divelab/Sys2Bench huggingface dataset:
Question: The average (arithmetic mean) of four numbers is 7x + 3. If one of the numbers is x, what is the average of the other three numbers?
Options:
A)x + 1
B)9x + 4
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 + 3) = 28x + 12. If one of the numbers is x, then the average of the remaining three numbers would be: (28x + 12 - x)/3 = (27x + 12)/3 = 9x + 4.
Answer is B.
Answer: B
Question: A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 5 days before the project is completed, in how many days total will the project be completed?
Options:
A)12
B)15
C)18
D)21
E)24
Rationale: A's rate is 1/20 of the project per day.
B's rate is 1/30 of the project per day.
The combined rate is 1/12 of the project per day.
In the last 5 days, B can do 1/6 of the project.
Thus A and B must complete 5/6 of the project, which takes 10 days.
The total number of days is 10 + 5 = 15.
The answer is B.
Answer: B
Question: In a garden, there are 10 rows and 12 columns of mango trees. The distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden. The length of the garden is?
Options:
A)12
B)27
C)24
D)29
E)11
Rationale: Each row contains 12 plants.
There are 11 gapes between the two corner trees (11 x 2) metres and 1 metre on each side is left.
Therefore Length = (22 + 2) m = 24 m.
Answer: C
Answer: C
Question: A man buys an item at Rs. 750 and sells it at the loss of 10 percent. Then what is the selling price of that item
Options:
A)Rs. 660
B)Rs. 675
C)Rs. 860
D)Rs. 960
E)None of these
Rationale: Explanation:
Here always remember, when ever x% loss,
it means S.P. = (100 - x)% of C.P
when ever x% profit,
it means S.P. = (100 + x)% of C.P
So here will be (100 - x)% of C.P.
= 90% of 750
= 90/100 * 750
= 675
Option B
Answer: B
Question: The length, breadth and height of a room are in the ratio 7 : 4 :4. If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will
Options:
A)(a) remain the same
B)(b) decrease by 13.64%
C)(c) decrease by 27.27%
D)(d) decrease by 18.75%
E)(e) decrease by 30%
Rationale: Length (L) = 7
Breadth (B) = 4
Height (H) = 4
Total Area of Walls = 2(BH + LH) = 2*(4*4 + 7*4) = 2*(16+28) = 88
Then, Finally
Length (L) = 2*7 = 14
Breadth (B) = 4/2 = 2
Height (H) = 4/2 = 2
Total Area of Walls = 2(BH + LH) = 2*(2*2 + 14*2) = 2*(4+28) = 64
% change in Area of four walls = (Final Area-Initial Area)*100 /Initial Area
i.e. % change in Area of four walls = (64-88)*100 /88=- 27.27% (Decrease)
Answer: Option C
Answer: C
Question: A boat can move upstream at 20 kmph and downstream at 40 kmph, then the speed of the current is?
Options:
A)5
B)8
C)10
D)3
E)2
Rationale: US = 20
DS = 40
M = (40- 20)/2
= 10
Answer:C
Answer: C
Question: Abel can complete a work in 10 days, Ben in 14 days and Carla in 15 days. All of them began the work together, but Abel had to leave after 2 days and Ben 3 days before the completion of the work. How long did the work last?
Options:
A)6
B)7
C)7 10/29
D)9
E)10
Rationale: Abel in the 2 days that he worked completed 1/5 of the job = 4/5 remains
Then if Ben had to leave 3 days before the completion, this means that Carla had to work alone for these 3 days in which she completed 1/5 of the job.
Now together, Ben and Carla completed the job in (1/14 + 1/15)(t) = 3/5
29/210 (t) = 3/5 ---> t = 126/29
Therefore, these 4 10/29 days worked plus the 3 days that Carla had to work by herself add to 7 10/29 days
Answer: C
Answer: C
Question: First-grade tobacco costs $30 per kilogram while second-grade tobacco costs $20 per kilogram. If a blend contains only first and second grade tobacco, what must be the percentage of second-grade tobacco so that the blend would cost $22 per kilogram?
Options:
A)20%
B)30%
C)60%
D)75%
E)80%
Rationale: Let x denote the share of the second-grade tobacco in the blend. Then the cost of a kilogram of the blend would go down as x∗20+(1−x)30=22 from where x=0.8 or 80%.
Answer: E
Answer: E
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. 20.25, the number of the member is the group is:
Options:
A)57
B)67
C)45
D)47
E)97
Rationale: Money collected =(20.25 x 100) paise = 2025 paise
numbers of members = 2025 squareroot = 45
Answer C
Answer: C
Question: If a is an integer greater than 6, which of the following must be divisible by 3?
Options:
A)a (a+5) (a-6)
B)a (a+2) (a-1)
C)a (a+3) (a-5)
D)a (a+4) (a-2)
E)a (a+1) (a-4)
Rationale: anything in the form of (a-1) (a) (a+1) is divisible by 3. in other word, a product of any 3 consecutive intevers is divisible by 3.
a (a+1) (a-4) = a (a+1) ((a-1)-3) is equivalant to (a-1) (a) (a+1)
a (a+2) (a-1) is equivalant to (a+1) missing.
a (a+3) (a-5) is equivalant to (a-1) missing and a repeating.
a (a+4) (a-2) is equivalant to odd/even consqcutive integers
a (a+5) (a-6) is equivalant to (a+1) missing and a repeating.
Answer : E
Answer: E
Question: If xy > 0, which of the following must be negative?
Options:
A)x+y
B)x-y
C)-xy
D)-x * -y
E)x/y
Rationale: x,y must both positive or both negative. so that mn > 0 is true
positive * negative = negative
Answer : C
Answer: C
Question: What is the square root of 96,721?
Options:
A)476
B)489
C)289
D)511
E)311
Rationale: 1) Checking the last digits in the answer options A, C, E are out since last digit of the square is known to be 1.
2) C = 489^2 and E = 511^2
C = (300-11)^2 and E = (300 + 11)^2
Since we need the answer less than 90000 => C is out.
Thus we have E as the ans.
Answer: E
Question: There is enough provisions for 2400 women in an army camp for 100 days. If there were 1200 men less, how long will the provision last?
Options:
A)170
B)180
C)190
D)200
E)210
Rationale: We have, M1D1 = M2D2
2400*100= 1200* D2
D2 = 2400*100/1200 = 200 days.
ANSWER:D
Answer: D
Question: Sanji and Sapna start a business investing Rs.9000 each, and after 6 months, Sapna withdraws half of her capital . How should they share the profits at the end of the 24 months?
Options:
A)4:3
B)3:2
C)15:11
D)8:5
E)5:3
Rationale: Sanji invests Rs.9000 for 24 months, but Sapna invests Rs.9000 for the first 6 months and then withdraws Rs.4500. So, the investment of Sapna for remaining 18 months is Rs.4500 only.
Sanji:Sapna
9000*24 : (9000*6) + (4500*18)
216000 : 135000
Sanji:Sapna = 8:5
Answer: D
Answer: D
Question: A father is now three times as old as his son. Five years back, he was four times as old as his son. The age of the son (in years) is
Options:
A)12
B)15
C)18
D)20
E)25
Rationale: If father's age is F and son's age is S, then
F=3S
and
F-5 = 4*(S-5)
3S-5 =4S-20
S=15
F=45 years
ANSWER:B
Answer: B
Question: Find the quantities of two types of rice to be mixed, first variety is of Rs.12 per kg and second variety is of Rs.20 per kg. to get 12kg of rice mixture worth Rs.15 per kg? (in kg)
Options:
A)3.5, 8.5
B)7, 5
C)7.5, 4.5
D)8, 4
E)8, 5
Rationale: from allegation & mixture ratio=c-m/m-d=20-15/15-12=5/3.
from the option c r=7.5/4.5=5/3
ANSWER:C
Answer: C
Question: 3 people decided to put a down payment on a car for 3500 dollars. How much money do they each have to pay, given that that they have to pay the same amount, and they cannot use any bills below $1?
Options:
A)$1166
B)$1168
C)$1166.6
D)$1167
E)None of the above
Rationale: To keep the amount exact when dividing for 3, we have to work backwards through division.
Dividing 3500 by 3 will give us 1166.66
Then by subtracting .66, we get 1166, and we multiply it by 3 to get 3498.
To get enough for the down payment, we add 3 to 3498.
Dividing the result by 3 gives us our answer.
Correct Option: D
Answer: D
Question: What is the scope including 1/51+1/52+1/53+......+1/60?
Options:
A)1/6~1/5
B)1/5~1/4
C)1/4~1/3
D)1/3~1/2
E)1/2~1
Rationale: For Maximum value : It should be less than 1/51 + 1/51 +1/51... 10 times = 10/51 ~ 1/5
For Minimum Value : It should be greater than 1/60+ 1/6+ 1/60 .. 10 times = 10/60 = 1/6.
Thus, the answer should lie between 1/6 and 1/5. Correct ans :A.
Answer: A
Question: A Cone, a hemisphere and a cylinder stand on equal bases and have the same height .Find ratio of their volumes.
Options:
A)2:1:3
B)2:1:4
C)1:2:3
D)4:1:7
E)5:1:8
Rationale: Let R be the radius of each
Height of the hemisphere = Its radius = R.
Height of each = R.
Ratio of volumes = (1/3)∏ R2 x R : (2/3)∏R3 : ∏ R2 x R = 1:2:3
ANSWER C 1:2:3
Answer: C
Question: (9^5.6x 9^10.3) ÷ 9^2.56256 = 9^?
Options:
A)11.34
B)12.34
C)13.34
D)14.34
E)15.34
Rationale: 5.6 + 10.3 = 15.9
i.e.. 15.9 - 2.56 = 13.34
so ur answer is 9^13.34
ANSWER:C
Answer: C
Question: In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 60 questions and secures 140 marks, the no of questions he attempts correctly is :
Options:
A)35
B)38
C)40
D)42
E)44
Rationale: Explanation:
Let the number of correct answers be X.
Number of incorrect answers = (60 – X).
4x – (60 – x) = 140
=> 5x = 200
=> x = 40
Answer: C
Answer: C
Question: Two trains of length 150 m and 250 m are 150 m apart. They start moving towards each other on parallel tracks, at speeds 36 kmph and 72 kmph. In how much time will the trains cross each other?
Options:
A)55/3
B)55/7
C)55/6
D)55/8
E)55/9
Rationale: Relative speed = (36 + 72)* 5/18 = 6 * 5 = 30 mps.
The time required = d/s = (150 + 150 + 250)/30
= 550/30 = 55/3 sec.
Answer: A
Answer: A
Question: In a fuel station the service costs $1.65 per car, every liter of fuel costs 0.65$. Assuming that a company owns 12 cars and that every fuel tank contains 55 liters and they are all empty, how much money total will it cost to fuel all cars?
Options:
A)320$
B)380$
C)420$
D)448.8$
E)480$
Rationale: Total Cost = ( 1.65*12 ) + ( 0.65 * 12 * 55 ) = 19.8 + 429 => 448.8
Hence answer will be (D)
Answer: D
Question: If there are 30 cans out of them one is poisoned if a person tastes very little he will die within 14 hours so if there are mice to test and 24 hours to test, how many mices are required to find the poisoned can?
Options:
A)3
B)2
C)5
D)6
E)1
Rationale: Number the cans from 1 to 30.
Mouse can be forced to taste every can after a gap of 5 minutes.
Calculating the time if death from start, the poisoned can no can be found.
ANSWER:E
Answer: E
Question: A man invested Rs. 1552 in a stock at 97 to obtain an income of Rs. 128. The dividend from the stock is:
Options:
A)7.5%
B)8%
C)9.7%
D)10%
E)None of these
Rationale: By investing Rs. 1552, income = Rs. 128
By investing Rs. 97, income = Rs. (128/1552 * 97) = Rs. 8
Dividend = 8%
Answer = B
Answer: B
Question: The sides of a rectangular field are in the ratio 3 : 4. If the area of the field is 8112 sq. m, the cost of fencing the field @ 25 paise per metre is
Options:
A)Rs. 55.50
B)Rs. 67.50
C)Rs. 86.50
D)Rs. 91.00
E)None of these
Rationale: Solution
Let length = (3x) metres and breadth = (4x) metres.
Then, 3x × 4x = 7600 ⇔ 12x2 = 8112 ⇔ x2 = 676 ⇔ x = 26
So, length = 78 m and breadth = 104 m.
Perimeter = [2(78 + 104)] m = 364 m.
∴ Cost of fencing = Rs. (0.25 × 364) = Rs. 91. Answer D
Answer: D
Question: A lady builds 12cm length, 16cm width, and 6cm height box using 3cubic cm cubes. What is the minimum number of cubes required to build the box?
Options:
A)345
B)384
C)378
D)398
E)300
Rationale: Number of cubes required = Volume of box/Volume of cube
= 12*16*6/3
=384 cubes
ANSWER:B
Answer: B
Question: In an election a candidate who gets 60% of the votes is elected by a majority of 1380 votes. What is the total number of votes polled?
Options:
A)A)4500
B)B)5200
C)C)6900
D)D)7520
E)E)6000
Rationale: Let the total number of votes polled be x
Then, votes polled by other candidate = (100-60)% of x = 40% of x
60% of x - 40% of x = 1380
20x/100 = 1380
x = 1380*100/20 = 6900
Answer is C
Answer: C
Question: Out of first 26 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is -.
Options:
A)1/2
B)16/19
C)4/5
D)21/26
E)3/5
Rationale: n(S) = 26
n(Even no) = 13 = n(E)
n(Prime no) = 9 = n(P)
P(EᴜP) = 13/26 + 9/26 - 1/26 = 21/26
ANSWER:D
Answer: D
Question: f1(x)f1(x) = 2x - 1 and fn(x)=f1(fn−1(x))fn(x)=f1(fn−1(x)) for n ≥≥ 2. Find f5(2)
Options:
A)7
B)6
C)78
D)9
E)1
Rationale: Answer:A
Answer: A
Question: If f(x) = 5x − √x and g(x) = x^2, what is f(g(6))?
Options:
A)-4
B)8
C)16
D)32
E)174
Rationale: g(x) = x²
g(6) = 6² = 36
So, f(g(6)) = f(36)
f(x) = 5x − √x
So, f(36) = 5(36) − √36
= 180 - 6
= 174
= E
Answer: E
Question: How much interest can a person get on Rs. 8000 at 17.5% p.a. simple interest for a period of two years and six months?
Options:
A)3587.58
B)3500
C)3587.5
D)3587.52
E)3587.56
Rationale: I = (8000 * 2.5 * 17.5)/100 = (8000 * 5 * 35)/(100 * 2 * 2) = Rs. 3500.Answer: B
Answer: B
Question: Choose the missing terms out of the given alternatives.
AZ, CX, FU, ?
Options:
A)IR
B)IV
C)JQ
D)KP
E)QC
Rationale: C
JQ
The first letter moves 2, 3, 4 ... steps forward. The second letter moves 2, 3, 4 ... steps backward.
Answer: C
Question: A bag contains 12 red marbles. If someone were to remove 2 marbles from the bag, one at a time, and replace the first marble after it was removed, the probability that neither marble would be red is 25/36. How many marbles are in the bag?
Options:
A)24
B)48
C)60
D)72
E)84
Rationale: ok let me see if i can explain what went on in the previous post
lets say i have x marbles in the bag in total --> out of them 12 are red
so the probability of pulling a non-red marble is (x -12) / x
now the marble is placed back in the bag and we have x marbles again, of which again 12 are red. so the probability of pulling a non-red marble out is (x-12) / x
probability theorm states that if the probability of event A occuring is m and the probability of event B occuring is n then the probability of both A and B occuring is m*n
so therefore the probability of 2 non-red marbles getting pulled out is [(x-12)/x ] * [(x-12)/x]
this is given as 25/36
-->(x-12)^2= 25/36
x^2
square rooting u have x-12/x = 5/6 or 6x-72 =5x therefore x = 72
B
Answer: B
Question: An oil cylinder was 3/4th full. When FOUR bottles of oil is poured into it, it is 4/5th full. How many bottles of oil
can the full cylinder hold?
Options:
A)90
B)75
C)70
D)80
E)85
Rationale: (4/5 -3/4) cylinder is filled by 4 bottles
0.8 -0.75 = 0.05 cylinder is filled by 4 bottles
1 cylinder is filled by 4/0.05 = 80 bottles
ANSWER:D
Answer: D
Question: If v is a positive integer, then 3^v + 3^(v +1) =
Options:
A)4^a
B)3^a − 1
C)3^(2a) + 1
D)3^a*(a − 1)
E)4(3^v)
Rationale: 3^v + 3^(v +1)
= 3^v + (3^v * 3^1)
= 3^v (1 + 3)
= 3^v(4)
Ans. E) 4(3^v)
Answer: E
Question: In a certain neighborhood, there are half as many beige houses as white houses, and four times as many white houses as brown houses. What is the ratio of the number of brown houses to the number of beige houses?
Options:
A)1:4
B)1:2
C)1:8
D)3:2
E)5:1
Rationale: The ratio of beige:white:brown = 2:4:1
The answer is B.
Answer: B
Question: The below sequence is a bit tricky. Can you solve it to find the next number?
9, 29, 329, 4329, ?
Options:
A)29816
B)54329
C)54325
D)38290
E)55291
Rationale: See the pattern. With every digit, the previous numbers are added after that digit
So the next number in the series is 54329
Answer : B
Answer: B
Question: Two trains of length 100 m and 200 m are 150 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. After how much time will the trains meet?
Options:
A)21/9 sec
B)32/3 sec
C)20/7 sec
D)32/3 sec
E)30/7 sec
Rationale: They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (54 + 72)*5/18 = 7*5 = 35 mps.
The time required = d/s = 150/35 = 30/7 sec.
Answer:E
Answer: E
Question: A boat can travel with a speed of 13 km/hr in still water.If the speed of the stream is 4 km/hr,find the time taken by the boat to go 68 km downstream.
Options:
A)2 hours
B)3 hours
C)4 hours
D)5 hours
E)None of these
Rationale: Solution
Speed downstream = km/hr = 17 km/hr.
Time taken to travel 68 km downstream =(68/17) hrs = 4 hrs. Answer C
Answer: C
Question: A wire in the form of a circle of radius 3.5 m is bent in the form of a rectangule, whose length and breadth are in the ratio of 6 : 5. What is the area of the rectangle?
Options:
A)11
B)30
C)88
D)66
E)41
Rationale: The circumference of the circle is equal to the permeter of the rectangle.
Let l = 6x and b = 5x 2(6x + 5x) = 2 * 22/7 * 3.5
=> x = 1
Therefore l = 6 cm and b = 5 cm Area of the rectangle = 6 * 5 = 30 cm2
Answer:B
Answer: B
Question: A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 720sq. feet, how many feet of fencing will be required?
Options:
A)34
B)92
C)68
D)88
E)None
Rationale: EXPLANATION
We have: l = 20 ft and lb = 720 sq. ft.
So, b = 36 ft.
Length of fencing = (l + 2b) = (20 + 72) ft = 92 ft.
Answer B
Answer: B
Question: A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in metres) is :
Options:
A)130
B)360
C)500
D)540
E)650
Rationale: Explanation:
Speed = (78 *5/18)m/sec =65/3m/sec
Time = 1 minute = 60 sec.
Let the length of the tunnel be x metres.
Then,800+X/60=65/3
=> 3 (800 + x) = 3900 =>X=500.
ANSWER IS C
Answer: C
Question: P and Q had the same number of candies. P gave Q 18 candies so that now Q has five times as many candies as P has. How many candies does Q have now?
Options:
A)35
B)40
C)45
D)50
E)55
Rationale: Let P and Q be the number of candies they had at the start.
P = Q
5(P-18) = Q+18
5(Q-18) = Q+18
4Q = 108
Q = 27
Now person Q has 27+18 candies which is 45 candies.
The answer is C.
Answer: C
Question: If a < 0 and b > 5, which of the following is true?
I. a * b > 0
II. a * b < 0
III. a^2 * b > 0
Options:
A)I only
B)II only
C)III only
D)I and III only
E)II and III only
Rationale: I. Not true, example: a = -1, b = 6, so a * b = -6
II. True, since a is negative and b is positive, a * b is negative and the a * b < 0
III. True, a^2 is positive and so is b so the product is positive
E
Answer: E
Question: For any positive integer n, n>1, thelengthof n is the number of positive primes (not necessary distinct) whose product is n. For ex, the length of 30 is 3, since 50=2x5x5. What is the greatest possible length of a positive integer less than 1000.
Options:
A)10
B)9
C)8
D)7
E)6
Rationale: you are missing something in your post:
For any positive integer n , n > 1, thelengthof n is the number of positive primes (not distinct) whose product is n. For example, the length of 50 is 3 since 50 = (2)(5)(5)
the lenght of 1000 = (2)(5)(2)(5)(2)(5) = 6
but we need n < 1000
using 2 as the base = (2)(2)(2)(2)(2)(2)(2)(2)(2) = 6 the length of 512.
the answer is (E)
Answer: E
Question: In a camp, food was was sufficient for 2000 people for 54 days. After 15 days, more people came and the food last only for 20 more days. How many people came?
Options:
A)1900
B)1800
C)1940
D)2000
E)None of these
Rationale: Explanation :
Given that food was sufficient for 2000 people for 54 days
Hence, after 15 days, the remaining food was sufficient for 2000 people for 39 days (∵ 54 - 15 = 39)
Let x number of people came after 15 days.
Then, total number of people after 15 days = (2000 + x)
Then, the remaining food was sufficient for (2000 + x) people for 20 days
More men, Less days (Indirect Proportion)
⇒Men 2000:(2000+x)}:: 20 : 39
⇒2000 × 39 = (2000 + x)20
⇒ 100 × 39 = (2000 + x)
⇒ 3900 = 2000 + x
x = 3900 − 2000 = 1900. Answer : Option A
Answer: A
Question: If 1 > 1 - ab > 0, which of the following must be true?
I. a/b > 1
II. a/b > 0
III. ab < 1
Options:
A)I only
B)II only
C)III only
D)II and III only
E)I and III only
Rationale: MANHATTAN GMATOFFICIAL SOLUTION:
You can manipulate the original compound inequality as follows, making sure to perform each manipulation on every term:
1 > 1 - ab > 0
0 > -a b > -1 Subtract 1 from all three terms.
0 < ab < 1 Multiply all three terms by -1 and flip the inequality signs.
Therefore you know that 0 < ab < 1. This tells you that ab is positive, so a/b must be positive (a and b have the same sign). Therefore, I must be true. However, you do not know whether a/b < 1, so II is not necessarily true. But you do know that ab must be less than 1, so III must be true.
Therefore, the correct answer is (D).
Answer: D
Question: There are 990 male and female participants in a meeting. Half the female participants and one-quarter of the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female?
Options:
A)75
B)100
C)125
D)175
E)165
Rationale: female = x
Male = 990-x
x/2 + 990-x/4 = 1/3* (990)= 330
x= 330
x/2 = 165 is supposed to be the answer
M is missing something
Correct Option E
Answer: E
Question: In one alloy there is 10% chromium while in another alloy it is 8%. 15 kg of the first alloy was melted together with 35 kg of the second one to form a third alloy. Find the percentage of chromium in the new alloy.
Options:
A)9.0%
B)9.4%
C)9.2%
D)8.8%
E)8.6%
Rationale: The amount of chromium in the new 15+35=50 kg alloy is 0.10*15+0.08*35=4.3 kg, so the percentage is 4.3/50*100=8.6%.
Answer: E.
Answer: E
Question: A train passes a platform in 30 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is
Options:
A)150 meter
B)240 meter
C)200 meter
D)260 meter
E)None of these
Rationale: Explanation:
Speed of the train = 54 km/hr = (54×10)/30 m/s = 15 m/s
Length of the train = speed × time taken to cross the man = 15×20 = 300 m
Let the length of the platform = L
Time taken to cross the platform = (300+L)/15
=> (300+L)/15 = 30
=> 300+L = 15×30 = 450
=> L = 450-300 = 150 meter
Answer: Option A
Answer: A
Question: I bought two books; for Rs.500. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?
Options:
A)337
B)280
C)299.67
D)266.67
E)291.67
Rationale: x*(85/100) = (500 - x)119/100
x = 291.67
Answer: E
Answer: E
Question: If 1 + x^4 + x^3 + x^2 + x = 80, then the average (arithmetic mean)Y of x, x^2, x^3, x^4 and x^5 is equal to which of the following?
Options:
A)12x
B)13x
C)14x
D)16x
E)20x
Rationale: 1 + x^4 + x^3 + x^2 + x = 81
i.e. 1 +x+ x^2+ x^3+ x^4 = 81
x+ x^2+ x^3+ x^4 = 80
x(1 +x+ x^2+ x^3) = 80
x(81-x^4) = 80
81x - x^5 = 80
x^5 = 81x -80
Now x+ x^2+ x^3+ x^4+ x^5 = 80 + 81x -80 = 81x
Average of Y{x, x^2, x^3, x^4, x^5} = 81x/5 ~ 16x
AnswerD
Answer: D
Question: Two numbers N and 14 have LCM = 56 and GCF = 12. Find N.
Options:
A)48
B)34
C)44
D)54
E)64
Rationale: The product of two integers is equal to the product of their LCM and GCF. Hence.
14 × N = 56 × 12
N = 56 × 12 / 14 = 48
correct answer A
Answer: A
Question: The membership of a committee consists of 3 science teachers, 4 Mathematics teachers, and 2 Social Studies teachers. If 2 committee members are to be selected at random to write the committee’s report, what is the probability that the two members selected will both be science teachers?
Options:
A)1/12
B)1/3
C)2/9
D)1/14
E)1/24
Rationale: Probability of first member an science teacher = 3/9
Probability of second member an science teacher = 2/8
Probability of both being english teacher = 3/9 x 2/8 =1/12 (A)
Answer: A
Question: A shopkeeper fixes the marked price of an item 30% above its cost price. The percentage of discount allowed to gain 8% is
Options:
A)15.92%
B)16.92%
C)17.92%
D)18.92%
E)None of these
Rationale: Explanation:
Let the cost price = Rs 100
then, Marked price = Rs 130
Required gain = 8%,
So Selling price = Rs 108
Discount = 130 - 108 = 22
Discount% = (22/130)*100 = 16.92%
Option B
Answer: B