divelab/Sys2Bench huggingface dataset:
Question: When John can do a work in 15 days and Marry in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is?
Options:
A)2/15
B)3/25
C)8/15
D)9/15
E)None
Rationale: A's 1 day's work =	1	;
15
B's 1 day's work =	1	;
20
(A + B)'s 1 day's work =	(	1	+	1	)	=	7	.
15	20	60
(A + B)'s 4 day's work =	(	7	x 4	)	=	7	.
60	15
Therefore, Remaining work =	(	1 -	7	)	=	8/15
15
C
Answer: C
Question: There are some pigeons and hares in a zoo. If heads are counted, there are 200. If legs are counted, there are 580. The number of hares in the zoo is?
Options:
A)16
B)19
C)90
D)17
E)91
Rationale: 200*2 = 400
580
-----
180
1----2
?----180 = 90
Answer: C
Answer: C
Question: The edges of three metal cubes are 1 cm, 3 cm, and 4 cm respectively. A new cube is made by melting these three cubes together. What is the edge of the new cube (in centimeters)?
Options:
A)3.9
B)4.2
C)4.5
D)4.8
E)5.1
Rationale: The total volume is 1^3+3^3+4^3=92
The edge of the new cube is the cube root of 92 which is about 4.5 cm.
The answer is C.
Answer: C
Question: The average of 10 numbers is 23. If each number is increased by 5, what will the new average be?
Options:
A)36
B)28
C)72
D)29
E)22
Rationale: Sum of the 10 numbers = 230
If each number is increased by 5, the total increase =
5 * 10 = 50
The new sum = 230 + 50 = 280 The new average = 280/10
= 28.
Answer:B
Answer: B
Question: From the given integer n, if n*n*n is odd, then which is true from below options?
Options:
A)n is
B)n is odd and n*n is even
C)n*n is even
D)n is even
E)n*n is odd
Rationale: n is odd and n*n is even
Option B
Answer: B
Question: In a room there are 9 people. Each person shook hands with every other person. How many hand shakes were there?
Options:
A)36
B)40
C)44
D)48
E)52
Rationale: 9C2 = 36
The answer is A.
Answer: A
Question: In order to complete a reading assignment on time, Terry planned to read 60 pages per day. However, she read only 30 pages per day at first, leaving 480 pages to be read during the last 6 days before the assignment was to be completed. How many days in all did Terry have to complete the assignment on time?
Options:
A)10
B)8
C)6
D)12
E)14
Rationale: D=60*X - according to the plan, assignment to be completed on time reading 60 pages per day for next X days. But, Terry's plans changed so she read as follow:
30 pages for first Y days and 480 pages for last 6 days, we get these equations:
30*Y+480=60*X
X-Y=6 --------->>X planned number of days, Y - actually used reading 30 pages per day and 6 leftover days used to complete a lump 780 pages
From above we find that X=Y+6 and 30Y+480=60Y+360 or 30Y=120 --->>>>> Y=4, hence X=10
Answer : A
Answer: A
Question: If m is a positive integer and m^2 is divisible by 54, then the largest positive integer that must divide m is?
Options:
A) 3
B) 6
C) 18
D) 12
E) 16
Rationale: M^2 is divisible by 48 so M^2 must be multiple of 48.
If the value of M is Multiples of 18 then it will satisfy the condition. If we If M is 12 or 24 or 36 then it ans is C but if M = 54 then answer should be 16.
Is the question right? Or am i missing some thing?
C
Answer: C
Question: Today is Monday. After 37 days, it will be:
Options:
A)Sunday
B)Saturday
C)Friday
D)Thursday
E)Wednesday
Rationale: Each day of the week is repeated after 7 days.
So, after 35 days, it will be Monday.
After 37 days, it will be Wednesday.
Answer :E
Answer: E
Question: In the storage room of a certain bakery, the ratio of sugar to flour is 5 to 4, and the ratio of flour to baking soda is 10 to 1. If there were 60 more pounds of baking soda in the room, the ratio of flour to baking soda would be 8 to 1. How many pounds of sugar are stored in the room?
Options:
A)600
B)1200
C)1500
D)1600
E)3000
Rationale: Sugar:Flour = 5:4 = 25:20;
Flour:Soda = 10:1 = 20:2;
Thus we have that Sugar:Flour:Soda = 25x:20x:2x.
Also given that 20x/(2x+60) = 8/1 --> x=120 --> Sugar = 25x =3,000
Answer: E.
Answer: E
Question: A 300 meter long train crosses a platform in 42 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
Options:
A)99
B)289
C)350
D)882
E)400
Rationale: Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 42 = 50/3
3(x + 300) = 2100 è x = 400m.
Answer: E
Answer: E
Question: A and B invests Rs.10000 each, A investing for 6 months and B investing for all the 12 months in the year. If the total profit at the end of the year is Rs.24000, find their shares?
Options:
A)8000, 16000
B)1599,2000
C)7290,3000
D)15000,4000
E)72821,5000
Rationale: The ratio of their profits A:B =6:12 = 1 : 2
Share of A = 1 * 24000/3 = 8000
Share of B = 2 * 24000/3 = 16000
Answer : A
Answer: A
Question: If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is
Options:
A)4/12
B)4/29
C)4/22
D)4/13
E)4/17
Rationale: P(SᴜK) = P(S) + P(K) - P(S∩K), where S denotes spade and K denotes king.
P(SᴜK) = 13/52 + 4/52 - 1/52
= 4/13
Answer:D
Answer: D
Question: A batsman scored 120 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?
Options:
A)45(4/11) %
B)50 %
C)45(5/11) %
D)44(5/11) %
E)None of these
Rationale: Explanation :
Total runs scored = 120
Total runs scored from boundaries and sixes = 3 x 4 + 8 x 6 = 60
Total runs scored by running between the wickets = 120 - 60 = 60
Required % = (60/120) × 100 = 50%
Answer : Option B
Answer: B
Question: The wheel of a car A is having a diameter of 40 inches is rotating at the rate of x inches/minute. The wheel of another car B is having a diameter of 20 inches and is rotating at the rate of y inches/minute. What is the value of x in terms of y if both the rims reach their starting positions at the same time after every rotation?
Options:
A)4y
B)2y
C)6y
D)3y
E)1y
Rationale: t=S1/V1=S2/V2
or 40/x=20/y
or x=40y/20=2y
Answer is B
Answer: B
Question: In a game of eight players lasting for 70 minutes, six substitutes alternate with each player. This means that all players, including the substitutes, are on the pitch for the same length of time. For how long?
Options:
A)43 minutes
B)46 minutes
C)39 minutes
D)40 minutes
E)30 minutes
Rationale: D
40 minutes
(70 Ã— 8)Ã· 14.
Total time for eight players = 70 Ã— 8 = 560 minutes.
However, as 14 people are each on the pitch for an equal length of time, they are each on the pitch for 40 minutes (560 Ã· 14);
Answer: D
Question: If the Average (mean ) of 3 positive temperatures is x degrees fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be
Options:
A)6x
B)3x
C)5x/3
D)3x/2
E)3x/5
Rationale: Let the 5 numbers be 1,2,3,4(since no restrictions are given). There mean is 2.5 (x).
Now the sum of greatest three would be 2+3+4= 9
so the answer has to be 3x....that is option B
Answer: B
Question: The effective annual rate of interest corresponding to a nominal rate of 16% per annum payable half-yearly is?
Options:
A)16.64%
B)16.07%
C)16.08%
D)16.09%
E)16.19%
Rationale: Amount of Rs. 100 for 1 year when compounded half-yearly = [100 * (1 + 8/100)2] = Rs. 116.64 Effective rate = (116.64 - 100) = 116.64%
ANSWER:A
Answer: A
Question: A monkey ascends a greased pole 17 metres high. He ascends 2 metres in first minute and slips down 1 metre in the alternate minute. In which minute, he reaches the top ?
Options:
A)31st
B)22nd
C)23rd
D)24th
E)None of these
Rationale: In 2 minutes, he ascends = 1 metre
âˆ´ 15 metres, he ascends in 30 minutes.
âˆ´ He reaches the top in 31st minute.
Answer A
Answer: A
Question: A type of extra-large SUV averages 12.2 miles per gallon (mpg) on the highway, but only 7.6 mpg in the city. What is the maximum distance, in miles, that this SUV could be driven on 22 gallons of gasoline?
Options:
A)190
B)284.6
C)300
D)268
E)312
Rationale: so 12.2 * 22 = 268..
IMO option D is correct answer..
Answer: D
Question: The equal amounts of money are deposited in two banks each at 15% per annum for 3.5 years and 5 years respectively. If the difference between their interests is Rs.144, find the each sum?
Options:
A)Rs.578
B)Rs.125
C)Rs.640
D)Rs.220
E)Rs.300
Rationale: Explanation:
(P*5*15)/100 - (P*3.5*15)/100 = 144
75P/100 – 52.5P/100 = 144
22.5P = 144 * 100
=> P = Rs.640
Answer: C
Answer: C
Question: If Aaron is now twice as old as Bailey was 20 years ago, and B is Bailey's current age in years, which of the following represents the sum of Aaron and Bailey's ages 4 years from now?
Options:
A)3B-22
B)3B-25
C)4B-22
D)4B-24
E)4B-25
Rationale: B is Bailey's current age.
Let Aaron's current age be A.
given A = 2(B-20).
four years from now Aaron's age will be = 2(B-20) + 4 = 2B-36
four years from now Bailey's age will be = B+4
Sum of ages of Mason and Gunther's after 4 years = 2B-36+B+4 = 3B-22
Ans : A
Answer: A
Question: A group consists of 4 men, 6 women and 5 children. In how many ways can 2 men , 3 women and 1 child selected from the given group?
Options:
A)657 ways
B)600 ways
C)345 ways
D)876 ways
E)415 ways
Rationale: Two men, three women and one child can be selected in ⁴C₂ * ⁶C₃ * ⁵C₁ ways
= (4 * 3)/(2 * 1) * (6 * 5 * 4)/(3 * 2) * 5
= 600 ways.
Answer: B
Answer: B
Question: Two persons starting from the same place walk at a rate of 0.5kmph and 5.5kmph respectively. What time will they take to be 75km apart, if they walk in the same direction?
Options:
A)17 hrs
B)22 hrs
C)25 hrs
D)12 hrs
E)15 hrs
Rationale: The relative speed of the boys = 5.5kmph â€“ 0.5kmph
= 5 kmph
Distance between them is 75 km
Time= 75km / 5 kmph = 15 hrs
Answer : E.
Answer: E
Question: How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
Options:
A)388
B)277
C)500
D)2887
E)212
Rationale: Let length of tunnel is x meter
Distance = 800+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
800+x = (65/3) * 60
800+x = 20 * 65 = 1300
x = 1300 - 800 = 500 meters.Answer: C
Answer: C
Question: 28,14,15,22.5,24.5,61.25,64.25,?
Options:
A)224.875
B)234.875
C)244.875
D)254.875
E)264.875
Rationale: 28*0.5=14
15*1.5=22.5
24.5*2.5=61.25
64.25*3.5=224.875
ANSWER:A
Answer: A
Question: If 12 boys meet at a reunion and each boy shakes hands exactly once with each of the others, then what is the total number of handshakes
Options:
A)41
B)42
C)43
D)66
E)45
Rationale: n(n-1)/2 =12*11/2
=66
ANSWER:D
Answer: D
Question: For 600 km journey it will take 8hrs, if 120 km is done by bus and the rest by car. It takes 20 minutes more, if 200 km is done by busand the rest by car. The ratio of the speed of the train to that of the cars is?
Options:
A)1 : 3
B)3 : 4
C)2 : 5
D)3 : 7
E)4 : 9
Rationale: Let the speed of the train be x km/hr and that of the car be y km/hr.
Then, 120 + 480 = 8 1 + 4 = 1 ....(i)
x y x y 15
And, 200 + 400 = 25 1 + 2 = 1 ....(ii)
x y 3 x y 24
Solving (i) and (ii), we get: x = 60 and y = 80.
Ratio of speeds = 60 : 80 = 3 : 4.
B
Answer: B
Question: Which of the following lines is perpendicular to y = − 2x + 3 and has the same y-intercept as y = 2x − 3?
Options:
A)y = -1/2*x + 3
B)y = 1/2*x - 3
C)y = 1/2*x + 3
D)y = 2x + 3
E)y = 2x − 3
Rationale: Slope of y = − 2x + 3 is -2.
Product of slope of Perpendicular lines is always -1. Therefor slope of a line perpendicular to the above line is 1/2
1/2*-2 = -1
General equation of a line perpendicular to y = − 2x + 3 is y = 1/2x + k where is the k is the y intercept.
y-intercept of y = 2x − 3 is -3
Therefore equation of the required line is
y = 1/2 x - 3
Answer B
Answer: B
Question: Joe’s average (arithmetic mean) test score across 4 equally weighted tests was 45. He was allowed to drop his lowest score. After doing so, his average test score improved to 50. What is the lowest test score that was dropped?
Options:
A)20
B)30
C)55
D)65
E)80
Rationale: The arithmetic mean of 4 equally weighted tests was 45. So what we can assume is that we have 4 test scores, each 45.
He dropped his lowest score and the avg went to 50. This means that the lowest score was not 45 and other three scores had given the lowest score 5 each to make it up to 45 too. When the lowest score was removed, the other 3 scores got their 5 back. So the lowest score was 3 *5 = 15 less than 45.
So the lowest score = 45 - 15 = 30
Answer (B)
Answer: B
Question: Joe has a total of $200 in his two pockets. He takes one fourth of the
money in his left pocket and puts it in his right pocket. He then takes
$20 from his left pocket and puts it in his right pocket. If he now has
an equal amount of money in each pocket, then how much money did he
originally have in his left pocket?
Options:
A)$120
B)$130
C)$140
D)$150
E)$160
Rationale: Joe had $100 in his left and $100 in his right pocket at the end. So, he had $120
in his left pocket (and $80 in his right pocket) before moving $20 from his left to his
right pocket. Thus, he had $160 in his left pocket originally (solve x − x/4 = 120).
correct answer E
Answer: E
Question: In a 3 x 3 grid, comprising 9 tiles can be painted in red or blue. When tile is rotated by 180 degrees, there is no difference which can be spotted. How many such possibilities are there?
Options:
A)22
B)32
C)771
D)99
E)77
Rationale: This grid even rotated 180 degrees the relative positions of the tiles do not change. So we paint tile number 1's with red or blue (only one color should be used) , 2's with red or blue.....tile 5 red or blue. Then total possibilities are 2525 = 32
Answer:B
Answer: B
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
Options:
A)32
B)50
C)99
D)77
E)51
Rationale: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x
= 50 km/hr.
Answer: B
Answer: B
Question: A store owner estimates that the average price of type A products will increase by 25% next year and that the price of type B products will increase by 10% next year. This year, the total amount paid for type A products was $4500 and the total price paid for type B products was $8300. 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?
Options:
A)$14,755
B)$15,325
C)$16,000
D)$16,225
E)$17,155
Rationale: cost of type A products next year = 1.25 * 4500 = 5625
cost of type B products next year = 1.1 * 8300 = 9130
total 5625 + 9130 = 14755
ANSWER:A
Answer: A
Question: How many pages the book have, if total 294 digits are used to form the page numbers?
Options:
A)134 pages
B)136 pages
C)137 pages
D)138 pages
E)139 pages
Rationale: First 9 pages .. 9 digits
next 90 pages .. 180 digits
next 35 pages ... 105 digits
----------------------
Total ...134 pages ...300 digits
ANSWER:A
Answer: A
Question: Lilly has 10 fish and Rosy has 9 fish. In total, how many fish do they have in all?
Options:
A)16
B)17
C)18
D)19
E)20
Rationale: 10+9=19
The answer is D.
Answer: D
Question: The average (arithmetic mean) of four numbers is 7x + 6. If one of the numbers is x, what is the average of the other three numbers?
Options:
A)9x + 8
B)3x + 3
C)5x + 1
D)5x + 4
E)15x + 12
Rationale: If the average of four numbers is 7x + 3, then the sum of all four numbers if 4 * (7x + 6) = 28x + 24. If one of the numbers is x, then the average of the remaining three numbers would be: (28x + 24 - x)/3 = (27x + 24)/3 = 9x + 8.
Answer is A.
Answer: A
Question: If n is an integer and 5^n > 4,000,000, what is the least possible value of n?
Options:
A)7
B)8
C)9
D)10
E)11
Rationale: When you separate the 4000000 into factors of 5 and 2 you get - > 10^6 x 2^2 = 5^6 x 2^8
2 to the ^ 8 = 256 so its 256 x 5^6
that means 5^6 x 5^x must be greater
5^x > 256
5^1=5
5^2=25
5^3= 125
5^4= 625 - > so x must be at least 4
5^(6+4)= 5^10
ANSWER:D
Answer: D
Question: If two sides of a triangle have lengths 6 and 10, which of the following could be the perimeter of the triangle?
I. 10
II. 15
III. 25
Options:
A)I only
B)II only
C)II and III only
D)I, II, and III
E)none
Rationale: The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.
Therefore:
(10-6) < {third side} < (10+6).
4< {third side} < 16.
Perimeter = {third side} + 4 + 16= {third side} + 20.
24 < {perimeter} < 36
Answer: E.
Answer: E
Question: x and y are positive integers. If xy + 2x is odd, then which of the following must be even?
Options:
A)x
B)y +2
C)x + y
D)xy − x
E)x^2 − y
Rationale: Given that xy + 2x is odd, which means x(y+2) is odd.
Product of two nos. will be odd only if both the nos. are odd.
Hence x is odd, y+2 is also odd.
y+2 is even. Answer will be B.
Answer: B
Question: A man swims downstream 30 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water?
Options:
A)7
B)8
C)6
D)4
E)2
Rationale: 30 --- 3 DS = 10
? ---- 1
18 ---- 3 US = 6
? ---- 1 M = ?
M = (10 + 6)/2 = 8
Answer: B
Answer: B
Question: Two trains each 475 m long are running in opposite directions on parallel tracks. Their speeds are 55 km/hr and 40 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
Options:
A)77 sec
B)66 sec
C)48 sec
D)36 sec
E)45 sec
Rationale: Relative speed = 55+40 = 95 km/hr.
95 * 5/18 = 475/18 m/sec.
Distance covered = 475 + 475 = 950 m.
Required time = 950 * 18/475 = 36 sec.
Answer: D
Answer: D
Question: Present ages of Sameer and Anand are in the ratio of
5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?
Options:
A)24
B)27
C)40
D)cannot be determined
E)None
Rationale: Solution
Let the present ages of sameer and anand be 5x years and 4x years respectively.
Then	5x+3/4x+3=11/9
≈9(5x+3)=11(4x+3)
x=6.
Anands's present age	= 4x
=24 years.
Answer A
Answer: A
Question: If 15 toys cost Rs, 234, what do 35 toys cost?
Options:
A)Rs.546
B)Rs.754
C)Rs.590
D)Rs.520
E)Rs.600
Rationale: . Let the required cost be Rs. x. Then,
More toys, More cost	(Direct Proportion)
.	15 : 35 : : 234 : x  (15 x x) = (35 x 234)  x=(35 X 234)/15 =546
Hence, the cost of 35 toys is Rs. 546.
Answer is A
Answer: A
Question: A number increased by 40% gives 700. The number is
Options:
A)250
B)500
C)450
D)500
E)520
Rationale: Formula = TOTAL=100% ,INCRESE = "+" DECREASE= "-"
A number means = 100 %
That same number increased by 40 % = 140 %
140 % ------->700 (140× 5 = 700)
100 % -------> 700 (100 × 5 = 500)
B)
Answer: B
Question: A train crosses a platform of 110 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
Options:
A)150
B)88
C)77
D)310
E)52
Rationale: Length of the train be â€˜Xâ€™
X + 110/15 = X + 250/20
4X + 440 = 3X + 750
X = 310m
Answer: D
Answer: D
Question: The smallest 3 digit prime number is:
Options:
A)103
B)106
C)107
D)112
E)101
Rationale: A
103
The smallest 3-digit number is 100, which is divisible by 2.
100 is not a prime number.
√101< 11 and 101 is not divisible by any of the prime numbers 2, 3, 5, 7, 11.
101 is a prime number.
Hence 101 is the smallest 3-digit prime number.
Answer: A
Question: Walking at 5/6 of its usual speed, a train is 10 minutes too late. What is usual time to cover the journey?
Options:
A)70 minutes
B)2 hours
C)2/3 hours
D)5/6 hours
E)85 minutes
Rationale: et Speed be S and Time to cover the journey be T
S * T = D (distance of journey) --- 1
now as per the question stem we have
(5/6)S * (T + 10) = D ----2
Equating Value of D from (1) in (2) we get T = 50mins or 5/6hrs .
Answer: D
Answer: D
Question: The difference between the heights of two trees is 20 cm. Ten years ago, the taller one was thrice as taller as the shorter one. The present height of the taller tree is
Options:
A)300cm
B)15cm
C)20cm
D)10cm
E)40cm
Rationale: Let their heights of x cm and (x + 20) cm respectively.
Then, (x + 20) - 10 = 3(x - 10)
⇔ x +10= 3x - 30
⇔ 2x = 40
∴ Present height of taller tree = (20 + 10)
= 30cm.
Answer :30cm
Answer: A
Question: The set X consists of the following terms: {4,44,444,4444,.....}, where the nth term has n 4's in it for example 10th term is 4444444444. What is the hundreds digit of the sum of the first 75 terms of set X?
Options:
A)0
B)2
C)4
D)6
E)8
Rationale: 75*4 + 74*40 + 73*400 = 300 + 2960 + 29200 = 32460
The hundreds digit is 4.
The answer is C.
Answer: C
Question: A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:
Options:
A)5kmph
B)7kmph
C)6kmph
D)4kmph
E)4.5kmph
Rationale: Let the speed of the stream be x km/hr. Then,
Speed downstream = (15 + x) km/hr,
Speed upstream = (15 - x) km/hr.
30/(15+x) + 30/(15-x) = 4.5
9 * x^2 = 225
x^2 = 25
x = 5 kmph
Ans- A
Answer: A
Question: A searchlight on top of the watch-tower makes 3 revolutions per minute. What is the probability that a man appearing near the tower will stay in the dark for at least 15 seconds?
Options:
A)1/4
B)1/3
C)1/2
D)2/3
E)3/4
Rationale: 3 revolutions per minute = 1 revolution every 20 seconds
So no matter what anybody appearing at the tower cannot stay in the dark for more than 20 seconds. This will be our total number of possibilities i.e the denominator.
P(man in dark for at least 15 seconds) = 1 - P (man in dark for max of 15 seconds) = 1 - 15/20 = 1 - 3/4 = 1/4
or the other way would be:
P(man in dark for at least 5 seconds) is like saying he can be in dark for 5,6,7...all the way to 20 seconds because that is the max. In this approach it would be 5/20 seconds = 1/4.
Answer is A
Answer: A
Question: A ship went on a voyage after 180 miles a plane statrted with 10 times speed that of the ship.Find the distance when they meet from starting point.
Options:
A)200 miles
B)179 miles
C)146 miles
D)149 miles
E)143 miles
Rationale: Let the distance traveled by the ship after 180 miles to meet the plane be 'd'
Speed of the ship be 'x' and speed of the ship be '10x'
Time taken by plane to travel 180+d dist. = time take by ship for 'd' dist.
(180+d)/10x=d/x
180+d=10d
d=180/9=20.
So the distance traveled when they meet from starting point=180+d=200 miles
ANSWER:A
Answer: A
Question: A polygon has 230 diagonals. How many sides does it have?
Self made
Options:
A) 22
B) 23
C) 24
D) 25
E) 26
Rationale: The best way to solve this problem is to use the formula: An n sided polygon can have n*(n - 3)/2 diagonals
n*(n - 3)/2 = 230
n*(n - 3) = 460
Substitute n from the answer choices. n = 23
Answer: B
Answer: B
Question: If x : y = 1 : 3, find the value of (2x + 3y) : (5x – y)
Options:
A)11:3
B)11:2
C)3:2
D)7:2
E)9:5
Rationale: Explanation:
Given: x/y = 1/3
(2x + 3y)/(3x – y)
= (2*1 + 3*3) : (5*1 – 3)
= 11:2
ANSWER: B
Answer: B
Question: Stacy and Helon are 30 miles apart and walk towards each other along the same route. Stacy walks at constant rate that is 1 mile per hour faster than helon's constant rate of 5 miles/hour. If Helon starts her journey 24 minutes after Stacy, how far from the original destination has Helon walked when the two meet?
Options:
A)5 miles
B)8 miles
C)6 miles
D)13 miles
E)12 miles
Rationale: Original distance between S and H = 30 miles.
Speed of S = 5+1 = 6 mph, Speed of H = 5 mph.
Time traveled by H = t hours ---> time traveled by S = t+24/60 = t+2/5 hours.
Now, the total distances traveled by S and H = 20 miles ---> 6*(t+2/5)+5*t=30 ---> t= 138/55 hours. Thus H has traveled for 138/55 hours giving you a total distance for H = 5*138/55 = 13 miles.
D is thus the correct answer.
P.S.: based on the wording of the question, you should calculatehow far from theoriginal destination has Heather walkedwhen the two meet. 'Original destination' for H does not make any sense. Original destination for H was situated at a distance of 20 miles.
Answer: D
Question: 9873 + x = 13200, then x is ?
Options:
A)3327
B)3237
C)3337
D)2337
E)None of these
Rationale: Answer
x = 13200 - 9873 = 3327
Option: A
Answer: A