divelab/Sys2Bench huggingface dataset:
Question: A man buys 58 pens at marked price of 46 pens from a whole seller. If he sells these pens giving a discount of 1% , what is the profit percent?
Options:
A)7.6 %
B)7.7 %
C)24.82 %
D)13.6 %
E)27.82 %
Rationale: Explanation:
Let Marked price be Re. 1 each
C.P. of 58 pens = Rs. 46
S.P. of 58 pens = 99% of Rs. 58 = Rs. 57.42
Profit % = (Profit /C.P.) x 100
Profit% = (11.42/46) x 100 = 24.82 %
ANSWER: C
Answer: C
Question: A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 2:3 and B:C = 2:5. If the total runs scored by all of them are 100, the runs scored by C are?
Options:
A)59
B)58
C)60
D)61
E)12
Rationale: A:B = 2:3
B:C = 2:5
A:B:C = 4:6:15
15/25 * 100 = 60
Answer:C
Answer: C
Question: If 0.75: x :: 5:11, then x is equal to:
Options:
A)1.12
B)1.65
C)1.2
D)1.3
E)None of these
Rationale: Explanation:
(x * 5) = (0.75 *11)
X=8.25/5 = 1.65
Answer: B
Answer: B
Question: The size of a flat-screen television is given as the length of the screen’s diagonal. How many square inches greater is the screen of a square 28-inch flat-screen television than a square 25 -inch flat-screen television?
Options:
A)79.5
B)89.3
C)85.5
D)75.4
E)72.5
Rationale: If we take a square with side length x and draw a diagonal, we get two isosceles right triangles.
If we focus on one such right triangle, we see that the legs have length x.
square 28-inch flat-screen television
The diagonal (hypotenuse) = 28
So, we can apply the Pythagorean Theorem to get x² + x² = 28²
Simplify: 2x² = 28²
Divide both sides by 2 to get: x² = 28²/2
Since the area of the square = x², we can see that the area of this square is 28²/2
square 25-inch flat-screen television
The diagonal (hypotenuse) = 25
So, we can apply the Pythagorean Theorem to get x² + x² = 25²
Simplify: 2x² = 25²
Divide both sides by 2 to get: x² = 25²/2
Since the area of the square = x², we can see that the area of this square is 25²/2
DIFFERENCE IN AREAS =28²/2-25²/2
= (28²- 25²)/2 = (784-625)/2 =159/2=79.5
A
Answer: A
Question: If the C.I. on a sum for 2 years at 12 1/2 % per annum is Rs. 510, the S.I. on the same sum at the same rate for the same period of time is?
Options:
A)Rs. 400
B)Rs. 450
C)Rs. 460
D)Rs. 480
E)Rs. 580
Rationale: Let the sum be Rs. P. Then,
[P(1 + 25/(2 * 100))2 - P] = 510
P[(9/8)2 - 1] = 510.
Sum = Rs. 1920
So, S.I. = (1920 * 25 * 2) / (2 * 100) = Rs. 480
ANSWER:D
Answer: D
Question: In how many different number of ways 6 men and 4 women can sit on a shopa which can accommodate persons?
Options:
A)200
B)210
C)90
D)250
E)270
Rationale: 10p2 = 10 X 9 = 90
C)
Answer: C
Question: Ayush was born two years after his father's marriage. His mother is five years younger than his father but 22 years older than Ayush who is 10 years old. At what age did the father get married ?
Options:
A)22years
B)23years
C)24years
D)25years
E)26years
Rationale: Explanation:
Ayush's present age = 10 years.
His mother's present age = (10 + 22) years = 32 years.
Ayush's father's present age = (32+ 5) years = 37 years.
Ayush's father's age at the time of Ayush's birth = (37 - 10) years = 27 years.
Therefore Ayush's father's age at the time of marriage = (27 - 2) years = 25 years.
Answer: D) 25 year
Answer: D
Question: Find the odd man out. 187, 264, 326, 473, 682, 781
Options:
A)187
B)326
C)781
D)682
E)473
Rationale: In all numbers except 326, the middle digit is the sum of other two digits.Answer is B
Answer: B
Question: An old priest fell on a bottom of the well of a church.
The well is 16 inches deep.
At day time, the old priest climbs 5-inches but when at dark he slip back 4 inches.
In how many days priest will come out of the well ?
Options:
A)12-days
B)14-days
C)11-days
D)19-days
E)10-days
Rationale: A
12-days
In 11-days, he will climb 11-inch and when he climbs 5 inch more, he will be out of the well :-)
Answer: A
Question: there is 6 letter d,f,g,h,r,t.then how many word of 2 letter can be form through these letters?
Options:
A)720
B)360
C)48
D)30
E)24
Rationale: it will comes like 6P2
6!/4!=(1*2*3*4*5*6)/1*2*3*4=30
answer D
Answer: D
Question: what is 5+7
Options:
A)2
B)4
C)10
D)12
E)11
Rationale: D
Answer: D
Question: If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is ?
Options:
A)1/6
B)1/2
C)1/9
D)1/5
E)1/1
Rationale: The number of exhaustive outcomes is 36.
Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2
P(E) = 1 - 1/2 = 1/2.
Answer:B
Answer: B
Question: If 233/0.233 = 23.3/x, what is the value of x
Options:
A)233
B)23.3
C)0.233
D)0.0233
E)None of these
Rationale: Explanation :
233/0.233 = 23.3/x
⇒ 233000/233 = 23.3/x
⇒ 1000 = 23.3/x
⇒ x = 23.3/1000 = 0.0233. Answer : Option D
Answer: D
Question: Four car rental agencies A, B, C and D rented a plot for parking their cars during the night. A parked 15 cars for 12 days, B parked 12 cars for 20 days, C parked 18 cars for 18 days and D parked 16 cars for 15 days. If A paid Rs. 1305 as rent for parking his cars, what is the total rent paid by all the four agencies?
Options:
A)2388
B)2778
C)1279
D)6150
E)7134
Rationale: The ratio in which the four agencies will be paying the rents = 15 * 12 : 12 * 20 : 18 * 18 : 16 * 15
= 180 : 240 : 324 : 240 = 45 : 60 : 81 : 60
Let us consider the four amounts to be 45k, 60k, 81k and 60k respectively.
The total rent paid by the four agencies = 45k + 60k + 81k + 60k= 246k
It is given that A paid Rs. 1305
45k = 1305 => k = 29
246k = 246(29) = Rs. 7134
Thus the total rent paid by all the four agencies is Rs. 7134.
Answer: E
Answer: E
Question: Latha took a loan of Rs. 2000 with simple interest for as many years as the rate of interest. If she paid Rs.180 as interest at the end of the loan period, what was the rate of interest?
Options:
A)5
B)4
C)7
D)3
E)9
Rationale: Let rate = R% and time = R years.
Then, (2000 * R * R) / 100 = 180
20R2 = 180
R2 = 9 => R = 3
Answer:D
Answer: D
Question: A four years NSC certificate was purchased for Rs. 500 with Rs. 1000 being the maturity value. Find the rate of S.I.
Options:
A)24%
B)22%
C)16%
D)25%
E)32%
Rationale: Explanation:
P = Rs. 500
SI = Rs.500
T = 4
R = ?
R = (100×SI)/PT = (100×500)/(500×4) =100/4 = 25%
Answer: Option D
Answer: D
Question: The length of a bridge in meters, which a train 90-meters long and traveling at 45 km/hr can cross in 30 seconds is?
Options:
A)145
B)215
C)265
D)285
E)375
Rationale: 45 km/h = 45000 m/3600 s = 12.5 m/s
In 30 seconds, the train can go 30(12.5) = 375 meters
Let x be the length of the bridge.
x+90 = 375 meters
x = 285 meters
The answer is D.
Answer: D
Question: If 20 typists can type 60 letters in 20 minutes, then how many letters will 30 typists working at the same rate complete in 1 hour?
Options:
A)240
B)200
C)270
D)300
E)310
Rationale: No. of letters typing by 20 typists in 20 minutes = 60
No. of letters typing by 20 typists in 60 minutes = 60*3 = 180
No. of letters typing by 30 typists in 60 minutes = 180/20*30 = 270
Answer : C
Answer: C
Question: I lost Rs 68 in two races. My loss in the second race is Rs 6 more than my lose in the first race. My friend lost Rs 4 more than me in the second race. Then what is the amount lost by my friend in the second race?
Options:
A)Rs 41
B)Rs 40
C)Rs 31
D)Rs 51
E)Rs 81
Rationale: I lost Rs 68 in two races. My loss in the second race is Rs 6 more than my lose in the first race.
so I lost Rs 31 in first race and Rs 37 in 2nd race.
My friend lost Rs 4 more than me in the second race.
My friend lost 37+4= Rs 41 in the second race.
ANSWER:A
Answer: A
Question: In an exam, Amar scored 64 percent, Bhavan scored 36 percent and Chetan 44 percent. The maximum score awarded in the exam is 600. Find the average mark scored by all the three boys?
Options:
A)384
B)826
C)207
D)269
E)288
Rationale: Average mark scored by all the three boys =
[64/100 (600) + 36/100 (600) + 44/100 (600)] / 3
= 288
Answer: E
Answer: E
Question: 1/0.08 is equal to
Options:
A)25.5
B)2.5
C)12.5
D).25
E)None of these
Rationale: Explanation:
1/0.08 = (1 * 100)/8 = 100/8 = 12.5
Option C
Answer: C
Question: T = {2, 3, 4, 5}
B = {4, 5, 6, 7, 8}
Two integers will be randomly selected from the sets above, one integer from set T and one integer from set B. What is the probability that the sum of the two integers will equal 9 ?
Options:
A) 0.15
B) 0.20
C) 0.25
D) 0.30
E) 0.33
Rationale: The total number of pairs T,B possible is 4*5=20. Out of these 20 pairs only 4 sum up to 9: (2, 7); (3, 6), (4, 5) and (5, 4). The probability thus is 4/20=0.2.
Answer: B.
Answer: B
Question: A batsman in his 12th innings makes a score of 70 and thereby increases his average by 3 runs. What is his average after the 12th innings if he had never been ‘not out’?
Options:
A)42
B)37
C)44
D)45
E)46
Rationale: Let ‘x’ be the average score after 12 th innings
⇒ 12x = 11 × (x – 3) + 70
∴ x = 37
Answer B
Answer: B
Question: A man can row upstream 10 kmph and downstream 20 kmph. Find the man rate in still water and rate of the stream.
Options:
A)0,5
B)5,5
C)15,5
D)10,5
E)None of these
Rationale: Explanation:
Please remember,
If a is rate downstream and b is rate upstream
Rate in still water = 1/2(a+b)
Rate of current = 1/2(a-b)
=> Rate in still water = 1/2(20+10) = 15 kmph
=> Rate of current = 1/2(20-10) = 5 kmph
Option C
Answer: C
Question: On an order of 5 dozen boxes of a consumer product, a retailer receives an extra dozen free. This is equivalent to allowing him a discount of?
Options:
A)16 2/6%
B)16 8/3%
C)16 2/3%
D)16 2/8%
E)16 1/3%
Rationale: Clearly, the retailer gets 1 dozen out of 6 dozens free.
Equivalent discount = 1/6 * 100 = 16 2/3%.
Answer: C
Answer: C
Question: Let ABCD be a convex quadrilateral with BA = BC and DA = DC. Let E and F be the
midpoints of BC and CD respectively, and let BF and DE intersect at G. If the area of CEGF
is 50, what is the area of ABGD?
Options:
A)100
B)200
C)300
D)400
E)500
Rationale: Let [XY Z] denote the area of a polygon XY Z.
Observe that BF and DE are two medians of 4BCD, so G is the centroid of 4BCD. Since
the medians of a triangle divide the triangle into six parts of equal area, we have
[CGF] = [CGE] =
1/2
[CEGF] = 25:
It follows that [CBD] = 6 25 = 150 and [BGD] = 2 25 = 50.
Furthermore, since BA = BC, DA = DC, and BD = BD, we have that 4ABD = 4CBD, so
[ABD] = [CBD] = 150. Finally,
[ABGD] = [ABD] + [BGD] = 150 + 50 = 200
correct answer B
Answer: B
Question: Two friends decide to get together; so they start riding bikes towards each other. They plan to meet halfway. Each is riding at 6 MPH. They live 36 miles apart. One of them has a pet carrier pigeon and it starts flying the instant the friends start traveling. The pigeon flies back and forth at 15 MPH between the 2 friends until the friends meet. How many miles does the pigeon travel?
Options:
A)54
B)66
C)80
D)45
E)96
Rationale: D
45
It takes 3 hours for the friends to meet; so the pigeon flies for 3 hours at 18 MPH = 45 miles
Answer: D
Question: What is the sum of all the multiples of 8 between 30 and 100?
Options:
A)485
B)72
C)547
D)104
E)624
Rationale: You first have to know all the multiples of 8 between 30 and 100. They are 8, 16, 24,32,40,48,56,64,72,80,88 and96. If you add all these numbers together, you get 624.
Final Answer:E
Answer: E
Question: Look at this series: 201, 202, 204, 207, ... What number should come next?
Options:
A)211
B)205
C)209
D)210
E)212
Rationale: A
Answer: A
Question: The functions f and g are defined for all the positive integers n by the following rule: f(n) is the number of perfect squares less than n and g(n) is the number of primes numbers less than n. If f(x) + g(x) = 16, then x is in the range:
Options:
A)30 < x < 36
B)30 < x < 37
C)31 < x < 37
D)31 < x < 38
E)32 < x < 38
Rationale: f(n) = number of perfect squares less than n
1,4,9,16,25,36
f(25) = 4
f(26)=f(27)=...=f(35)=f(36) = 5
f(37) = 6
g(n) = number of prime numbers less than n
2,3,5,7,11,13,17,19,23,29,31,37
g(31)=10
g(32)=g(33)=...=g(36)=g(37) = 11
g(38)=12
f(x)+g(x)=16 implies that f(x)=5 and g(x)=11.
So, x = 32,33,34,35,or36.
Answer C, 31 < x < 37.
Answer: C
Question: In how many ways can 8 different gifts be divided among four children such that each child receives exactly two gifts?
Options:
A)16^4
B)(4!)^4
C)8!/(2!)^4
D)8!/4!
E)4^16
Rationale: Total 8 different Gifts, and 4 children.
Thus any one child gets 8C2 gifts,
then the other child gets 6C2 gifts(8 total - 2 already given),
then the third one gets 4C2 gifts,
and the last child gets 2C2 gifts.
Since order in which each child gets the gift is not imp, thus, ans :
8C2 * 6C2 * 4C2 * 2C2= 8! / (2!)^4
Ans : C.
Answer: C
Question: Of 10 applicants for a job, 3 had at least 5 years of prior work experience, 4 had advanced degrees, and 2 had at least 5 years of prior work experience and advanced degrees. How many of the applicants had neither 5 years of prior work experience nor advanced degrees?
Options:
A)3
B)9
C)5
D)4
E)8
Rationale: Had advanced degrees and 5 years work experience: 2
Only had 5 years work experience: 3-2 = 1
Only had advanced degrees: 4-2 = 2
10-2-1-2=5
Answer: C
Answer: C
Question: The market value of a certain machine decreased by 25 percent of its purchase price each year. If the machine was purchased in 1982 for its market value of $8,000, what was its market value two years later?
Options:
A) $8,000
B) $5,600
C) $3,200
D) $4,000
E) $800
Rationale: D.
Market value in 1982= $ 8000
Market value in 1983 = $ 8000- ($ 8000 x 25/100) = 8000-2000= $ 6000
Market value in 1984 = Market value in 1983 - (25 % of $8000)= 6000-2000 = $4000
Answer: D
Question: The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 867 sq m, then what is the breadth of the rectangular plot?
Options:
A)16 m
B)17 m
C)87 m
D)27 m
E)34 m
Rationale: Let the breadth of the plot be b m.
Length of the plot = 3 b m
(3b)(b) = 867
3b2 = 867
b2 = 289 = 172 (b > 0)
b =17 m.
Answer: B
Answer: B
Question: Which of the following values is the greatest
Options:
A)a) 11% of 89
B)b) 22% of 78
C)c) 50% of 67
D)d) 44% of 56
E)e) 55% of 45
Rationale: Are you sure that you checked the answer key correctly? I just signed up forVeritas(haven't started yet, not until March) but I have access to the materials and the answer key I'm looking at says C
Answer: C
Question: If an average hard drive had a capacity of 0.3 TB in 2000, and average hard drive capacities double every 5 years, what will be the average hard drive capacity in 2050?
Options:
A)3072
B)512
C)768
D)1024
E)1536
Rationale: 0.3*2^10=0.3*1024=307.2
The answer is A.
Answer: A
Question: If 42.24 = k(14 + m/50), where k and m are positive integers and m < 50, then what is the value of k + m ?
Options:
A)6
B)7
C)8
D)9
E)10
Rationale: 42.24 = 14K + Km/50...we can rewrite the number as follows:
42+ 0.24= 14K + Km/50........Since K is integer, then 42=14K..........K=3
0.24=Km/50......24/100=3m/50......m=4
k+m=3+4=7
Answer: B
Answer: B
Question: A batsman scored 120 runs which included 5 boundaries and 8 sixes. What % of his total score did he make by running between the wickets
Options:
A)43.33%
B)50%
C)65%
D)70%
E)75%
Rationale: Number of runs made by running = 120 - (5 x 4 + 8 x 6)
= 120 - (68)
= 52
Now, we need to calculate 60 is what percent of 120.
=> 52/120 * 100 = 43.33 %
A
Answer: A
Question: If 11 men working 6 hours a day can do a work in 88 days. Then 6 men working 8 hours a day can do it in how many days?
Options:
A)78 days.
B)121 days.
C)49 days.
D)48 days.
E)67 days.
Rationale: B
121 days.
From the above formula i.e (m1*t1/w1) = (m2*t2/w2)
so (11*6*88/1) = (6*8*d/1)
on solving, d = 121 days.
Answer: B
Question: Last year Sandy saved 10% of her annual salary. This year, she made 10% more money than last year, and she saved 6% of her salary. The amount saved this year was what percent of the amount she saved last year?
Options:
A)66%
B)80%
C)112%
D)136%
E)148%
Rationale: Let last year's salary be x.
Last year, Sandy save 0.1x
This year, Sandy saved 0.06*1.1x = 0.066x
0.066x / 0.1x = 0.66 = 66%
The answer is A.
Answer: A
Question: Ujakar and Keshab attempted to solve a quadratic equation. Ujakar made a mistake in writing down the constant term. He ended up with the roots (4,3). Keshab made a mistake in writing down the coefficient of x. He got the roots as (4,3). What would be the exact root of the original quadratic equation ?
Options:
A)(6, 1)
B)(-3,-4)
C)( 4, 3)
D)(-4, -3)
E)None of these
Rationale: Explanation :
Equation of quadratic equation is
ax2 + bx + c = 0 .
x2 + bx + c = 0 . First roots = (4, 3)
Sum of the roots -b / a = -7 .
=> b = 7.
Product of the roots = c / a = 12.
=> c =12.
∴ Equation formed x2 – 7b + 12 = 0 ............ (i)
Another boy gets the wrong roots (2, 3).
∴ Sum of the roots = -b / a = -5.
=> b = 5.
Products of the roots = c / a = 6.
=> c = 6.
Equation formed x2 – 5b + 6 = 0 ............ (ii)
x2 + b′x + c1 = 0.
b′ = 2 + 3 .
∴ c = 6
Hence, x2 – 7x + 6 = 0.
=> x2 – 6x – x + 6 = 0.
=> x(x – 6) – 1(x – 6) = 0.
=> (x – 6)(x – 1) = 0.
∴ x = 6, 1.
Hence, the actual roots = (6, 1).
Answer : A
Answer: A
Question: The G.C.D. of 1.08, 0.36 and 0.4 is:
Options:
A)0.04
B)0.9
C)0.18
D)0.108
E)0.118
Rationale: Given numbers are 1.08, 0.36 and 0.40. H.C.F. of 108, 36 and 40 is 18,
H.C.F. of given numbers = 0.04.
Answer: Option A
Answer: A
Question: A parking space have 9 different slots. 9 cars has to arrange in 8 slots. But there are exactly 4 cars between 5 specified cars. In how many ways cars can be arranged?
Options:
A)1210
B)650
C)1500
D)1640
E)2880
Rationale: we arranged 4 specified cars in 4 slots = 4!
remaining 5 cars in 5 slots = 5!
number of ways = 4!*5! = 1440
correct option is E
Answer: E
Question: Since 2001, the standard serial numbers on a New York state license plate are 3 letters followed by 4 digits. How many different license plates are possible if letters and digits can be repeated?
Options:
A)26 × 3 × 10 × 4
B)26 × 25 × 24 × 10 × 9 × 8 × 7
C)26³ × 9 × 9 × 9 × 9
D)26 × 25 × 24 × 10 000
E)26³ × 10 000
Rationale: Solution:
3 repeated letters can be chosen as 26 * 26 * 26
4 repeated digits can be chosen as 10 * 10 * 10 * 10
Answer E
Answer: E
Question: There are some fruits in box, 1/3rd eaten by children . Then 2/5th of the remaining by men , then 2/3rd of the remaining by women . At last 4 were remaining . How many fruits were in total ?
Options:
A)45
B)30
C)28
D)26
E)91
Rationale: Sol:
If x fruits were there in total , then
x × (1 – 1/3)× (1 – 2/5) ×(1 – 2/3) = 4
x×2/3 × 3/5 × 1/3 = 30
x = 30
Answer:B
Answer: B
Question: The average age of 15 students of a class is 15 years. Out of these, the average age of 3 students is 14 years and that of the other 11 students is 16 years. The age of the 15th student is
Options:
A)9 years
B)11 years
C)14 years
D)7 years
E)25 years
Rationale: Solution
Age of the 15th student	=[15x15-(14x3+16x11)]
= (225 - 218)
= 7 years.
Answer D
Answer: D
Question: A company, Chauncy Co., has an annual travel budget of $51,000. The accounting department estimates that transportation expenses will increase 5 percent in the coming year, and nontransportation travel expenses will increase by 15 percent in the coming year. Last year, Chauncy Co. spent $19,500 on transportation-related expenses, and $35,000 on nontransportation travel expenses. If the annual travel budget does not increase this year, and if the accounting department’s estimates are correct, how far over the annual travel budget will expenses be this year?
Options:
A)Expenses will not go over the budget.
B)$500
C)$4,225
D)$9,725
E)$60,725
Rationale: annual travel budget of $51,000
Let, Transportation expenses = T = 19500
and Non-Transportation expenses = N=35000
i.e. Increased Transportation expenses = 1.05T = 20475
and Increased Non-Transportation expenses = 1.15N = 40250
Total Expense = 20475+40250 = 60725
Expense over Budget = Budget - expense = 51000-60725 = 9725
Answer: Option D
Answer: D
Question: On a certain test, Bill scored 20 more points than John, but half as many points as Sue. If the sum of the scores of the three students was 140 points, how many points did Bill receive?
Options:
A)30
B)40
C)50
D)80
E)100
Rationale: consider john's points as x
so bill's points are x +20
So sue's points are 2x +40
total of all three students is 4x +60, but this total is given as 140
x = 20
so bill's points = 20 +20 = 40
correct answer option B
Answer: B
Question: A sporting goods store ordered an equal number of white and yellow tennis balls. The tennis ball company delivered 30 extra white balls, making the ratio of white balls to yellow balls 6:5. How many tennis balls did the store originally order?
Options:
A)120
B)150
C)180
D)300
E)330
Rationale: (X+30)/(X)= 6/5
Cross multiply: 5X + 150 = 6X
X = 150
And since we originally ordered 2X balls the answer is 300.D
Answer: D
Question: Can you find a seven digit number which describes itself.
The first digit is the number of zeros in the number.
The second digit is the number of ones in the number, etc.
For example, in the number 21200, there are 2 zeros, 1 one, 2 twos, 0 threes and 0 fours.
Options:
A)4211000
B)1211000
C)5211000
D)2211000
E)3211000
Rationale: E
3211000
Answer: E
Question: A train travelling at 48 kmph completely crosses another train having half its length and travelling in opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is
Options:
A)400 m
B)450 m
C)560 m
D)600 m
E)700 m
Rationale: Explanation:
Let the length of the first train be x metres.
Then, the length of the second train is(x/2)metres.
Relative speed = (48 + 42) kmph =(90x5/18)m/sec = 25 m/sec.
[x + (x/2)]/25	= 12 or	3x/2	= 300 or x = 200.
Length of first train = 200 m.
Let the length of platform be y metres.
Speed of the first train =(48 x5/18)m/sec =	40	/3m/sec.
(200 + y) x	3/40=45
600 + 3y = 1800
y = 400 m.
ANSWER IS A
Answer: A
Question: The average of 50 numbers is 38. If two numbers namely 45 and 55 are discarded, The average of
remaining numbers is?
Options:
A)35.5
B)37.5
C)39.5
D)34.5
E)38.5
Rationale: Total of 50 numbers = 50 * 38 = 1900
Average of 48 numbers = 1900-(45+55) / 48
= 1800 / 48 = 37.5
Answer is B.
Answer: B
Question: If n is a positive integer, which of the following expressions must be even?
Options:
A)(n − 5)( n + 3)
B)(n − 6)( n + 3)
C)(n − 6)( n + 8)
D)(n − 7)( n + 5)
E)(n − 9)( n + 11)
Rationale: Whether n is even or odd, (n-6)(n+3) will have one odd factor and one even factor.
The product will be even.
The answer is B.
Answer: B
Question: Set A of 8 positive integers may have the same element and have 35. And set B of 8 positive integers must have different elements and have 35. When m and n are the greatest possible differences between 35 and other elements’ sums in set A and set B, respectively, m-n=?
Options:
A)20
B)26
C)23
D)25
E)21
Rationale: This is maximum-minimum. Hence, 35-(1+1+1+1+1+1+1)=28 and 35-(1+2+3+4+5+6+7)=7. So, 28-7=21. The correct answer is E.
Answer: E
Question: average weight of 20 boys and 15 girls in a class is 29 kg and 22 kg respectively.find the average weight of all the students in the class.
Options:
A)20 kg
B)26 kg
C)22 kg
D)24 kg
E)28 kg
Rationale: totl wght of boy's=20*29=580
simrlly girls=15*22
totl ave=(totlboywght+tolgirlwght)/tole no of boys and gils
26 kg
ANSWER:B
Answer: B
Question: A car travels a distance of 160 miles in 2 hours and 40 minutes, what is the speed of the car in miles per hour?
Options:
A)54
B)60
C)84
D)116
E)120
Rationale: Given time = 2 hours 40 mins
40 mins can be written as 40/60 hours = 2/3 hrs
total time = 2 + (2/3) = 8/3 hrs
therefore, speed = 160 /(8/30) = 60
option B
Answer: B
Question: In a certain alphabet, 9 letters contain a dot and a straight line. 24 letters contain a straight line but do not contain a dot. If that alphabet has 40 letters, all of which contain either a dot or a straight line or both, how many letters contain a dot but do not contain a straight line?
Options:
A)7
B)8
C)14
D)20
E)28
Rationale: We are told that all of the letters contain either a dot or a straight line or both, which implies that there are no letters without a dot and a line (no line/no dot box = 0).
First we find the total # of letters with lines: 9 +24 = 33;
Next, we find the total # of letters without line: 40 - 33 = 7;
Finally, we find the # of letters that contain a dot but do not contain a straight line: 7- 0 = 7.
A
Answer: A