divelab/Sys2Bench huggingface dataset:
Question: Working alone, Printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 12, 40, and 50 hours, respectively. What is the ratio of the time it takes Printer X to do the job, working alone at its rate, to the time it takes Printers Y and Z to do the job, working together at their individual rates?
Options:
A) 4/11
B) 1/2
C) 15/22
D) 200/9
E) 11/4
Rationale: P1 takes 12 hrs
Rate for P2P3 together = 1/40 + 1/50 = 9/200
Therefore they take 200/9
Ratio = 200/9 = D
Answer: D
Question: If X is to be chosen at random from the integers between 1 to 7, inclusive, and Y is to be chosen at random from the integers between 8 and 12, inclusive, what is the probability that X + Y will be even?
Options:
A)2/5
B)3/7
C)5/7
D)17/35
E)24/35
Rationale: X+Y will be even if X and Y are both even or both odd.
P(X and Y are both even) = 3/7*3/5 = 9/35
P(X and Y are both odd) = 4/7*2/5 = 8/35
P(X+Y is even) = 9/35 + 8/35 = 17/35
The answer is D.
Answer: D
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 4 days before the completion of the work. In how many days was the work completed?
Options:
A)33
B)77
C)66
D)11
E)99
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 4 days = 4*(1/24 + 1/30) = 3/10
Remaining work = 7/10
The number of days required for this initial work = 7 days.
The total number of days required = 4 + 7 = 11 days.
Answer:D
Answer: D
Question: A reduction of 30% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg?
Options:
A)46
B)47
C)48
D)49
E)50
Rationale: 800*(30/100) = 240 ---- 5
? ---- 1 => Rs.48
Answer: C
Answer: C
Question: The number of positive integer solutions for the equation x +y +z + t = 30 is
Options:
A)3854
B)3654
C)3764
D)3960
E)4964
Rationale: The number of positive integer solutions for the equatio fx1+x2+⋯+xn=k
(k-1)C(n-1)- where k is the number and n is number of variable in the equation.
30-1 C 4-1 = 29C3 = 3654
Answer : B
Answer: B
Question: Michael cashed a check for $1,100 and received only $10 and $50 bills in return. During the course of a day, he used 15 bills and then lost the rest of the money. If the number of $10 bills used was either one more or one less than the number of $50 bills used, what is the minimum possible amount of money that was lost?
Options:
A) $630
B) $800
C) $770
D) $730
E) $700
Rationale: 1. 15 bills spent
2. Number of $10 bills is one more or one less than number of $50 bills.
So, 2 choices
1. 7*10 + 8*50 = $470
2. 8*10 + 7*50 = $430
Least money lost implies most money spent. i.e $470
Therefore, lost money = 1100 - 470 = 630.
Answer A
Answer: A
Question: 350 metres long yard, 26 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between 2consecutive trees
Options:
A)10
B)12
C)14
D)16
E)17
Rationale: 26 trees have 25 gaps between them,
Required distance (350/25) = 14
C
Answer: C
Question: Working together, Wayne and his son can shovel the entire driveway in three hours. If Wayne can shovel five times as fast as his son can, how many hours would it take for his son to shovel the entire driveway on his own?
Options:
A)4
B)6
C)8
D)9
E)12
Rationale: W: the time for Wyane to do the job
S: the time for his son to do the job
We have 1/W + 1/S = 1/5 and W = 5S
Then we have 1/(5*S) + 1/S = 1/5<=> 6/(5*S) = 1/5 <=> S = 6
ANS: B
Answer: B
Question: Mrs. B. invested $30,000; part at 5%, and part at 8%. The total interest on the investment was $2,100. How much did she invest at each rate?
Options:
A)x = $1,000, y = $29,000
B)x = $5,000, y = $25,000.
C)x = $10,000, y = $20,000.
D)x = $15,000, y = $15,000
E)x = $20,000, y = $10,000
Rationale: 2100 = (30000-x) 5/100 + 8x/100
Solving, we get x = 20000
So, answer is 10000 & 20000
Answer = C
Answer: C
Question: In a kilometer race, A beats B by 50 meters or 10 seconds. What time does A take to complete the race?
Options:
A)289
B)190
C)277
D)266
E)255
Rationale: Time taken by B run 1000 meters = (1000 * 10)/50 = 200 sec.
Time taken by A = 200 - 10
= 190 sec.
Answer:B
Answer: B
Question: Q=(429)^2 * 237 * (1243)^3 is thrice of ?
Options:
A)33605 * 31960 * (1243)^2
B)33654 * 538219 * (1243)^2
C)33891 * 533247 * (1243)^2
D)34122 * 532004 * (1243)^2
E)34606 * 534572 * (1243)^2
Rationale: Q=(429)^2*237*(1243)^3 is an odd number.
Among answer choices only C is an odd number, (so thrice C also will be an odd number).
Answer: C.
Answer: C
Question: The ratio of the number of ladies to gents at a party was 1:2 but when 2 ladies and 2 gents left, the ratio became 1:3. How many people were at the party originally?
Options:
A)22
B)88
C)12
D)99
E)14
Rationale: x, 2x
(x-2):(2x-2) = 1:3
3x-6 = 2x-2
x = 4
x+2x = 3x
=> 3*4 = 12
Answer: C
Answer: C
Question: Hydraulic press Machines P and Q are two different machines that cover jars in a factory. When Machine P works alone, it covers 5 jars in m hours. When Machines P and Q work simultaneously at their respective rates, they cover 5 jars in n hours. In terms of m and n, how many hours does it take Machine Q, working alone at its constant rate, to cover 5 jars?
Options:
A)m
B)n
C)m+n
D)5n/25-mn
E)m-n
Rationale: working rate p = 5/m ; working rate pq =( 1/p +1/q)* n =5 or mn/5 +n/q =5 0r n/q = 5-mn/5 = 25-mn/5
q = 5n/25-mn
E
Answer: E
Question: If 6^w is a factor of (10!)^2, What is the greatest possible value of w ?
Options:
A)2
B)4
C)6
D)8
E)10
Rationale: w 10!= 10*9*8*7*6*5*4*3*2*1 = 2*5*3*3*2*2*2*7*2*3*5*2*2*3*2 = 2^8*3^4*5^2*7
6= 2*3
Therefore only the exponents of 2 and 3 are relevant, 2^8 or 3^4 -> higher number counts = 8 -> Answer Choice D
Answer: D
Question: A library has an average of 500 visitors on Sundays and 140 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is :
Options:
A)100
B)200
C)300
D)400
E)550
Rationale: Explanation:
Since the month begins with a Sunday, so there will be five Sundays in the month,
Required average = (500 * 5 + 140 * 25) / 30 = 6000/30 = 200
Answer: B) 200
Answer: B
Question: What is 35% of 4/13 of 650?
Options:
A)50
B)60
C)70
D)80
E)90
Rationale: This problem can be solved easily if we just use approximation: 35% is a little over 1/3, while 4/13 is a little less than 4/12, which is 1/3. Thus, the answer is about 1/3 of 1/3 of 650, or 1/9 of 650. Since the first 1/3 is a slight underestimate and the second 1/3 is a slight overestimate, the errors will partially cancel each other out. Our estimate will be relatively accurate.
The number 650 is a bit more than 630, so (1/9)*630 will be about 70.
Keeping track not only of your current estimate, but also of the degree to which you have overestimated or underestimated , can help you pinpoint the correct answer more confidently.
The answer is C.
Answer: C
Question: A starts a business with $3500. After 5 months, B joins with A as his partner. After a year, the profit is divided in the
ratio 2 : 3. B's contribution in the capital is
Options:
A)7000
B)9000
C)8000
D)9900
E)7900
Rationale: Ratio in which profit is divided =2:3
Assume that B's contribution to the capital=b
3500×12:b×7=2:3
⇒3500×12×3=2×b×7
⇒b = 3500×12×3 / 2×7
=500×6×3=9000
ANSWER:B
Answer: B
Question: Together, Victor and Tami Vargas earn $33,280 per year. Tami earns $4,160 more per
year than Victor earns. How much do Tami earn per year?
Options:
A)$28,720
B)$8,720
C)$18,720
D)$38,720
E)$58,720
Rationale: You are asked to find two unknown amounts. Victor’s earnings: x
Represent the amounts using algebra. Tami’s earnings: x 4,160
Write an equation showing that the sum of the
two amounts is $33,280. Solve the equation. x x 4,160 33,280
Combine like terms. 2x 4,160 33,280
Subtract 4,160 from both sides of the equation. 2x 4,160 4,160 33,280 4,160
2x 29,120
Divide both sides by 2.
x 14,560
Now go back to the beginning, when you first wrote the amounts in algebraic language. Since
x represents Victor’s earnings, you know that Victor earns $14,560 per year. Tami’s earnings are
represented by x+4,160. Add: 14,560+4,160=18,720. Tami earns $18,720 per year.
Answer: Victor earns $14,560, and Tami earns $18,720.
correct answer C
Answer: C
Question: A man invested Rs. 14,400 in Rs. 100 shares of a company at 20% premium.If the company declares 7% dividend at the end of the year,then how much does he get ?
Options:
A)Rs. 500
B)Rs. 840
C)Rs. 650
D)Rs. 720
E)None
Rationale: Solution
Number of shares = (14400/120) = 120.
Face value = Rs. (100x120 ) = Rs. 12000.
Annual income = Rs.(7/100x12000) = Rs. 840.
Answer B
Answer: B
Question: A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
Options:
A)277
B)277
C)120
D)882
E)272
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 6 = 120 m.
Answer: C
Answer: C
Question: Four dice are thrown simultaneously. Find the probability that all of them show the same face.
Options:
A)1/216
B)1/215
C)5/300
D)1/415
E)1/500
Rationale: Total no of elementary events = 6^4
n(S) = 6^4
x={(1,1,1,1)(2,2,2,2).....(6,6,6,6)}
n(X)=6
n(X)/n(S) =6/6^4
=1/216
ANSWER A
Answer: A
Question: Working at their respective constant rates, Paul, Abdul and Adam alone can finish a certain work in 3, 4, and 5 hours respectively. If all three work together to finish the work, what fraction R of the work will be done by Adam?
Options:
A) 1/4
B) 12/47
C) 1/3
D) 5/12
E) 20/47
Rationale: Let the total work be 60 units. Pual does 60/3 =20 units of work per hr. abdul does 15 units per hr and adam does 12 units per hr. If all work together they do (20 + 15 + 12) units per hr = 47 units per hr. So the time taken to finish the work = 60/47 hrs.
adam will do 60/47 * 12 units of work in 60/47 hr . fraction of work adam does =work done by adam / total work
R>( 60/47 *12)/60 =12/47
Answer B
Answer: B
Question: If five numbers are randomly selected without replacement from set {1, 2, 3, 4, 5}, what is the probability that the numbers are selected in ascending order?
Options:
A)1/256
B)1/120
C)1/480
D)1/240
E)1/50
Rationale: The total number of ways to arrange 5 numbers is 5! = 120.
There is only one way to arrange the numbers in ascending order.
P(ascending order) = 1/120
The answer is B.
Answer: B
Question: The average age of a class of 39 students is 15 years. If the age of the teacher be included, then the average increases by3 months. Find the age of the teacher.
Options:
A)25years
B)45years
C)12years
D)6years
E)16years
Rationale: Total age of 39 persons = (39 x 15) years
= 585 years.
Average age of 40 persons= 15 yrs 3 months
= 61/4 years.
Total age of 40 persons = (_(61/4 )x 40) years= 610 years.
:. Age of the teacher = (610 - 585) years=25 years.
Ans: A
Answer: A
Question: In the first 10 overs of a cricket game, the run rate was only 3.6. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?
Options:
A)6.25
B)6.5
C)6.15
D)7
E)8
Rationale: 10 overs - run rate = 3.6
runs scored in first 10 overs = 36
remaining overs 40
total runs to be scored= 282
32 runs already scored 282-36=246
246 runs to be scored in 40 overs
let required runrate be x
40*x=246
x=246/40
x=6.15
the required runrate is 6.15
ANSWER:C
Answer: C
Question: John has $1,600 at the beginning of his trip, after spending money, he still has exactly $600 less than he spent on the trip. How much money does John still have?
Options:
A)$200
B)$400
C)$600
D)$800
E)$500
Rationale: Suppose total money spent = x
Not spend (Money he still has)= x-600
x+x-600 = 1600
x= 1100
Money not spend= 1100-600= 500
Answer : E
Answer: E
Question: Donovan and Michael are racing around a circular 400-meter track. If Donovan runs each lap in 48 seconds and Michael runs each lap in 40 seconds, how many laps will Michael have to complete in order to pass Donovan, assuming they start at the same time?
Options:
A)5
B)7
C)8
D)9
E)6
Rationale: One way of approaching this question is by Relative speed method
1. Speed/ Rate of Donovan = Distance/ time => 400/48 =>50/6
2. Speed/ Rate of Michael = Distance/ time => 400/40 => 10
Relative Speed between them = 10 - 50/6 => 10/6 (We subtract the Rates if moving in the same direction and add the rates if moving in the opposite direction)
In order to pass Donovan-
Distance to be covered = 400, Relative Rate = 10/6
Total Time taken by Micheal to surpass Donovan = Distance / rate => 400*6/10 => 2400/10 => 240
No. of laps taken by Michael = Total time / Michael's rate => 240/40 => 6
Hence correct answer is 6 Laps.
E
Answer: E
Question: A cab driver 5days income was $25, $50, $60, $65 , $70. Then his average income is?
Options:
A)A)$58
B)B)$54
C)C)$65
D)D)$48
E)E)$62
Rationale: avg = sum of observations/number of observations
avg income=(25+50+60+65+70)/5 = 54
Answer is B
Answer: B
Question: If a committee of 3 people is to be selected from among 7 married couples so that the committee does not include two people who are married to each other, how many such committees are possible?
Options:
A)20
B)40
C)50
D)180
E)280
Rationale: You now have your Committee of 3 people. But you've selected them in an order, when order doesn't matter.
Selection #1 = Jack
Selection #2 = Susan
Selection #3 = Mary
Assume this is a good committee where Jack is not married to Susan or Mary and Susan and Mary are not married. The above committee will be the same as the following committee:
Selection #1 = Susan
Selection #2 = Mary
Selection #3 = Jack
To account for the fact that the order does not matter, we must divide out the number of ways a single committee can be the same members but in different order. 3 places = 3!, 3*2*1 = 6.
14*12*10 / 6 = 280. Answer E.
Answer: E
Question: What is the remainder when 14,456 × 15,657 × 16,788 is divided by 10?
Options:
A)6
B)8
C)4
D)3
E)2
Rationale: Only the unit's digit of the product will decide the remainder when divided by 10.
Hence, 6*7*8= will give units digit as 6
So, whatever be the number, if it ends in 6, the remainder after dividing with 10 will be 6.
OptionA
Answer: A
Question: In the xy-plane, a triangle has vertices (0,0), (4,0) and (4,6). If a point (a,b) is selected at random from the triangular region, What is the probability that a-b>0?
Options:
A)1/5
B)1/3
C)1/2
D)2/3
E)4/5
Rationale: The area of the right triangle is (1/2)*4*6 = 12.
Only the points (a,b) below the line y=x satisfy a - b > 0.
The part of the triangle which is below the line y=x has an area of (1/2)(4)(4) = 8.
P(a - b > 0) = 8/12 = 2/3
The answer is D.
Answer: D
Question: Rs. 6000 is lent out in two parts. One part is lent at 4% p.a simple interest and the other is lent at 10% p.a simple interest. The total interest at the end of one year was Rs. 450. Find the ratio of the amounts lent at the lower rate and higher rate of interest?
Options:
A)5:1
B)5:7
C)5:2
D)5:8
E)5:2
Rationale: Let the amount lent at 4% be Rs. x
Amount lent at 10% is Rs. (6000 - x)
Total interest for one year on the two sums lent
= 4/100 x + 10/100 (6000 - x) = 600 - 3x/100
=> 600 - 3/100 x = 450 => x = 2500
Amount lent at 10% = 3500
Required ratio = 5:7
Answer:B
Answer: B
Question: 88% OF 370+24% OF 210-?=118
Options:
A)256
B)258
C)268
D)358
E)NONE OF THESE
Rationale: LET 88% OF 370+240% OF 210-X=118
THEN, X=(88/100*370)+(24/100*210)-118-325.60+50.40-118=376-118=258
CORRECT OPTION: B
Answer: B
Question: The smallest number which when diminished by 8, is divisible 8, 16, 24, 32 and 40 is:
Options:
A)1008
B)1015
C)488
D)490
E)590
Rationale: Required number = (L.C.M. of 8, 16, 24, 32, 40) + 8
= 480 + 8
= 488
Answer: Option C
Answer: C
Question: A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 72.25, the number of the member is the group is:
Options:
A)57
B)67
C)77
D)85
E)97
Rationale: Explanation:
Money collected = (72.25 x 100) paise = 7225 paise.
∴ Number of members = √(7225) = 85.
Answer: D
Answer: D
Question: A basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is
Options:
A)25/42
B)25/47
C)25/32
D)25/48
E)25/41
Rationale: :
Total fruits = 9
Since there must be at least two apples,
= 25/42.
Answer: A
Answer: A
Question: How many words can be formed by using all letters of the word ‘BIHAR’ ?
Options:
A)110
B)120
C)130
D)140
E)None
Rationale: Solution
The word BIHAR contains 5 different letters.
Required number of words = 5P5 = 5 ! = (5 x 4 x 3 x 2 x 1) = 120
Answer B
Answer: B
Question: A began a business with Rs. 85,000. He was joined afterwards by B with Ks. 42,500. For how much period does B join, if the profits at the end of the year are divided in the ratio of 4 : 1 ?
Options:
A)6 months
B)3 months
C)2 months
D)8 months
E)9 months
Rationale: Suppose B joined for x months . Then, ( 85000 * 12 )/(42500 * x) = 4. or x = (85000 * 12) / (42500 * 4) = 6.
So, B joined for 6 months.
Answer: A
Answer: A
Question: What will come in place of the x in the following Number series? 46080, 3840, 384, 48, 8, 2, x
Options:
A)1
B)3
C)5
D)6
E)7
Rationale: 46080 /12 = 3840
3840 /10 = 384
384 /8 = 48
48 /6 = 8
8/4 = 2
2 /2 = 1
A
Answer: A
Question: A, B and C rents a pasture for Rs.928. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay?
Options:
A)270
B)289
C)288
D)255
E)552
Rationale: 12*8 :16*9 = 18*6
8: 12: 9
9/29 * 928 = 288
Answer: C
Answer: C
Question: What is the difference between the place values of two sevens in the numeral 54707429 ?
Options:
A)699990
B)693000
C)99980
D)699930
E)None of these
Rationale: Explanation:
Required Difference
= 700000 - 7000 = 693000
Answer is B
Answer: B
Question: In an election between two candidates first candidate got 65% of votes polled and second Candidate got 2800 votes. The total number of votes polled was?
Options:
A)7000 votes
B)8000 votes
C)9000 votes
D)9800 votes
E)9900 votes
Rationale: Total = 100 %,
First person got 65%
second person got remaining 35 % of votes.
than 35 % = 2800
35% = 35Ã—80 = 2800
100% =100Ã—80 =8000 votes
B
Answer: B
Question: What is the sum of the 1st 5 prime numbers greater than 20?
Options:
A)121
B)151
C)168
D)164
E)161
Rationale: Required sum = (23 + 29 + 31 + 37 + 41) = 161
Note: 1 is not a prime number
Answer E
Answer: E
Question: Jason flips a coin three times. What is the probability W that the coin will land on the same side in all three tosses?
Options:
A)1/16
B)1/8
C)1/4
D)1/3
E)1/2
Rationale: Total outcome is 2^3=8
Favorable cases HHH or TTT
Therefore, probability W is 2/8 or 1/4.C
Answer: C
Question: From 5 positive numbers and 7 negative numbers, how many groups of 4 numbers, yielding a positive product, can be formed?
Options:
A)720
B)625
C)250
D)960
E)355
Rationale: The number of ways to choose 4 positive numbers is 5C4 = 5.
The number of ways to choose 4 negative numbers is 7C4 = 35.
The number of ways to choose 2 positive and 2 negative is 5C2*7C2 = 10*21 = 210.
The total number of groups is 5+35+210 = 250.
The answer is C.
Answer: C
Question: If 2x^2 – y^2 = 2xy, then (x - y)^2 =
Options:
A)x^2
B)3x^2
C)4xy
D)2y^2-x^2
E)– y^2
Rationale: (x-y)^2 = x^2 + y^2 - 2xy = x^2 + y^2- 2x^2+y^2 = 2y^2-x^2
correct option : D
Answer: D
Question: A squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 4 feet . How many feet does the squirrel travels if the post is 16 feet tall and 2 feet in circumference?
Options:
A)10 feet
B)8 feet
C)13 feet
D)15 feet
E)18 feet
Rationale: total circuit=16/4=4
total feet squirrel travels=4*2=8 feet
ANSWER:B
Answer: B
Question: Two tests had the same maximum mark. The pass percentages in the first and the second test were 40% and 45% respectively. A candidate scored 216 marks in the second test and failed by 36 marks in that test. Find the pass mark in the first test?
Options:
A)277
B)266
C)111
D)121
E)224
Rationale: Let the maximum mark in each test be M.
The candidate failed by 36 marks in the second test.
pass mark in the second test = 216 + 36 = 252
45/100 M = 252
Pass mark in the first test = 40/100 M = 40/45 * 252 = 224.
Answer:E
Answer: E
Question: Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 14 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
Options:
A)11
B)444
C)420
D)287
E)221
Rationale: 1h ----- 5
? ------ 60
12 h
RS = 14 + 21 = 35
T = 12
D = 35 * 12 = 420
Answer:C
Answer: C
Question: How many of the positive factors of 56 , 96 and how many common factors are there in numbers?
Options:
A)2
B)4
C)3
D)5
E)1
Rationale: factors of 56- 1, 2, 4, 7, 8, 14, 28, 56
factors of 96- 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
Comparing both, we have three common factors of 56 and 96- 1,2,4
Answer(C)
Answer: C
Question: Two airplanes take off from one airfield at noon. One flies due east at 204 miles per hour while the other flies directly northeast at 283 miles per hour. Approximately how many miles apart are the airplanes at 2 p.m.?
Options:
A)166
B)408
C)400
D)483
E)566
Rationale: B
In two hours:
the plane flying East will be 408 miles away from airport.
the other plane will be 566 miles away from airport.
566/408 = ~1.4 = ~sqrt(2)
This means that planes formed a right isocheles triangle => sides of such triangles relate as 1:1:sqrt(2) => the planes are 408 miles apart.B
Answer: B
Question: What is the smallest five digit number that is divisible by 15, 36, 40, and 54?
Options:
A)10400
B)10800
C)11200
D)11600
E)12000
Rationale: 15 = 3 * 5
36 = 2^2 * 3^2
40 = 2^3 * 5
54 = 2 * 3^3
LCM = 2^3 * 3^3 * 5 = 1080
The smallest five-digit number that is a multiple of 1080 is 10*1080 = 10,800
The answer is B.
Answer: B
Question: Karen places a bet with Tom that she will beat Tom in a car race by 4 miles even if Karen starts 4 minutes late. Assuming that Karen drives at an average speed of 60 mph and Tom drives at an average speed of 45 mph, how many E miles will Tom drive before Karen wins the bet?
Options:
A)15
B)18
C)21
D)24
E)27
Rationale: Let K and T be the speeds of Karen and Tom respectively.
t be the time that Karen will travel ----> t+4/60 will be the total time Tom will travel by the time the distance between Karen and Tom is 4 miles.
Thus, per the question , K(t) - T(t+4/60) = 4 ---> t = 7/15 hours
Thus the distance traveled by Tom when Karen is 4 miles ahead of him E: T*(t+4/60) = 45 (7/15+4/60) = 24 miles. D is the correct answer.
Answer: D
Question: What is the smallest of six consecutive odd integers whose average (arithmetic mean) is a + 2?
Options:
A)a - 5
B)a
C)a - 1
D)a - 3
E)a + 1
Rationale: Since the numbers are consecutive odd integers, mean = median = 3rd integer + 4th integer /2
And 1st integer= 3rd integer- 4
let's say 3rd integer = n and 4th integer = n+2
2n+2/2= a+2
n= a+1
1st integer= a+1-4= a-3
D is the answer
Answer: D
Question: The ratio of radius of a circle and the side of a square is 2 : 3. Find the ratio of their areas:
Options:
A)2 : 1
B)4 : 9
C)8 : 77
D)4 : 121
E)None
Rationale: radius/side = 2/3
â‡’ area of circle/area of square= 4/9
Answer: B
Answer: B
Question: On Saturday morning, Malachi will begin a camping vacation and he will return home at the end of the first day on which it rains. If on the first three days of the vacation the probability of rain on each day is 0.7, what is the probability that Malachi will return home at the end of the day on the following Monday?
Options:
A)0.063
B)0.128
C)0.488
D)0.512
E)0.64
Rationale: Re-phrasing the question:
What is the probability of: Saturday: No rain, Sunday: No rain, Monday: Rain
Probablity of rain = 0.7
Therefore, probability of no rain = 0.3
0.3*0.3*0.7 = 0.063
Hence A
Answer: A