divelab/Sys2Bench huggingface dataset:
Question: A train crosses a bridge of length 1500 m in 70 seconds and a lamp post on the bridge in 20 seconds. What is the length of the train in metres?
Options:
A)375 m
B)750 m
C)250 m
D)600 m
E)300 m
Rationale: Let Length of Train = L
Case-1: Distance = 1500+L (While crossing the bridge)
Time = 70 Seconds
i.e. Speed = Distance / Time = (1500+L)/70
Case-2: Distance = L (While passing the lamp post)
Time = 20 Seconds
i.e. Speed = Distance / Time = (L)/20
But Since speed has to be same in both cases so
(1500+L)/70 = (L)/20
i.e. 1500 + L = 3.5 L
i.e. 2.5L = 1500
i.e. L = 600
Answer: option D
Answer: D
Question: A train passes a station platform in 55 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Options:
A)180 m
B)525 m
C)240 m
D)320 m
E)None
Rationale: Sol.
Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x metres.
Then, x + 300 / 55 = 15 ⇔ x + 300 = 825 ⇔ x = 525 m.
Answer B
Answer: B
Question: The salary of a typist was at first raised by 10% and then the same was reduced by 5%. If he presently draws Rs.1045.What was his original salary?
Options:
A)28788
B)2788
C)1000
D)2877
E)28881
Rationale: X * (110/100) * (95/100) = 1045
X * (11/10) * (1/100) = 11
X = 1000
Answer: C
Answer: C
Question: 1 + 1 ÷ {1 + 1 ÷ (1 + 1/3)} = ?
Options:
A)1 1/3
B)1 4/7
C)1 1/8
D)1 2/3
E)None
Rationale: Answer
Given expression = 1 + 1 ÷ {1 + 1 ÷ (1 + 1/3)}
= 1 + 1 ÷ { 1 + 1 ÷ 4/3}
= 1 + 1 ÷ { 1 + 3/4}
= 1 + 1 ÷ 7/4
= 1 + 1 x 4/7
= 1 + 4/7
= 1 4/7
Correct Option: B
Answer: B
Question: If the sum of three consecutive even numbers is 48 more than the average of these numbers, then the largest of these numbers is?
Options:
A)20
B)24
C)22
D)26
E)27
Rationale: Explanation:
Let the smallest of these number be x. The other two numbers are (x + 2) and (x + 4).
x + (x + 2) + (x + 4) = (X + (X+2) + (x+4)) / 3 + 48
3x + 3*(x + 2) + 3*(x + 4) = x + (x + 2) + (x + 4) + 144
9x + 18 = 3x + 150
6x = 132
x = 22
Therefore, the largest number is 26.
ANSWER D
Answer: D
Question: A basketball player succeeds with 60% of her free throws. If she has a set of three free throws, what is the probability that she succeeds at least once?
Options:
A)0.856
B)0.872
C)0.936
D)0.952
E)0.985
Rationale: P(missing all 3 free throws) = 0.4^3 = 0.064
P(succeeding at least once) = 1 - 0.064 = 0.936
The answer is C.
Answer: C
Question: A five-character password consists of three letter of the alphabet and two different digits between 0 and 9, inclusive. The letter must appear as the second or third character of the password. How many different passwords are possible?
Options:
A)225,040
B)18,443,720
C)26,337,000
D)28,337,440
E)28,473,120
Rationale: 5 character password: DLDLL
First digit can be chosen in 10 ways.
The letter can be chosen in 26 ways.
Next digit can be chosen in 9 ways.
The letter can be chosen in 25 ways.
The letter can be chosen in 24 ways.
This gives us 10*26*9*25*24ways
Now, the letter can also be DDLD so there will be another 10*9*26*25*24 ways
Total = 10*26*9*25*24*2 = 28,473,120 ways
E
Answer: E
Question: What is the least number of squares tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad?
Options:
A)814
B)820
C)842
D)844
E)848
Rationale: Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm.
Area of each tile = (41 x 41) cm2.
Required number of tiles = (1517×902)/ (41×41) = 814
answer :A
Answer: A
Question: The sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter?
Options:
A)91.5 cm
B)11.5 cm
C)91.8 cm
D)92.5 cm
E)99.5 cm
Rationale: Perimeter of the sector = length of the arc + 2(radius)
= (135/360 * 2 * 22/7 * 21) + 2(21)
= 49.5 + 42
= 91.5 cm
Answer:A
Answer: A
Question: A jogger is running at 9 kmph alongside a railway track in 240 meters ahead of the engine of a 120 meters long train . The train is running at 45 kmph in the same direction. how much time does it take for the train to pass the jogger?
Options:
A)46 seconds
B)36 seconds
C)38 seconds
D)26 seconds
E)18 seconds
Rationale: Distance = 240+ 120 = 360 m
speed = 36 km/hr = 36×10/36 = 10 m/s
Time = distance/speed = 360/10 = 36 seconds
answer : B
Answer: B
Question: What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 56?
Options:
A)3944
B)920
C)3808
D)6928
E)3729
Rationale: Explanation:
Let the side of the square plot be a ft.
a2 = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 * 56 = Rs. 3808.
Answer: Option C
Answer: C
Question: What is the remainder when (55)(57) is divided by 7?
Options:
A)1
B)2
C)3
D)5
E)6
Rationale: (55)(57) = (56-1)(56+1) = 56^2 - 1 which is 1 less than a multiple of 7.
Then the remainder will be 6.
The answer is E.
Answer: E
Question: After decreasing 24% in the price of an article costs Rs.684. Find the actual cost of an article?
Options:
A)218
B)777
C)900
D)2688
E)1991
Rationale: CP* (76/100) = 684
CP= 9 * 100 => CP = 900
Answer: C
Answer: C
Question: A man is 36 years older than his son. In THREE years, his age will be THRICE the age of his son. The present age of this son is
Options:
A)28 years
B)22 years
C)18 years
D)16 years
E)15 years
Rationale: Let's Son age is x, then Father age is x+36.
=> 3(x+3) = (x+36+3)
=> 3x+9 = x+39
=> 2x = 30 years = 15 YEARS
Answer: E
Answer: E
Question: (3 x 10^5) + (2 x 10^3) + (4 x 10^2) =
Options:
A)302400
B)32400
C)30240
D)3240
E)324
Rationale: When you multiply a number by 10 you just add a zero
=> 3 x 10^5 => add 5 zeros => 3 x 10^5 = 300000
=>2 x 10^3 = 2000
=> 4 x 10^2 = 400
=>3 x 10^5 + 2 x 10^3 + 4 x 10^2 = 300000 + 2000 + 400 = 302400
=> answer is A ( 302400)
Answer: A
Question: Ravi, Gagan and Nitin are running a business firm in partnership. What is Gagan’s share in the profit earned by them?
I.Ravi, Gagan and Nitin invested the amounts in the ratio of 2 : 4 : 7.
II.Nitin’s share in the profit is Rs. 8750.
Options:
A)I alone sufficient while II alone not sufficient to answer
B)II alone sufficient while I alone not sufficient to answer
C)Either I or II alone sufficient to answer
D)Both I and II are not sufficient to answer
E)Both I and II are necessary to answer
Rationale: Explanation:
Let us name Ravi, Gagan and Nitin by R, G and N respectively.
I. R : G : N = 2 : 4 : 7.
II. N = 8750..
From I and II, we get:
When N = 7, then G = 4.
When N = 8750, then G = ( 4/7 x 8750) = 5000.
Thus, both I and II are needed to get the answer.
answer is (E).
Answer: E
Question: There are C girls in a class, and their average height is M inches. In the same class, there are D boys with an average height of N inches. What is the average height of all the students in the class?
Options:
A)(X + Y)/(M + N)
B)(M + N)/(X + Y)
C)(XM + YN)/(M + N)
D)(CM + DN)/(C+ D)
E)MN/XY
Rationale: Total height = CM+DN
No of students = C+D
Avg = (CM+DN)/(C+D)
Answer is D
Answer: D
Question: When x is multiplied by 3, the result is 10 more than the result of subtracting x from 26. What is the value of x?
Options:
A)-4
B)9
C)11
D)13
E)22
Rationale: The equation that can be formed is:
3x-10=26-x
or, 4x=36
or, x=9.
B answer.
Answer: B
Question: A boat can move upstream at 50 kmph and downstream at 100 kmph, then the speed of the current is?
Options:
A)10
B)45
C)25
D)40
E)20
Rationale: US = 50
DS = 100
M = (100- 50)/2
= 25
Answer:C
Answer: C
Question: A person takes 5hrs 45 min in walking to a place and ridingback. He would have gained 2hrs 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)7 hours 45 min
E)8 hours
Rationale: ----------------------------------------------------------------
Solution 1
----------------------------------------------------------------
Given that time taken for riding both ways will be 2 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 - 2 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 + 2 hours = 7 hours 45 min
D
Answer: D
Question: The price of the sugar rise by 25%. If a family wants to keep their expenses on sugar the same as earlier, the family will have to decrease its consumption of sugar by
Options:
A)25%
B)20%
C)80%
D)75%
E)None
Rationale: Solution: Let the initial expenses on Sugar was Rs. 100.
Now, Price of Sugar rises 25%. So, to buy same amount of Sugar, they need to expense,
= (100 + 25% of 100) = Rs. 125.
But, They want to keep expenses on Sugar, so they have to cut Rs. 25 in the expenses to keep it to Rs. 100.
Now, % decrease in Consumption,
(25/125)*100 = 20%.
Mind Calculation Method;
100-----25%↑---→125------X%↓---→100.
Here, X = (25/125)*100 = 20%.
Answer: Option B
Answer: B
Question: How many integers between 300 and 1100 are there such that their unit digit is odd?
Options:
A)200
B)300
C)400
D)500
E)600
Rationale: There are 800 numbers from 301 to 1100 (inclusive).
Half of the numbers are odd, so there are 400 odd numbers.
The answer is C.
Answer: C
Question: At 1:00 PM, Train X departed from Station A on the road to Station B. At 1:50 PM, Train Y departed Station B on the same road for Station A. If Station A and Station B are p miles apart, Train X’s speed is r miles per hour, and Train Y’s speed is s miles per hour, how many hours after 1:00 PM, in terms of p, r, and s, do the two trains pass each other?
Options:
A)0.5 + (p - 0.5s)/(r + s)
B)(p - 0.5s)/(r + s)
C)0.5 + (p - 0.5r)/r
D)(p - 0.5r)/(r + s)
E)0.5 + (p - 0.5r)/(r + s)
Rationale: The distance A is going to cover between 1:00 and 1:30
= .5r
now the distance between the two trains = (p-.5r)
the relative velocity = (r-(-s)) = r+s
From 1:30, time is going to take when they meet = (p-.5r)/(r+s)
số thẻ ans is .5+((p-.5r)/(r+s)) [.5 is added for the time from 1:00 tờ 1:30]
ans is A
Answer: A
Question: On dividing number by 56, we get 29 as remainder. On dividing the same number by 8, what will be the remainder?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: Let x be the number and y be the quotient.
Then, x = 357 * y + 39
= (17 * 21 * y) + (17 * 2) + 5
= 17 * (21y + 2) + 5.
Required remainder = 5.
ANSWER:B
Answer: B
Question: In 10 years, A will be twice as old as B was 10 years ago. If A is now 7 years older than B the present age of B is
Options:
A)37
B)38
C)39
D)40
E)41
Rationale: let present age of A be a and B be b
a+10 = 2*(b-10)
=> 2b-a = 30 ......(i)
a = b+7
=>2b-b-7 = 30
b=37
so the present age of b is 37 years
ANSWER:A
Answer: A
Question: In a class of 60 students 41 are taking French, 22 are taking German. Of the students taking French or German, 9 are taking both courses. How many students are not enrolled in either course?
Options:
A)6
B)15
C)24
D)33
E)54
Rationale: Formula for calculating two overlapping sets:
A + B - both + NOT(A or B) = Total
so in our task we have equation:
41 (french) + 22 (german) - 9 (both) + NOT = 60
54 + NOT = 60
NOT = 60 - 54 = 6
So answer is A
Answer: A
Question: Which of the following equations is NOT equivalent to 4u^2 = y^2 - 9 ?
Options:
A) 4u^2 + 9 = y^2
B) 4u^2 - y^2 = -9
C) 4u^2= (y + 3)(y - 3)
D) 2u = y - 3
E)u^2 = (y^2-9)/4
Rationale: 4X^2 = Y^2 - 9
The basic rule when dealing with equations is that you can do ANYTHING to both sides of an equation as long as you do it EQUALLY to BOTH sides. Everything gets a bit more complex when you're dealing with variables in the denominator of a fraction and/or inequalities, but neither of those subjects is a factor in this prompt.
Looking at Answer D, we have....
2u = Y - 3
While you COULD take the square root of both sides of the original equation, it's important to note that the square root of Y^2 - 9 is NOT (Y-3).
Y^2 - 9 can be factored into (Y-3)(Y+3), but neither of these parentheses is the square root of Y^2 - 9.
You can see the proof when you square either of the two parentheses:
(Y-3)^2 = Y^2 - 6u + 9
(Y+3)^2 = Y^2 + 6u + 9
Thus, D is NOT equivalent to the prompt.
Answer: D
Question: A used cars salesman receives an annual bonus if he meets a certain quota. This year, the salesman has so far sold 1/5 of last year's quota. If this year's quota is reduced by 25 percent from last year, the quantity that he still needs to sell this year in order to receive the annual bonus is what fraction of the preceding year's car quota?
Options:
A)4/15
B)4/20
C)3/4
D)11/20
E)9/20
Rationale: Let Last year Quota be = 100x
This year Quota = 100x - 25%of100x = 75x
Salesman has so far sold = 1/5(100x) = 20x
Quantity still need to be sold = 75 x - 20x = 55x
Question :: What fraction of 100x is 55x = 55x/100x = 11/20.
Ans:: D
Answer: D
Question: If the average marks of three batches of 56, 60 and 45 students respectively is 50, 55, 60, then the
average marks of all the students is
Options:
A)54.48
B)54.68
C)54.65
D)54.58
E)None of these
Rationale: Explanation:
(56Ã—50)+(60Ã—55)+(45Ã—60)/(56+60+46)=54.65
Answer: Option C
Answer: C
Question: A toy store's revenue in November was 3/5 of its revenue in December and its revenue in January was 3/4 of its revenue in November, then the store's revenue in December was how many times the average (arithmetic mean) of its revenues in November and January?
Options:
A) 1/4
B) 1/2
C) 2/3
D) 2
E) 4
Rationale: Let Dec rev =100
Then Nov rev is 3/5 (100) => 60
Therefore Jan rev = 3/4(Nov rev) = 3/4(60) => 45
Hence Dec rev = x*( Nov rev+Jan rev)/2
100 = x* (60+45)/2
x = 100/52.5 => 1.90=2
Ans) D
Answer: D
Question: The average age of three boys is 20 years and their ages are in the proportion 2 : 3 : 5. The age of the youngest boy is:
Options:
A)21 years
B)18 years
C)15 years
D)9 years
E)None of these
Rationale: Total age of 3 boys = (20 Ã— 3) years = 60 years. Ratio of their ages = 2 : 3 : 3.
Age of the youngest = (60 Ã— 3â„10) years = 18 years.
Answer B
Answer: B
Question: Each student at a certain business school is assigned a 3-digit student identification number. The first digit of the identification number cannot be zero, and the last digit of the identification number must be prime. How many different student identification numbers can the school create?
Options:
A)9,000
B)3,600
C)2,700
D)360
E)1,944
Rationale: The identification number is of the form _ _ _ _
1. First digit cannot be 0
2. Middle digits can be anything
3. Last digit has to be prime - 2, 3, 5, 7
We can have the following number of possibilities for each space
__ __ __ __
9 10 4
Total cases = 360
Answer : D
Answer: D
Question: The radius of the two circular fields is in the ratio 3: 5 the area of the first field is what percent less than the area of the second?
Options:
A)84%
B)24%
C)54%
D)64%
E)34%
Rationale: r = 3 πr2 = 9
r = 5 πr2 = 25
25 π – 16 π
100 ---- ? => 64%
Answer: D
Answer: D
Question: A train 125 m long passes a man, running at 15 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
Options:
A)40
B)50
C)60
D)79
E)80
Rationale: Speed of the train relative to man = 125/10 = 25/2 m/sec.
= 25/2 * 18/5 = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 15) km/hr.
x - 15 = 45 => x = 60 km/hr.
Answer: Option C
Answer: C
Question: A train moves at average speed of 40kmph reaches its destination on time.what its average speed becomes 35kmph , then it reaches its destination 15 late. find the length of the journey?
Options:
A)70km
B)85km
C)38km
D)14km
E)1km
Rationale: Difference between timings=15 mis=1/4hr
let the length of the journey be x km.
then x/35-x/40=1/4
8x-7x=70
x=70km
Answer (A)
Answer: A
Question: In a sports club with 30 members, 16 play badminton and 19 play tennis and 2 do not play either. How many members play both badminton and tennis?
Options:
A)7
B)8
C)9
D)10
E)11
Rationale: Let x play both badminton and tennis so 16-x play only badminton and 19-x play only tennis. 2 play none and there are total 30 students. hence,
(16-x)+(19-x)+x+2=30
37-2x+x=30
37-x=30
x=7
So 7 members play both badminton and tennis.
A
Answer: A
Question: If (x/y)=(8/5), find the value (x^2+y^2)/(x^2-y^2)
Options:
A)89/39
B)59/11
C)51/77
D)41/11
E)None of them
Rationale: = (x^2+y^2)/(x^2-y^2) = ( x^2 /y^2+ 1)/ ( x^2 /y^2-1) = [(8/5)^2+1] / [(8/5)^2-1]
= [(64/25)+1] / [(64/25)-1] = 89/39
Answer is A.
Answer: A
Question: Marginal cost is the cost of increasing the quantity produced (or purchased) by one unit. If the fixed cost for n products is $10,000 and the marginal cost is $200, and the total cost is $40,000, what is the value of n?
Options:
A) 30
B) 50
C) 60
D) 80
E) 150
Rationale: Total cost for n products = fixed cost for n products + n*marginal cost --> $40,000 = $10,000 + n * $200 --> n = 150.
Answer: E.
Answer: E
Question: A person can row at 10 kmph and still water. He takes 5 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 2 kmph?
Options:
A)32 km
B)25 km
C)28 km
D)24 km
E)20 km
Rationale: Let the distance between A and B be x km.
Total time = x/(10 + 2) + x/(10 - 2) = 5
=> x/12 + x/8 = 5 => (2x + 3x)/24 = 5 => x = 24 km.
ANSWER:D
Answer: D
Question: If a certain sample of data has a mean of 25.0 and the value 36.0 is more than 2.5 standard deviations from the mean, which of the following could be the standard deviation of the sample
Options:
A)3.75
B)3.5
C)3.25
D)3.0
E)4.35
Rationale: 36.0 is more than 2.5 standard deviations from 25 --> 36 > 25 + 2.5*{SD} --> 2.5*{SD} < 11 --> {SD} < 4.4. Only option E offers the standard deviation less than 4.4.
Answer: E.
Answer: E
Question: The integer x is divisible by both 15 and 25. Which of the following must be an integer?
Options:
A)x/11
B)x/75
C)x/84
D)x/36
E)x/26
Rationale: Prime factorization of 15 = 5*3
Prime factorization of 25= 5*5
LCM of 15 and 25 = 5^2 * 3 = 75
Therefore x/75 must be an integer
Answer B
Answer: B
Question: The H.C.F of 2^4*3^2*5^3*7, 2^3*3^3*5^2*7^2 and 3*5*7*11 is?
Options:
A)105
B)1155
C)2310
D)27720
E)None of these
Rationale: H.C.F= Product of lowest power of factors=3*5*7=105
Correct Option: A
Answer: A
Question: Four brothers Adam, Bill, Charles and David together contributed certain amount of money and purchased a car. The contribution made by Adam is half that of the total contribution made by the other three brothers, contribution made by Bill is one-fourth of the total contribution made by the other three brothers and the contribution made by Charles is two-third of the total contribution made by the other three brothers. If the total price of the car is $9000, find the contribution made by David.
Options:
A)$540
B)$580
C)$600
D)$660
E)$680
Rationale: Given that A:(B+C+D)= 1:2.
Hence A contributed 1/3rd of the total price.
Given B:(A+C+D)=1:4
Hence B contributed 1/5th of the total price.
Given C:(A+B+D)=2:3
Hence C contributed 2/5th of the total price.
Thus the contribution made by A,B and C= 1/3+1/5+2/5=14/15
So, the remaining 1/15th of the price is contributed by David.
Hence David's contribution= 1/15×9000=$600.
The answer is C.
Answer: C
Question: The salary of A, B, C, D, E is Rs. 8000, Rs. 5000, Rs. 16000, Rs. 7000, Rs. 9000 per month respectively, then the average salary of A, B, C, D, and E per month is
Options:
A)Rs. 7000
B)Rs. 8000
C)Rs. 8500
D)Rs. 9000
E)None
Rationale: Answer
Average salary
= 8000 + 5000 + 16000 + 7000 + 9000 / 5
= Rs. 9000
Correct Option: D
Answer: D
Question: How many words can be formed by using all letters of the word ‘COMPUTER’ ?
Options:
A)32240
B)36180
C)40320
D)45860
E)48240
Rationale: The word contains 8 different letters.
The number of permutations is 8! = 40320
The answer is C.
Answer: C
Question: A side of beef lost 35 percent of its weight in processing. If the side of beef weighed 560 pounds after processing, how many pounds did it weigh before processing?
Options:
A) 191
B) 355
C) 737
D) 861
E) 1,560
Rationale: Let weight of side of beef before processing = x
(65/100)*x = 560
=> x = (560 * 100)/65 = 861
Answer D
Answer: D
Question: In a game of 90 points, A can give B 20 points and C 25 points. then how many points can B give C in a game of 80?
Options:
A)1.71
B)6.71
C)5.71
D)7.71
E)3.71
Rationale: In a game of 90 points,A give B 20 points and c 25 points means B=70,C=65
In 70 points B give 5 since 70-65=5
In 80 points B gives=80*5/70=5.71
ANSWER:C
Answer: C
Question: In how much time will a train of length 100 m, moving at 36 kmph cross an electric pole?
Options:
A)17 sec
B)18 sec
C)19 sec
D)10 sec
E)15 sec
Rationale: Convert kmph to mps. 36 kmph = 36 * 5/18 = 10 mps.
The distance to be covered is equal to the length of the train.
Required time t = d/s
= 100/10
= 10 sec.
Answer: D
Answer: D
Question: If (10^4 * 3.456789)^9 is written as a single term, how many digits would be to the right of the decimal place?
Options:
A)6
B)12
C)18
D)32
E)48
Rationale: 3.456789^9 has 6*9 = 54 decimal places.
10^36 moves the decimal place to the right 36 places.
(10^4 * 3.456789)^9 has 54-36 = 18 digits after the decimal point.
The answer is C.
Answer: C
Question: A car drove from Town A to Town B without stopping. The car traveled the first 70 miles of its journey at an average speed of 25 miles per hour. What was the car’s average speed, in miles per hour, for the remaining 90 miles if the car’s average speed for the entire trip was 40 miles per hour?
Options:
A)28
B)48
C)50
D)55
E)75
Rationale: KAPLANOFFICIAL SOLUTION:
To solve this problem, you must remember that average speed means total distance divided by total time over an entire journey. This should not be confused with the average of the speeds. The total distance in this problem is 160 miles, but we will need to express the total time in a more complex way.
For the first 70 miles, the car traveled at 25 miles per hour. Therefore, we can say that the time this took was 70/25, because distance divided by rate equals time.
For the last 90 miles, we are trying to solve for the rate, so we can call this speed R. Thus, the time for the final 90 miles is 90/R.
If we put all of this together, knowing that the average speed over the entire journey is 40 miles per hour, we get the equation 160/(70/25 + 90/R) = 40. We can now solve for R and reach our answer.
160/(70/25 + 90/R) = 40
R = 75
75 is choice (E) and that’s our correct answer.
Answer: E
Question: A train 560 m in length crosses a telegraph post in 16 seconds. The speed of the train is?
Options:
A)126 kmph
B)77 kmph
C)54 kmph
D)71 kmph
E)88 kmph
Rationale: S = 560/16 * 18/5 = 126 kmph
Answer:A
Answer: A
Question: A certain car dealership sells economy cars, luxury cars, and sport utility vehicles. The ratio of economy to luxury cars is 6:2. The ratio of economy cars to sport utility vehicles is 5:3. What is the ratio of luxury cars to sport utility vehicles?
Options:
A)9:8
B)8:9
C)6:2
D)2:3
E)1:2
Rationale: The ratio of economy to luxury cars is 6:2 --> E:L = 6:2 = 30:10.
The ratio of economy cars to sport utility vehicles is 5:3 --> E:S = 5:3 = 30:18.
Thus, L:S = 10:18 = 5:6.
Answer: B.
Answer: B
Question: if log 5 = 0.69897, the number of digits in 5128 is
Options:
A)90
B)39
C)88
D)28
E)11
Rationale: Explanation:
log(5128) = 128log(5) = 128 × 0.69897 ≈ 89.46
ie, its characteristic = 89
Hence, number of digits in 2128 = 89+1 = 90
Answer: Option A
Answer: A
Question: Suganya and Suriya are partners in a business. Suganya invests Rs. 35,000 for 8 months and Suriya invests Rs.42,000 for 10 months. Out of a profit of Rs.31,570. Suganya's share is
Options:
A)Rs.9471
B)Rs.12,628
C)Rs.18,040
D)Rs.18,942
E)None
Rationale: Solution
Ratio of their shares	=(35000×8):(42000×10)
= 2 : 3.
Suganya's share	= Rs.(31570 ×2/5)
= Rs.12628.
Answer C
Answer: C
Question: Due to construction, the speed limit along an 5-mile section of highway is reduced from 52 miles per hour to 36 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options:
A)A) 3.12
B)B) 8
C)C) 10
D)D) 2.57
E)E) 24
Rationale: Old time in minutes to cross 5 miles stretch = 5*60/52 = 5*15/13 = 5.76
New time in minutes to cross 5 miles stretch = 5*60/36 = 5*5/3 = 8.33
Time difference = 2.57
Ans:D
Answer: D