land of the village is:
Options:
A)0.20833
B)0.35424
C)0.10982
D)0.20933
E)0.10984
Rationale: Total land of Sukhiya = \inline \frac{480x}{0.6} = 800x
\therefore Cultivated land of village = 384000x
\therefore Required percentage = \inline \frac{800x}{384000}\times 100 = 0.20833
A
Answer: A
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions.
Options:
A)287 m
B)704 m
C)176 m
D)186 m
E)197 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.
= 500 * 2 * 22/7 * 22.4
= 70400 cm
= 704 m
Answer:B
Answer: B
Question: A can do a job in 18 days and B can do it in 30 days. A and B working together will finish twice the amount of work in ------- days?
Options:
A)14 ½ days
B)16 ½ days
C)22 ½ days
D)11 ½ days
E)19 ½ days
Rationale: C
22 ½ days
1/18 + 1/30 = 8/90 = 4/45
45/4 = 11 ¼ *2 = 22 ½ days
Answer: C
Question: There is a 40 cm line marked at each centimeter and an insect is placed at every centimeter. 9 frogs are trained to jump a constant distance. The first one jumps 2 cm in every leap, the second one jumps 3 cm and so on until the 9th one jumps 10 cm in every leap and they eat any insect that is available at that spot. If all of them start from start line and finish the entire 40 cm, how many insects were still left after the race was over?
Options:
A)0
B)4
C)6
D)8
E)10
Rationale: Only the prime numbers greater than 10 and less than 40 were left.
That is 11, 13, 17, 19, 23, 29, 31, and 37.
The total is 8.
The answer is D.
Answer: D
Question: When Rahul was born, his father was 32 years older than his brother and his mother was 25 years older than his sister. If Rahul's brother is 6 years older than him and his mother is 3 years younger than his father, how old was Rahul's sister when he was born ?
Options:
A)7 years
B)10 years
C)14 years
D)19 years
E)9 years
Rationale: let rahuls age =x
x=0(born) den bro's age=6
father=32+bro=32+6=38(at the time rahul was born)
mother=father-3=35
mother= 25+ sis
=>35-25=sis
=> sis=10.
ANSWER:B
Answer: B
Question: A bag contains 3 red, 5 yellow and 7 green balls. 3 balls are drawn randomly. What is the probability that the balls drawn contain balls of different colours?
Options:
A)2/7
B)3/5
C)3/13
D)1/4
E)7/16
Rationale: Total number of balls = 3+5+7 = 15
n(S) = 15C3 = 455
n(E) = 3C1 * 5C1 * 7C1 = 105
Probability = 105/455 = 3/13
Answer is C
Answer: C
Question: A group of 6 students bought movie tickets in one row next to each other. If Bob and Lisa are in this group, what is the probability that Bob and Lisa will each sit next to only one of the five other students from the group?
Options:
A)5.6%
B)6.7%
C)15.5%
D)20.4%
E)25.7%
Rationale: The question basically asks about the probability that Bob and Lisa sit at the ends.
The total # of sitting arrangements is 6!.
Desired arrangement is either BWXYZL or LWXYZB. Now, WXYZ can be arranged in 4! ways, therefore total # of favorable arrangements is 2*4!.
P=(favorable)/(total)=(2*4!)/6!=1/15.
Answer: B.
Answer: B
Question: The diagonals of a rhombus are 15 cm and 21 cm. Find its area?
Options:
A)277
B)266
C)150
D)288
E)157.5
Rationale: 1/2 * 15 * 21 = 157.5
Answer: E
Answer: E
Question: A can complete a project in 10 days while B can complete same project in 30 days. If A and B start working together and A leaves the work 10 days before completion of project, then in how many days the project will be completed?
Options:
A)15
B)19
C)20
D)21
E)22
Rationale: A's 1day work=1/10;
B's 1day work=1/30;
(A+B) 1day work=(1/10+1/30)=2/15;
It is given that A leaves the work 10 days before completion of the project..
Thus,B alone does the remaining job in 10 days.
So,In 10 days ,B can do 1/3 w ..
Thus,(A+B) have worked (1-1/3)=2/3 w..
(A+B)can do 2/15 work in 1 day...
They did 2/3 w in 5 days.
Total days=(5+10) = 15
ANSWER:A
Answer: A
Question: The H.C.F. of two numbers is 12 and their L.C.M. is 600. If one of the number is 30, find the other?
Options:
A)100
B)240
C)120
D)200
E)150
Rationale: Other number = 12*600/30 = 240
Answer is B
Answer: B
Question: One train is traveling 45 kmph and other is at 10 meters a second. Ratio of the speed of the two trains is?
Options:
A)5:4
B)5:8
C)5:2
D)5:2
E)5:1
Rationale: :
45 * 5/18 = 10
25:20 => 5:4
Answer: A
Answer: A
Question: A motorcyclist goes from Bombay to Pune, a distance of 180 kms at an average of 20 kmph speed. Another man starts from Bombay by car 2 Â½ hours after the first, and reaches Pune Â½ hour earlier. What is the ratio of the speed of the motorcycle and the car?
Options:
A)1:2
B)2:3
C)1:9
D)1:5
E)1:1
Rationale: T = 180/20 = 9 h
T = 9 - 3 = 6
Time Ratio = 9:6= 3:2
Speed Ratio = 2:3
Answer: B
Answer: B
Question: Harkamal purchased 8kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 45 per kg. How much amount did he pay to the shopkeeper?
Options:
A)A)1000
B)B)1055
C)C)965
D)D)1075
E)E)1080
Rationale: Cost of 8 kg grapes = 70 × 8 = 560.
Cost of 9 kg of mangoes = 45 × 9 = 405.
Total cost he has to pay = 560 + 405 = 965.
C)
Answer: C
Question: Suppose the sales tax be reduced from 3 1/2% to 3 1/3%, then what difference does it make to a person who purchase an article with marked price of Rs. 7200 ?
Options:
A)Rs 12
B)Rs 16
C)Rs 10
D)Rs 14
E)None of these
Rationale: Explanation :
Solution: required difference = (3 1/2% of Rs. 7200) - (3 1/3% of 7200)
= (7/2 - 10/3)% of 7200 = 1/6 % of Rs. 7200
= Rs. ((1/6) * (1/100) *7200) = Rs. 12.
Answer : A
Answer: A
Question: Peter must choose a lab partner by picking a name out of a bag. If the bag has 9 male names and F female names, what is the least number of female names in the bag if the probability of choosing a male lab partner is less than 3 out of 7?
Options:
A)11
B)12
C)13
D)14
E)16
Rationale: Male Names in the bag = 9
Female Names in the bag = F
Probability of selecting a male name is = P = 9/(9+F)
The question asked is "what is the least number of female names in the bag if the probability of choosing a male lab partner is less than 3 out of 7?"
so, we need to find out the minimum value of F for which P<3/7
9/(9+F) < 3/7
Solving for F gives the equation;
F>12
Since the question asked is the minimum value F should be 13
( F should be an integer).
ANSWER:C
Answer: C
Question: 2)	An bus covers a certain distance at a speed of 240 kmph in 5 hours. To cover the samedistance in 1hr, it must travel at a speed of?
Options:
A)700 km/hr
B)720 km/hr
C)740 km/hr
D)780 km/hr
E)800 km/hr
Rationale: Distance = (240 x 5) = 1200 km.
Speed = Distance/Time
Speed = 1200/(5/3) km/hr. [We can write 1 hours as 5/3 hours]
Required speed = 1200 x 3 km/hr = 720 km/hr.
B
Answer: B
Question: Ada and Paul received their scores on three tests. On the first test, Ada's score was 10 points higher than Paul's score. On the second test, Ada's score was 2 points higher than Paul's score. If Paul's average (arithmetic mean) score on the three tests was 3 points higher than Ada's average score on the three tests, then Paul's score on the third test was how many points higher than Ada's score?
Options:
A)9
B)14
C)17
D)21
E)25
Rationale: My take is Option D (23)
I followed a simple approach (explained below):
Test 1: Ada's score = Paul's score + 10
Test 2: Ada's score = Paul's score + 4
Avg. of Paul's score = 3 points higher than Avg. of Ada's score
This implies that : Sum of Paul's score [3 Tests] = 9 points higher than Sum of Ada's score [3 Tests] (9 points higher since 3 points were given in terms of average of 3 scores)
So, Paul needs to score 23 points higher than Ada in Test 3, since Paul needs to compensate for the lower score in test 1 and Test 2 ( 21 = 10 + 2 + 9)
D
Answer: D
Question: A sum of money is sufficient to pay Y's wages for 10 days and Z's wages for 15 days. The same money is sufficient to pay the wages of both for?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: Let the total money be $x
Y's 1day work = $ x/10
Z's 1day work = $ x/15
Y+Z 1day work = $ x/6
Money is sufficient to pay the wages of both for 6days
Answer is E
Answer: E
Question: Excluding stoppages, the speed of a bus is 50 kmph and including stoppages, it is 43 kmph. For how many minutes does the bus stop per hour?
Options:
A)70 min
B)16 min
C)20 min
D)8.4 min
E)40 min
Rationale: D
8.4 min
Due to stoppages, it covers 7 km less.
Time taken to cover 9 km = (7/50 x 60) min = 8.4 min
Answer: D