divelab/Sys2Bench huggingface dataset:
Question: Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train catches and completely passes the slower train in 72 seconds. What is the length of each train (in meters)?
Options:
A)70
B)80
C)90
D)100
E)110
Rationale: The relative speed = 46 - 36 = 10 km/hr = 10 * 5/18 = 25/9 m/s
In 72 seconds, the relative difference in distance traveled is 72 * 25/9 = 200 meters
This distance is twice the length of each train.
The length of each train is 200/2 = 100 meters
The answer is D.
Answer: D
Question: A certain article of clothing was discounted during a special sale to 2/3 of its original retail price. When the clothing didn't sell, it was discounted even further to 1/2 of its original retail price during a second sale. By what percent did the price of this article of clothing decrease from the first sale to the second sale?
Options:
A)50%
B)22.22%
C)25%
D)16.66%
E)12.5%
Rationale: Say the original retail price of the item was $200.
The price after the first sale = 2/3 * $200 = $400/3.
The price after the second sale = 1/2 * $200 = $100.
The percent change from the first sale to the second = (400/3 - 100) / 150 = 1/3 = 22.22%.
Answer: B.
Answer: B
Question: In a lottery, there are 10 prizes and 20 blanks. A lottery is drawn at random. What is the probability of getting a prize?
Options:
A)1/10
B)2/5
C)1/3
D)5/7
E)None
Rationale: Solution
P(getting a prize)	= 10 / (10+20)
‹=› 10 / 30
‹=› 1/ 3.
Answer C
Answer: C
Question: In a 500 m race, Ravi beats Ramesh by 5 seconds or 100 m. They decide to run another race and this time Ravi gives Ramesh a head tart of 200 m. If Ravi’s speed is twice his previous speed and Ramesh’s speed is one and half times his previous speed, how far from the starting point should the winning post be so that they finish at the same time?
Options:
A)500 m
B)1000 m
C)1500 m
D)2000 m
E)2500 m
Rationale: Ravi beats ramesh by 5 sec or 100 mtr....means ramesh cover 100mtr in 5 sec....by this we can get ramesh speed in 20m/sec
20.............in 1 sec
500........in 500/20=25 sec(Ramesh's time)
so ravi take 20 sec to cover 500 mtr......by this we can get that ravis speed is 25m/sec
now assume x be the distance from staring line where we need to put the winning post.
According to question ravi’s speed will be 25*2=50m/sec & ramesh’s speed will be 20*1.5=30 m/sec
now assume x be the distance from staring line where we need to put the winning post.
they will take same time to reach the wining post.
As ravi gives Ramesh a 200 m ahead start so he has to accede x meter and Ramesh has to accede (x-200) meter
Hence we may write,
x/50=(x-200)/30
x=500 meter
ANSWER:A
Answer: A
Question: What is the Compound Interest on Rs.9500 at 6% p.a. compounded half-yearly for 1 1/2 years.
Options:
A)810.91
B)840.91
C)880.91
D)887.91
E)980.91
Rationale: Compound interest : A = P(1 + r/n)nt
A = 10,380.91
C.I. >> 10,380.91 - 9500 >> Rs. 880.91
Answer:C
Answer: C
Question: Five farmers have 7,9,11,13 & 14 apple trees respectively in their orchards.last year each of them discovered that every tree in their own orchard bore exactly d same no of apples.further,if d 3rd farmer gives one apple to the 1st,& the 5th gives 3 to each of the 2nd & d 4th,they would all exactly have the same no of apples, what were d yields per tree in the orchards of d 3rd & 4th farmers?
Options:
A)8,9
B)10,11
C)11,12
D)11,9
E)11,8
Rationale: Let a, b, c, d & e be the number of apples bored last year in each farmer's tree.
Given that 7a + 1 = 9b + 3 = 11c - 1 = 13d + 3 = 14e - 6
But the question is to find the number of apples bored per tree in 3rd nd 4th orchard.It is enough to consider 11c - 1 = 13d + 3..
Therefore 11 c - 1 = 13 d + 3
By trial and error method, we get the value for c and d as 11 and 9.
5th nd 4th
14e - 6 = 13d + 3
14e - 13d = 9
here if u put e=d=1, result ll be 1, e=d=2 difference ll be 2, .... e=d=9 ,result ll be 9
so e=9 , d=9
So 5ht tree ll give 14 * 9 = 126 no. of apples
4th tree ll give 13 * 9 = 117 no. of apples
for 5th nd 2nd
14 * 9 -6 = 9 * b + 3
120=9b + 3
b = 13
So 2nd tree ll give 9 * 13 = 117
A= 119 , per tree = 17
B= 117 , per tree = 13
C= 121, per tree = 11
D= 117, per tree = 9
E = 126 , per tree = 9
3'rd farmer have 11 apples per tree and
4'th farmer have 9 apples per tree.
ANSWER:D
Answer: D
Question: Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is ?
Options:
A)17/27
B)17/25
C)17/76
D)17/20
E)17/23
Rationale: n(S) = 20
n(Even no) = 10 = n(E)
n(Prime no) = 8 = n(P)
P(EᴜP) = 10/20 + 8/20 - 1/20
= 17/20
Answer: D
Answer: D
Question: Find the probability that a non leap year selected at random will have 53 Sundays
Options:
A)6/7
B)5/7
C)4/7
D)3/7
E)1/7
Rationale: There are 365 days in a leap year: 52 weeks and 1 more days. So, 52 Sundays and 1 days.
This 1 days can be {Mon, Tue, Wed, Thu, Fri, Sat,Sun} (7 cases). In order to have 53 Sundays we should have Sun case.
The probability of that is 1/7.
Answer: E.
Answer: E
Question: Of the 200 employees in a certain company, 25 percent will be relocated to City X and the remaining 75 percent will be relocated to City Y. However, 45 percent of the employees prefer City Y and 55 percent prefer City X. What is the highest possible number of employees who will be relocated to the city they prefer?
Options:
A) 65
B) 100
C) 115
D) 130
E) 135
Rationale: 110 prefer X (Group 1);
90 prefer Y (Group 2).
City Y needs 150 people: letall 90 who prefer Y (entire Group 2) be relocated there, the rest 60 will be those who prefer X from Group 1;
City X needs 40 people: 110-60=40 from Group 1 will be relocated to X, which they prefer.
So, the highest possible number of employees who will be relocated to the city they prefer is 90+40=130.
Answer: D.
Answer: D
Question: Johnny has 4 classes. He averaged a mark of 83 in those classes. If Johnny takes night school and scores an 88 in the course, what will his new average be?
Options:
A)83
B)84
C)85
D)85.5
E)86
Rationale: (sum of the 4 marks)/4 = 83
sum of the 4 marks = 332
new sum = 332 + 88 = 420
new average = 420/5 = 84
ans: B
Answer: B
Question: A student chose a number, multiplied it by 7, then subtracted 150 from the result and got 130. What was the number he chose?
Options:
A)40
B)42
C)44
D)46
E)48
Rationale: Let x be the number he chose, then
7⋅x−150=130
7x=280
x=40
correct answer A
Answer: A
Question: The surface area of a cube is 1734 sq. cm. Find its volume
Options:
A)2334 cubic.cm
B)3356 cubic.cm
C)4913 cubic.cm
D)3478 cubic.cm
E)None of these
Rationale: Explanation:
Let the edge of the cube bea. Then,
6a2 = 1734
=> a = 17 cm.
Volume = a3 = 173 = 4193 cm3
Answer: C
Answer: C
Question: A certain pilot flew 400 miles to City K at an average speed of 350 miles per hour with the wind and made the trip back at an average speed of 150 miles per hour against the wind. Which of the following is closest to the pilot’s average speed, in miles per hour, for the round-trip?
Options:
A)280
B)210
C)300
D)310
E)320
Rationale: Avg speed = total distance/ total time
total distance = 800
total time = 400/350 + 400/150 = 80/21
=> avg speed = (800*21)/80 = 210(approx)
ans is B
Answer: B
Question: The average of 11 numbers is 10.6. If the average of the first six numbers is 10.5 and that of the last six numbers is 11.4, then the middle number is
Options:
A)71.5
B)11.5
C)81.5
D)14.8
E)21.5
Rationale: Explanation:
Middle numbers = [(10.5 x 6 + 11.4 x 6) - 10.6 x 11] = 14.8.
Answer: D
Answer: D
Question: A toy store regularly sells all stock at a discount of 10 percent. If an additional 10 percent were deducted from the discount price during a special sale, what would be the lowest possible price of a toy costing $10 before any discount?
Options:
A) $7.20
B) $8.00
C) $8.10
D) $8.27
E) $9.00
Rationale: sale price = (original price - 10% decrease) - 10% decrease
price = [10 * (90/100)] * (90/100) = 10 * (.90) * (.90) = 9 * .90 = 8.10
The answer is C.
Answer: C
Question: A merchant gains or loses, in a bargain, a certain sum. In a second bargain, he gains 680 dollars, and, in a third, loses 80. In the end he finds he has gained 250 dollars, by the three together. How much did he gain or lose bv the first ?
Options:
A)-280
B)300
C)-350
D)-380
E)None
Rationale: In this sum, as the profit and loss are opposite in their nature, they must be distinguished by contrary signs. If the profit is marked +, the loss must be -.
Let x = the sum required.
Then according to the statement x + 680 - 80 = 250
And x = -350.
Answer C
Answer: C
Question: In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?
Options:
A)30%
B)70 percent
C)100%
D)120%
E)None
Rationale: Solution
Let C.P. = Rs. 100.	Then, Profit = Rs.320,
S.P. = 420.
Let C.P. = Rs. 125% of Rs. 100	= Rs.125.
New S.P. = Rs.420.
Profit = Rs. (420 - 125)	= Rs.295.
∴ Required percentage	= (295 / 420 x 100)%
= 1475 / 21%
= 70%.
Answer B
Answer: B
Question: 6+3+2 = 242116
8+9+1 = 727216
5+7+4 = 505644
2+7+5 =?
Options:
A)224210
B)224220
C)224230
D)224240
E)224250
Rationale: 6+3+2 = 242116 = 6*(3+2-1) 3*(6+2-1) 2*(6+3-1)=6*4 3*7 2*8= 242116
8+9+1 = 727216
5+7+4 = 505644 = (5*10) (7*8) (4*11)
2+7+5 = 2*(7+5-1) 7*(2+5-1) 5*(2+7-1) = 224240
ANSWER:D
Answer: D
Question: The ratio 25:50 expressed as percent equals to
Options:
A)50 %
B)85 %
C)25 %
D)75 %
E)None of above
Rationale: Explanation:
Actually it means 25 is what percent of 50, which can be calculated as,
(25/50)*100 = 25 * 2 = 50
Answer: Option A
Answer: A
Question: Find the C.I. on a sum of Rs.10000 for 6 months at 25% per annum, interest being compounded quarterly?
Options:
A)10290
B)5290
C)1289
D)1290
E)2290
Rationale: C.I.= 2000(21/20)^2-1800
= 1289
Answer: C
Answer: C
Question: If pqr < 0 and qr > 0, which of the following must be positive?
Options:
A) xy
B) xz
C) (p^2)qr
D) p(q^2)r
E) xy(z^2)
Rationale: Given that qr is positive and pqr is negative, you can say that p MUST be negative. As for q and r either they are both positive or both negative.
Option (C) has p^2 which is positive and qr which is positive. So (C) must be positive.
Answer: C
Question: 56 +57+58+59=230. How many such 4 consecutive numbers are there less than 500 when added gives a sum which is divisible by 10?
Options:
A)100
B)200
C)300
D)400
E)500
Rationale: since 1+2+3+4=10 & 6+7+8+9=30
any combination with these no be will give u desirable result...
so total no in 100 will be 20 & that's why in in 500,it will be 20x5=100.
ANSWER:A
Answer: A
Question: Consider a quarter of a circle of radius 36. Let r be the radius of the circle inscribed in this quarter of a circle. Find r.
Options:
A)16*(sqr2 -1)
B)8*(sqr3 -1)
C)4*(sqr7 - 1)
D)36* (sqr2 -1)
E)None of these
Rationale: I got 36/(sqr2 +1) and just forgot to multiply by (sqr2 -1).
Answer is D
Answer: D
Question: In how many ways can 8 Indians and, 4 American and 4 Englishmen can be seated in a row so that all person of the same nationality sit together?
Options:
A)3!*8!*4!*4! ways
B)8!*4!*4! ways
C)3!4! ways
D)3!*5! ways
E)3!*6! ways
Rationale: Taking all person of same nationality as one person, then we will have only three people.
These three person can be arranged themselves in 3! Ways.
8 Indians can be arranged themselves in 8! Way.
4 American can be arranged themselves in 4! Ways.
4 Englishman can be arranged themselves in 4! Ways.
Hence, required number of ways = 3!*8!*4!*4! Ways.
ANSWER A
Answer: A
Question: A woman named Ragavi started a business investing Rs. 7,000. Roja joined him after six months with an amount of Rs. 7,000 and Sachin joined them with Rs. 7,000 after another six months. The amount of profit earned should be distributed in what ratio among Ragavi, Roja and Sachin respectively, 3 years after A woman started the business ?
Options:
A)7:6:10
B)12:15:16
C)42:45:56
D)42:45:55
E)6:5:4
Rationale: Explanation :
Akash : Roja : Sachin = (7000 x 36) : (7000 x 30) : (7000 x 24)
= 36:30:24 => 6:5:4
Answer :E
Answer: E
Question: Dan's age after 16 years will be 4 times his age 8 years ago. What is the present age of Dan?
Options:
A)12
B)16
C)20
D)24
E)28
Rationale: Let Dan's present age be x.
x+16 = 4(x-8)
3x = 48
x = 16
The answer is B.
Answer: B
Question: A train covers a distance of 18 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
Options:
A)120m
B)180m
C)240m
D)220m
E)280m
Rationale: Speed = (18/10 * 60) km/hr = (108 * 5/18) m/sec = 30 m/sec.
Length of the train = 30 * 6 = 180 m.
ANSWER:B
Answer: B
Question: Use distributive property to solve the problem below:
Maria bought 10 notebooks and 5 pens costing 3 dollars each.How much did Maria pay?
Options:
A)30 dollars
B)40 dollars
C)45 dollars
D)60 dollars
E)70 dollars
Rationale: Solution
3 × (10 + 5) = 3 × 10 + 3 × 5 = 30 + 15 = 45 dollars
Answer C
Answer: C
Question: The present ages of three persons in proportions 4 : 7 : 5. Eight years ago, the sum of their ages was 56. Find their present ages (in years).
Options:
A)8, 20, 28
B)16, 28, 36
C)20, 35, 25
D)16, 28, 34
E)16, 28, 33
Rationale: Let their present ages be 4x, 7x and 5x years respectively.
Then, (4x - 8) + (7x - 8) + (5x - 8) = 56
16x = 5.
Their present ages are 4x = 20 years, 7x = 35 years and 5x = 25 years respectively.
Answer:C
Answer: C
Question: Jackson has $313,192 dollars in his investment accounts. What is the least amount of money (in whole number of dollars) that he must remove from his account if he wants to split this money evenly among nine new investors?
Options:
A)$1
B)$2
C)$3
D)$4
E)$5
Rationale: In order to divide the sum in 9 parts, the amount must also be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 313,192 = 19 and 18 is divisible by 9.
Hence we need to subtract 1 to this number for it to be divisible by 9
Correct Option: A
Answer: A
Question: A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat(in still water) and the stream is
Options:
A)1:2
B)1:3
C)2:1
D)3:1
E)None
Rationale: Sol.
Let man’s rate upstream be x kmph. Then, his rate downstream = 2x kmph.
∴ (Speed in still water) : (Speed of stream)
= [2x + x / 2] : [2x - x / 2]
3x / 2 : x / 2 = 3:1.
Answer D
Answer: D
Question: How many words can be formed by using all letters of word ALIVE.
Options:
A)120
B)236
C)128
D)261
E)191
Rationale: Explanation:
The word ALIVE contains 5 different letters
Therefore,
Required number of words = 5p5 = 5!
= (5*4*3*2*1) = 120
ANSWER:A
Answer: A
Question: one person Tharak speed with the current is 10 km/hr and the speed of the current is 4 km/hr. Tharak's speed against the current is:
Options:
A)0 km/hr
B)1 km/hr
C)2 km/hr
D)3 km/hr
E)4 km/hr
Rationale: Man's speed with the current = 10 km/hr
=> speed of the man + speed of the current = 10 km/hr
speed of the current is 4 km/hr
Hence, speed of the man = 10-4 = 6 km/hr
man's speed against the current = speed of the man - speed of the current
= 6-4 = 2 km/hr
ANSWER:C
Answer: C
Question: A shopkeeper sells two articles at Rs.1000 each, making a profit of 20% on the first article and a loss of 20% on the second article. Find the net profit or loss that he makes?
Options:
A)8%
B)2%
C)3%
D)4%
E)6%
Rationale: SP of first article = 1000
Profit = 20%
CP = (SP)*[100/(100+P)] = 5000/6 = 2500/3
SP of second article = 1000
Loss = 20%
CP = (SP)*[100/(100-L)] = 5000/4 = 1250
Total SP = 2000
Total CP = 2500/3 + 1250 = 6250/3
CP is more than SP, he makes a loss.
Loss = CP-SP = (6250/3)- 2000 = 250/3
Loss Percent = [(250/3)/(6250/3)]*100
=0.04 * 100
= 4%
Answer:D
Answer: D
Question: The smallest number when increased by " 1 " is exactly divisible by 6,18,36,48, 60 is:
Options:
A)724
B)721
C)720
D)719
E)700
Rationale: LCM = 720
720 - 1 = 719
ANSWER:D
Answer: D
Question: A cyclist traveled for two days. On the second day the cyclist traveled 3 hours longer and at an average speed 10 mile per hour slower than she traveled on the first day. If during the two days she traveled a total of 280 miles and spent a total of 12 hours traveling, what was her average speed on the second day?
Options:
A)5 mph
B)10 mph
C)20 mph
D)30 mph
E)40 mph
Rationale: SOLUTION:
D = 280 Mi
T = 12 hrs
Day 1 time = T1
Day 2 time = T2
T2 - T1 = 4 hrs ----- (I)
T1 + T2 = 12 hrs ----- (II)
Adding I and II, T2 = 8 hrs and T1 = 4 hrs
Day 1 Rate = R1
Day 2 Rate = R2
R1 - R2 = 10 mph
i.e. R1 = 10 + R2
280 = 8R2 + 4R1
i.e. 280 = 8R2 + 4 (10 + R2)
i.e. R2 = 20 mph
ANSWER: B
Answer: B
Question: In a group of hats consisting of only blue hats, green hats, and purple hats, the ratio of blue hats to green hats to purple hats is 7:4:12. If there are a total of 161 hats in this group, how many of these hats are not blue?
Options:
A)28
B)42
C)48
D)112
E)76
Rationale: Since the hats Blue, Green and Purple are in ratio of 7:4:12...The total no. of balls will be
7x+4x+12x=161 or 23x=161...here 7x,4x and 12x represent hats of each type
23x=161 so x=7...Blue hats =7*7=49...Not blue will be 161-49=112.
Ans D
Answer: D
Question: By selling an article at Rs.600, a profit of 25% is made. Find its cost price?
Options:
A)288
B)992
C)678
D)480
E)131
Rationale: SP = 600
CP = (SP)*[100/(100+P)]
= 600 * [100/(100+25)]
= 600 * [100/125] = Rs.480
Answer:D
Answer: D
Question: A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 6km?
Options:
A)3
B)6
C)7
D)8
E)9
Rationale: M = 4
S = 2
US = 4 - 2 = 2
D = 6
T = 6/2 = 3
Answer: A
Answer: A
Question: X starts a business with Rs.45000. Y joins in the business after 3 months with Rs.30000. What will be the ratio in which they should share the profit at the end of the year?
Options:
A)1:2
B)1:3
C)2:1
D)1:4
E)1:5
Rationale: Ratio in which they should share the profit
= Ratio of the investments multiplied by the time period
=45000×12:30000×9
=45×12:30×9
=3×12:2×9
=2:1
Answer is C.
Answer: C
Question: 54.327 × 357.2 × 0.0057 is the same as :
Options:
A)5.4327 × 3.572 × 5.7
B)5.4327 × 3.572 × 0.57
C)5.4327 × 3.572 × 0.0000057
D)None of these
E)Cannot be determined
Rationale: Solution
Number of Decimal places in the given expression =8 .
Number of Decimal places in (a) = 8 .
Number of Decimal places in (b) =9 .
Number of Decimal places in (c) = 7 .
Number of Decimal places in (a) is the same as the given expression . Answer A
Answer: A
Question: A bag contains 4 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is
Options:
A)8/15
B)2/5
C)3/5
D)11/15
E)17/33
Rationale: Drawing two balls of same color from four green balls can be done in 4C₂ ways.
Similarly from eight white balls two can be drawn in ⁸C₂ ways.
P = 4C₂/¹⁵C₂ + ⁸C₂/¹⁵C₂ = 17/33
ANSWER:E
Answer: E
Question: If 100<x<190 and 10<y<100, then the product xy CANNOT be equal to:
Options:
A)18,104
B)18,303
C)18,356.732
D)19,502
E)18,909
Rationale: Correct Answer: (D)
Determine the range of xy by multiplying the two extremes of each individual range together. The smallest value of xy must be greater than 100 * 10. The largest value must be less than 190 * 100. This means that 1000 < xy < 19,000. (D) is outside of this range, so it is not a possible product of xy.
Answer: D
Question: A teacher prepares a test. She gives 6 objective type questions out of which 4 have to be answered. Find the total ways in which they can be answered if the first 3 questions have 3 choices and the last 3 have 4 choices.
Options:
A)255
B)1816
C)1872
D)100
E)144
Rationale: Two cases.
First Case: 2 Questions - 3 Choices, 2 Questions - 4 Choices
3C2 * 3C2 ways to select the questions
3C1 * 3C1 * 4C1 * 4C1 ways to answer the questions
= 3 * 3 * 3 * 3 * 4 * 4
=1296
Second Case: 1 Question - 3 Choices, 3 Questions - 4 Choices
3C1 * 3C3 ways to select the questions
3C1 * 4C1 * 4C1 * 4C1 ways to answer the questions
= 3 * 1 * 3 * 4 * 4 * 4
= 576
Total = 1296 + 576
= 1872
C
Answer: C
Question: Find 356 x 936 - 356 x 836 = ?
Options:
A)35600
B)34500
C)49630
D)93600
E)None
Rationale: Answer
356 x 936 - 356 x 836 = 356 x (936 - 836 )
= 356 x 100
= 35600.
Option: A
Answer: A
Question: The milk level in a rectangular box measuring 64 feet by 25 feet is to be lowered by 6 inches. How many gallons of milk must be removed? (1 cu ft = 7.5 gallons)
Options:
A)100
B)250
C)750
D)5625
E)6000
Rationale: 6 inches = 1/2 feet (there are 12 inches in a foot.), so 64*25*1/2=800 feet^3 of milk must be removed, which equals to 800*7.5=6000 gallons.
Answer: E.
Answer: E
Question: 7 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played?
Options:
A)40
B)48
C)45
D)42
E)22
Rationale: Though 2*(7C2) is the correct approcah to do this, but for people like me who find Perm, Comb n Prob a nightmare, an easy approach can be used.
The first guy has to play 2 matches with the rest of 6, so he'll play 12matches.
Similarly, second guy has to play with the rest of 5 as his 2 games with the first guy are already played. So he plays 10 matches.
This continues like this and the total matches are 12+10+8...+2
12+10+...+2 = 2(6+5+...+1) = 2((6*7)/2) = 6*7 =42.
ANSWER:D
Answer: D
Question: P can do a certain work in 16 days. Q is 60% more efficient than P. How many days does Q alone take to do the same job?
Options:
A)8
B)9
C)10
D)11
E)12
Rationale: Each day, P can do 1/16 of the work.
Each day, Q can do 1.6/16 of the work = 16/160 of the work
The time taken by B alone to complete the total work is 160/16 = 10 days.
The answer is C.
Answer: C
Question: A can do a piece of work in 15 days and B in 20 days. They began the work together but 5 days before the completion of the work, A leaves. The work was completed in?
Options:
A)11 3/9
B)19 3/7
C)11 3/5
D)11 3/7
E)11 3/1
Rationale: (x – 5)/15 + x/20 = 1
x = 11 3/7 days
Answer:D
Answer: D
Question: If KING is coded as 17 and MASS is coded as 29 Then DON is coded as
Options:
A)21
B)20
C)18
D)16
E)None of these
Rationale: KING = 11+9+14+7=41 i.e (4*4)+(1*1)=17
MASS = 13+1+19+19=52 i.e (5*5)+(2*2)=29
DON = 4+14+15=33 i.e(3*3)+(3*3)=18
ANSWER:C
Answer: C
Question: In March, Kurt ran an average of 1.2 miles an hour. If by June he had increased his pace by 20 seconds per mile, then which of the following expresses the number of hours it would take Kurt to complete one mile in June?
Options:
A)3590/60^2
B)2980/60^2
C)2390/60^2
D)3586/60
E)60^2/3590
Rationale: Kurt ran at an average of 1.2 miles/hour in march. So to run 1 mile he would take 1/1.2 hours = (60 * 60)/1.2 seconds = 3000 seconds.
If he increases his speed by 20 seconds, he will complete a mile in 2980 seconds. Converting in hours = 2980/(60 * 60) = 2980/(60^2)
ANSWER: B
Answer: B
Question: A distributor sells a product through an online store, which take a commission of 20% of the price set by the distributor. The distributor obtains the product from a producer at the price of $19 per item. What is the price that the buyer observers online if the distributor wants to maintain a 20% profit on the cost of the item?
Options:
A)$27.50
B)$28.50
C)$29.50
D)$30.50
E)$31.50
Rationale: Let x be the price that buyers see online.
The distributor wants to receive 1.2(original price) which should be 80% of x.
1.2(19) = 0.8x
x = 1.2(19) / 0.8 = 1.5(19) = $28.50
The answer is B.
Answer: B
Question: A person takes 5 hrs 45 min in walking to a place and riding back. He would have gained 4 hrs by riding both ways. The time he would take to walk both ways is?
Options:
A)5 hours 45 min
B)5 hours 55 min
C)6 hours 45 min
D)9 hours 45 min
E)10 hours
Rationale: ----------------------------------------------------------------
Solution 1
----------------------------------------------------------------
Given that time taken for riding both ways will be 4 hours lesser than
the time needed for waking one way and riding back
From this, we can understand that
time needed for riding one way = time needed for waking one way - 4 hours
Given that time taken in walking one way and riding back = 5 hours 45 min
Hence The time he would take to walk both ways = 5 hours 45 min + 4 hours = 9 hours 45 min
D
Answer: D