mathewhe/aqua_rat huggingface dataset:
Question: The area of a square is equal to four times the area of a rectangle of dimensions 52 cm * 13 cm. What is the perimeter of the square?
(A) 200
(B) 208
(C) 210
(D) 220
(E) 228
Rationale: Area of the square = s * s = 4(52 * 13)
=> s = 52 cm
Perimeter of the square = 4 * 52 = 208 cm.
Answer: Option B
Answer: (B) 208
Question: Two employees X and Y are paid a total of Rs. 650 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
(A) s.200.45
(B) s.250.45
(C) s.295.45
(D) s.300.45
(E) s.310.45
Rationale: Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 650
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 650
⇒ y[12/10 + 1] = 650
⇒ 22y/10 = 650
⇒ 22y = 6500
⇒ y = 6500/22 = Rs.295.45
C)
Answer: (C) s.295.45
Question: On dividing 52 by a number, the quotient is 16 and the remainder is 4. Find the divisor?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: d = (D-R)/Q
= (52 - 4)/16
= 48/16 = 3
B)
Answer: (B) 3
Question: If s and t are positive integers such that s/t = 4.12, which of the following could be the remainder when s is divided by t ?
(A) 2
(B) 4
(C) 8
(D) 20
(E) 30
Rationale: The remainder is 0.12 or 12/100. You can go one step further and say that X/Y=12/100, where X and Y are whole numbers. Plug in all the answer choices for X and see which one makes Y a whole number.
One thing that jumps out at me is that A, B, C, and D are all even. E on the other hand is odd. Why? Maybe I'll start plugging in here first.
30/Y=12/100
12Y=3000
Y=250
Answer: E.
Answer: (E) 30
Question: A table is bought for Rs.400/- and sold at Rs.500/- find gain or loss percentage
(A) 25% loss
(B) 25% gain
(C) 15% gain
(D) 15% loss
(E) None
Rationale: Formula = (Selling price ~ Cost price)/Cost price * 100
= (500 - 400)/400 = 25% gain
B
Answer: (B) 25% gain
Question: What is the next number: 3, 11, 83, __
(A) 631
(B) 731
(C) 831
(D) 849
(E) 901
Rationale: 3^0 + 2 = 3
3^2 + 2 = 11
3^4 + 2 = 83
3^6 + 2 = 731
The answer is B.
Answer: (B) 731
Question: A semicircle has a radius of 11. What is the approximate perimeter of the semicircle?
(A) 45
(B) 51
(C) 57
(D) 63
(E) 69
Rationale: The perimeter of a circle is 2*pi*r.
The perimeter of a semicircle is 2*pi*r/2 + 2r = pi*r + 2r
The perimeter is pi*11 + 2*11 which is about 57.
The answer is C.
Answer: (C) 57
Question: The cubic f(x) = x3 - 7x - 6 has three distinct roots, a, b, and c. Compute 1/a + 1/b + 1/c .
(A) -5/6
(B) -6/6
(C) -7/6
(D) -8/6
(E) -9/6
Rationale: 1/a+1/b+1/c=ab+bc+ca/abc
=-7/-6
=-7/6
correct answer C
Answer: (C) -7/6
Question: If x>=y and y>1 , what is the maximum value of log (base x) -(x/y) + log (base y)x^2/y?
(A) -0.5
(B) 0
(C) 0.5
(D) 1
(E) 2
Rationale: log -(x/y) + log ( x^2)/y => - log x/y + 2log (x/y)
x y x y
By Formula (i) - log x/y = log y/x (ii) log y/x = log y - log x
x x x x x
log y - log x + 2{log x - log y }
x x y y
log y -1 + 2log x - 2 ==> log y + 2log x -3
x y x y
by Sub x &y as 2 by Question Condition---> Ans 1+2-3 = 0
ANSWER:B
Answer: (B) 0
Question: 16 children are to be divided into two groups A and B of 10 and 6 children. The average percent marks obtained by the children of group A is 75 and the average percent marks of all the 16 children is 76. What is the average percent marks of children of group B ?
(A) 233/3
(B) 233/8
(C) 233/1
(D) 233/2
(E) 263/3
Rationale: Required average = [(76 * 16) - (75 * 10)] / 6
= (1216 - 750)/6 = 466/3
= 233 /3.
Answer: A
Answer: (A) 233/3
Question: Cereal A is 9% sugar by weight, whereas healthier but less delicious Cereal B is 2% sugar by weight. To make a delicious and healthy mixture that is 4% sugar, what should be the ratio of Cereal A to Cereal B, by weight?
(A)  2:9
(B)  2:5
(C)  1:6
(D)  1:4
(E)  1:3
Rationale: (9/100)A+(2/100)B = (4/100)(A+B)
5A =2B
=> A/B = 2/5
Answer is B.
Answer: (B)  2:5
Question: If a committee of 3 people is to be selected from among 9 married couples so that the committee does not include two people who are married to each other, how many such committees are possible?
(A) 420
(B) 540
(C) 550
(D) 672
(E) 720
Rationale: You now have your Committee of 3 people. But you've selected them in an order, when order doesn't matter.
Selection #1 = Jack
Selection #2 = Susan
Selection #3 = Mary
Assume this is a good committee where Jack is not married to Susan or Mary and Susan and Mary are not married. The above committee will be the same as the following committee:
Selection #1 = Susan
Selection #2 = Mary
Selection #3 = Jack
To account for the fact that the order does not matter, we must divide out the number of ways a single committee can be the same members but in different order. 3 places = 3!, 3*2*1 = 6.
18*16*14 / 6 = 672. Answer D.
Answer: (D) 672
Question: What will $3000 amount to in three years if it is invested at 20% per year compound interest, with the interest being compounded annually?
(A) $4316
(B) $4632
(C) $4864
(D) $5184
(E) $5548
Rationale: After one year: 1.2 * $3000
After two years: (1.2)^2 * $3000
After three years: (1.2)^3 * $3000 = $5184
The answer is D.
Answer: (D) $5184
Question: A man is 40 years older than his son. In six years, his age will be twice the age of his son. The present age of this son is
(A) 31 years
(B) 32 years
(C) 33 years
(D) 34 years
(E) 35 years
Rationale: Explanation:
Let's Son age is x, then Father age is x+40.
=> 2(x+6) = (x+40+6)
=> 2x+12 = x+46
=> x = 34 years
Answer: Option D
Answer: (D) 34 years
Question: Inland revenue paid $300 on its first 1000 watts of electricity and then $5000 on the next 10000 watts. By approximately what percent did the ratio of monies due to watts increase from the first $1000 watts to the next 10000 watts?
(A) A) 80%
(B) B) 6%
(C) C) 60%
(D) D) 20%
(E) E) 40%
Rationale: First 1000 watts (3/10)
Next 10000 (5/10)
percentage increase is (difference/initial quantity)*100
(3/10)/(5/10 )* 100= 60%
Correct options is C
Answer: (C) C) 60%
Question: A vendor buys 10 t-shirts at an average price of $14 per t-shirt. He then buys 15 more t-shirts at an average price of $11 per t-shirt. What is the average price S per t-shirt that the vendor paid for these purchases?
(A) $12.20
(B) $12.50
(C) $12.55
(D) $12.70
(E) $13.00
Rationale: Correct Answer: A
Explanation: The relevant formula for this problem is Average S= (Sum)/(Number of Terms). Another way to look at the formula is Sum = Average x Number of Terms. For the first purchase, the vendor's sum (total cost) was $140, since 14 x 10 = 140. For the second purchase, the vendor's cost was $165, since 11 x 15 = 165. The grand sum is then $140 + $165, which equals $305. The total number of shirts purchased was 25, so to get the average price per shirt, we divide 305 by 25, which equals $12.20. As a result, the correct answer is A.
NOTE: A relative understanding of weighted average offers a shortcut to this problem. Because the true average of 11 and 14 is 12.5, but the vendor sells more shirts at the lower price than at the higher price, the weighted average must be less than $12.50; only answer choice A is a possibility.
Answer: (A) $12.20
Question: A boat travels 80 km downstream in 8 hours and 48 km upstream in 12 hours. Find the speed of the boat in still water and the speed of the water current.
(A) 7 km/hr, 3 km/hr
(B) 5 km/hr, 4 km/hr
(C) 1 km/hr, 6 km/hr
(D) 2 km/hr, 1 km/hr
(E) 4 km/hr, 1 km/hr
Rationale: Downstream speed=80km/8hrs
=10kmph
upstream speed=48km/12hrs
=4kmph
speed of boat=avg of downstream and upstream speeds
speed of boat=(10+4)/2kmph
=7kmph.
current speed=half of the difference of downstream and upstream speeds
currend speed=(10-4)/2kmph
=3kmph
ans is 7km/hr,3km/hr
ANSWER:A
Answer: (A) 7 km/hr, 3 km/hr
Question: Marty's Pizza Shop guarantees that their pizzas all have at least 75% of the surface area covered with toppings, with a crust of uniform width surrounding them. If you order their best seller – a circular pizza with a diameter of 16 inches – what is the maximum width you can expect to see for the crust?
(A) 0.8 inches
(B) 1.1 inches
(C) 1.6 inches
(D) 2.0 inches
(E) 2.5 inches
Rationale: Total Area = 8 * 8 * pi
Radius = 64 pi
Surface = .75 * 64 * pi = 48 pi
Radius of surface = 4 sqrt (3) ~ 6.8
Radius width = 8 - 6.8 = 1.2
Answer: B
Answer: (B) 1.1 inches
Question: The manager at a health foods store mixes a unique superfruit juice cocktail that costs $1399.45 per litre to make. The cocktail includes mixed fruit juice and açai berry juice, which cost $262.85 per litre and $3104.35 per litre, respectively. The manager has already opened 34 litres of the mixed fruit juice. How many litres of the açai berry juice does he need to add?
(A) 17 litres
(B) 22.67 litres
(C) 11 litres
(D) 07 litres
(E) 38.67 litres
Rationale: 262.85(34)+3,104.35x = 1,399.45(34 + x)
Solve the equation.
262.85(34)+3,104.35x = 1,399.45(34 + x)
8936.9+ 3,104.35x = 47,581.3 + 1,399.45x
8936.9 + 1,704.9x = 47,581.3
1,704.9x = 38,644.40
x ≈ 22.67
Answer is B.
Answer: (B) 22.67 litres
Question: There is a 30% chance Jen will visit Chile this year, while there is a 50% chance that she will visit Madagascar this year. What is the probability that Jen will visit either Chile or Madagascar this year, but NOT both?
(A) 25.0%
(B) 37.5%
(C) 50.0%
(D) 62.5%
(E) 75%
Rationale: P(Chile and not Madagascar) = 0.3*0.5 = 0.15
P(Madagascar and not Chile) = 0.5*0.7 = 0.35
Total probability = 0.15 + 0.35 = 0.5 = 50%
The answer is C.
Answer: (C) 50.0%
Question: 9 3/4 + 7 2/17 - 9 1/15=?
(A) 7 719/1020
(B) 9 817/1020
(C) 9 719/1020
(D) 7 817/1020
(E) None of them
Rationale: Given sum=9+3/4+7+2/17-(9+1/15)
=(9+7-9)+(3/4+2/17-1/15)
=7+(765+120-68/1020
=7 817/1020
Answer is D
Answer: (D) 7 817/1020
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow?
(A) 2/28
(B) 2/129
(C) 2/21
(D) 2/20
(E) 2/25
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = Â³Câ‚‚/Â¹âµCâ‚‚ = (3 * 2)/(15 * 14) = 1/35
Probability that both are yellow = Â²Câ‚‚/Â¹âµCâ‚‚ = (2 * 1)/(15 * 14) = 1/105
Probability that one blue and other is yellow = (Â³Câ‚ * Â²Câ‚)/Â¹âµCâ‚‚ = (2 * 3 * 2)/(15 * 14) = 2/35
Required probability = 1/35 + 1/105 + 2/35
= 3/35 + 1/105 = 1/35(3 + 1/3)
= 10/(3 * 35) = 2/21
Answer: C
Answer: (C) 2/21
Question: 123 school girls are to be transported in small vans. Each van can carry 8 girls only. What is the smallest possible number of vans that are needed to transport all 123 school girls?
(A) 15
(B) 16
(C) 17
(D) 18
(E) 19
Rationale: To find the number of vans, we divide 123 by 8.
123 * 8 = 15 and remainder = 3
So 15 vans are needed to transport 15 * 8 = 120 girls, and 1 van is needed to transport the 3 remaining girls. A total of 16 vans are needed.
correct answer B
Answer: (B) 16
Question: The ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:10. If P invested the money for 5 months, find for how much time did Q invest the money?
(A) 7 months
(B) 10 months
(C) 9 months
(D) 11 months
(E) 8 months
Rationale: 7*5: 5*x = 7:10
x = 10
ANSWER:B
Answer: (B) 10 months
Question: Three archers each have an equal chance of hitting a target, and if only two of the three shoot the likelihood of the two hitting the target is 4/9 . What is the likelihood of all three men missing the target?
(A) probability is 1/27
(B) 16/81
(C) 8/27
(D) 19/27
(E) 26/27
Rationale: Let the probability of an archer hitting a target be xx. Then the probability of two hitting the target will be P=x∗x=49P=x∗x=49 - -> x=23x=23, so the probability of an archer missing the target will be P=1−23=13P=1−23=13.
The probability of all three men missing the target will be P=(13)3=127P=(13)3=127.
Answer: A.
Answer: (A) probability is 1/27
Question: When average age of 21 members are 0, how many members greater than 0?
(A) 17
(B) 20
(C) 21
(D) 24
(E) 25
Rationale: Average of 21 numbers = 0.
Sum of 21 numbers (0 x 21) = 0.
It is quite possible that 20 of these numbers may be positive and if their sum is a then 21st number is (-a)
Answer is 20 (B)
Answer: (B) 20
Question: An owner of a pizza stand sold small slices of pizza for Rs. 150 each and large slices for Rs. 250 each. One night he sold 5000 slices, for a total of Rs. 10.50 lakh. How many small slices were sold?
(A) 3000
(B) 2000
(C) 4000
(D) 2500
(E) 3500
Rationale: Explanatory Answer
This question is a word problem in linear equations. The problem is solved by framing two linear equations from the information given in the question and solving them.
Let 's' be the number of small slices and 'b' the number of large slices sold on that night.
Therefore, s + b = 5000 ... eqn (1)
Each small slice was sold for Rs.150.
Therefore, 's' small slices would have fetched Rs.150s.
Each large slice was sold for Rs.250.
Therefore, 'b' large slices would have fetched Rs.250b.
Total value of sale = 150s + 250b = 10,50,000 (note the left hand side is in Rupees and hence we have to convert right hand also to Rupees from Lakhs of Rupees)
Or 150s + 250b = 10,50,000 ... eqn (2)
Multiplying equation (1) by 150, we get 150s + 150b = 7,50,000 ... eqn (3)
Subtracting eqn (3) from eqn (2), we get 100b = 3,00,000
Or b = 3000
We know that s + b = 5000
So, s = 5000 - b = 5000 - 3000 = 2000.
2000 small slices were sold.
Answer B
Answer: (B) 2000
Question: Ten years ago, a mother was four times older than her daughter. After ten years, the mother will be twice older than daughter. The present age of the daughter is
(A) 22
(B) 21
(C) 24
(D) 20
(E) 19
Rationale: Let the mother’s present age be ’x’
Let the daughter’s age be ’y’;
10 years ago; (x - 10) = 4(y - 10) or x - 4y = - 30.. (1)
10 years later; (x + 10) = 2(y + 10) or x - 2y = 10.. (2)
Solving (1) & (2)
y = 20
ANSWER:D
Answer: (D) 20
Question: In what time will Rs.1000 become Rs.1331 at 10% per annum compounded annually
(A) 2 Years
(B) 3 Years
(C) 4 Years
(D) 5 Years
(E) None of these
Rationale: Explanation:
Principal = Rs.1000;
Amount = Rs.1331;
Rate = Rs.10%p.a.
Let the time be n years then,
1000(1+10100)n=1331(1110)n=13311000(1110)3=13311000
So answer is 3 years
Answer: B
Answer: (B) 3 Years
Question: The jogging track in a sports complex is 1000 meters in circumference. Deepak and his wife start from the same point and walk in opposite directions at 20 km/hr and 13 km/hr respectively. They will meet for the first time in?
(A) 50min
(B) 33min
(C) 35min
(D) 25min
(E) 20min
Rationale: Clearly, the two will meet when they are 1000 m apart
To be 20+13 = 33 km apart, they take 1 hour
To be 1000 m apart, they take 33 * 1000/1000 = 33 min.
Answer is B
Answer: (B) 33min
Question: In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?
(A) 63
(B) 25
(C) 40
(D) 65
(E) 98
Rationale: Required number of ways = (7C5 x 3C2) = (7C2 x 3C1) = = 63.
ANSWER A
Answer: (A) 63
Question: From the below series find the remainder? 1201 × 1203 ×1205 × 1207 is divided by 6?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 8
Rationale: If you don't know the above rule, this problem is really calculation intensive.
But by applying the above rule, when 1201, 1201, 1203, 1204 divided by 6, leaves remainders 1, 3, 5, 1. The product of these remainders = 15.
When 15 is divided by 6, Remainder is 3
A
Answer: (A) 3
Question: If 0 < a < b and k = (2a + 12b)/b , which of the following must be true?
(A) k < 2
(B) k < 7
(C) k < 9
(D) k > 9
(E) k > 11
Rationale: Please follow posting guidelines (link in my signature) especially writing the correct topic title. Also do mention the source of the question if you select the tag:Source-Other Please Specify.
As for your question, it is very simple and straightforward with number plug in.
Assume a=1 and b=2 as a<b, you get k = (2+24)/2 = 13. This eliminates all but option E , making it the correct answer.
Answer: (E) k > 11
Question: A plant manager must assign 12 new workers to one of five shifts. She needs a first, second, and third shift, and two alternate shifts. Each of the shifts will receive 2 new workers. How many different ways can she assign the new workers?
(A) 23760
(B) 47520
(C) 33000
(D) 48600
(E) 54000
Rationale: whatever : my take selecting team of 2 out of 12 to assign to the shifts = 12C2 = 66 ways.
now 2 out of 12 means total of 6 group possible.
so putting them in shifts = counting methode: first, second, third, alt , alt
= 6*5*4*3*2*1 = 720
here alt and alt are the same: so 720/2 = 360 ways.
total ways of selecting = (selecting 2 out of 12)*arranging those teams in shifts
= 66*360 = 23760
Ans: A
Answer: (A) 23760
Question: In the coordinate plane, Line A has a slope of -1 and an x-intercept of 1. Line B has a slope of 5 and a y-intercept of -5. If the two lines intersect at the point (a,b), what is the sum a+b?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: The equation of Line A is y = -x + 1
The equation of Line B is y = 5x - 5
5x - 5 = -x + 1
x = 1
y = 0
The point of intersection is (1,0) and then a+b = 1.
The answer is B.
Answer: (B) 1
Question: If A= {2, 4, 6}, B= {1, 2, 5, 7}, and C= {2, 3, 4, 6}. Find A-(B U C)
(A) {1 , 2}
(B) {2 ,3 ,5 }
(D) {5 }
(E) None of these
Rationale: Explanation :
A= {2, 4, 6},
B= {1, 2, 5, 7},
C = {2, 3, 4, 6}
Now,(B U C) = {1, 2, 5, 7} U {2, 3, 4, 6} = {1,2,3,4,5,6,7}
A-(B U C) = {2, 4, 6} - {1,2,3,4,5,6,7} = { }
Hence (C) is correct answer.
Answer : C
Answer: (C)
Question: A radio station has to choose two days of the seven in a week to broadcast a certain program, and that set will repeat each week. The program can be broadcast equally on any of the seven weekdays —- weekdays vs. weekends don’t matter at all —- nor does it matter whether the days the program airs are adjacent or not. Absolutely any three of the seven weekdays can be chosen. How many different three-day combinations of the seven weekdays can be constructed?
(A) 9
(B) 15
(C) 21
(D) 35
(E) 56
Rationale: Behind the story, we are really being asked to evaluate 7C2. We could use the factorial formula, but above we conveniently happen to have Pascal’s Triangle written out to the seventh row. We see that 7C2, the third entry of the seventh row, is 21. Answer = C.
Answer: (C) 21
Question: John has on his shelf four books of poetry, four novels, and two reference works. Suppose from these ten books, we were to pick two books at random. What is the probability that we pick one novel and one poetry?
(A) 1/2
(B) 2/5
(C) 3/10
(D) 7/20
(E) 16/45
Rationale: When we are picking two books, one novel and one reference work, we could either pick a novel first and then a reference book or pick a reference book and then a novel. Therefore the answer is 4/10*4/9 + 4/10*4/9 = 16/45.
Answer: E.
Answer: (E) 16/45
Question: How many trailing Zeroes does 53! + 54! have?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: 53! + 54! = 53! + 54 * 53!
= 53! (1 + 54)
= 53! * 55
Number of trailing 0s in 53! = number of 5s in the expansion of 53!
= 10 + 2 = 12
There is 1 more 5 in 55.
Hence, total number of trailing 0s = 12 + 1 = 13
Answer (B)
Answer: (B) 13
Question: A person took some amount with some interest for 5 years, but increase the interest for 1%, he paid Rs.250/- extra, then how much amount he took?
(A) Rs.5500/-
(B) Rs.6000/-
(C) Rs.4000/-
(D) Rs.5000/-
(E) None of these
Rationale: Explanation:5 years = Rs.250/-year = 250/5Rate of Interest = 1%100/1% × 250/5 = Rs.5000/-P = Rs.5000/- Answer: Option D
Answer: (D) Rs.5000/-
Question: One millisecond is 0.001 of a second. The costs for a single run of a computer program are $1.07 for operating-system overhead, $0.019 per millisecond of computer time, and $4.35 for the mounting of a data tape. What is the total of these three costs for 1 run of a program that requires 1.5 seconds of computer time ?
(A)  $7.15
(B)  $8.87
(C)  $33.92
(D)  $35.57
(E)  $39.62
Rationale: Operating system overhead for 1 run = 1.07 $
Mounting of data tape = 4.35$
Cost per 1 millisecond of computer time = .019 $
Total cost of 1 run of a program that requires 1.5 seconds of computer time
= 1.07 + (.019*1500) + 4.35
=1.07 + 28.5 + 4.35
= 33.92$
Answer C
Answer: (C)  $33.92
Question: Mr. Kramer, the losing candidate in a two-candidate election, received 942,568 votes, which was exactly 40 percent of all votes cast. Approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast?
(A) 10%
(B) 12%
(C) 15%
(D) 17%
(E) 20%
Rationale: Lets assume that candidate got 40% votes and total votes is 100.
Candidate won = 40
Remaining = 60
To get 50%, candidate requires 10 votes from 100 which is 10% and 10 votes from 60.
10/60 = 1/6 = .166 = 16.67%
Which is approx 17%. Hence the answer is D
Answer: (D) 17%
Question: Two trains, one from P to Q and the other from Q to P, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 36 hours respectively. The ratio of their speeds is
(A) 4:1
(B) 4:2
(C) 4:5
(D) 6:3
(E) 3:6
Rationale: Ratio of their speeds = Speed of first train : Speed of second train
= √36−−√9
= 6:3
Answer is D.
Answer: (D) 6:3
Question: If 1+2+3+...+n=n (n+1), then 3 (1+3+5+....+69)=?
(A) 3675
(B) 3575
(C) 3475
(D) 3375
(E) 3275
Rationale: Explanation :
To solve this use the formula of AP,
Sn= (n/2)(a+l) ................(1)
To find n, use
=> Tn= a+(n-1)d
=> 69=1+(n-1)2
=> n=35
Use value of n in (1)
then,
Sn = (35/2)(1+69) = 1225
Ans:- 3(Sn) = 3675
Answer : A
Answer: (A) 3675
Question: The length of a train and that of a platform are equal. If with a speed of 108 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
(A) 227
(B) 299
(C) 276
(D) 750
(E) 900
Rationale: Speed = [108 * 5/18] m/sec = 30 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 30 è x = 30 * 60 / 2 = 900
Answer: E
Answer: (E) 900
Question: Given that E and F are events such that P(E) = 0.16, P(F) = 0.4 and P(E n F) = 0.4,
find P (E|F) and P(F|E)
(A) 1/2
(B) 1/7
(C) 1/4
(D) 1/3
(E) 1/5
Rationale: Here, E and F are events
P(E|F) = P(EnF)/P(F) = 0.4/0.4 = 1
P(F|E) = P(EnF)/P(E) = 0.4/0.16 = 1/4.
C
Answer: (C) 1/4
Question: In 1995, there are 28 days in February and there are 365 days in the year. In 1996, there are 29 days in February and there are 366 days in the year. If the date February 12, 1995 is a Wednesday, then which one of the following would the date February 12, 1996 be?
(A) Thursday
(B) Friday
(C) Saturday
(D) Sunday
(E) Monday
Rationale: From the information given, Feb 12, 1996 is 366 days after Feb 12, 1995.
366 days = 52 weeks and 2 more days. Therefore if Feb 12, 1995 is a Wednesday, then Feb 12, 1996 is Wednesday + 2 days = Friday
Answer: B
Answer: (B) Friday
Question: In a covering a certain distance, the speeds of A and B are in the ratio of 3:4. A takes 30 minutes more than B to reach the destination. The time taken by A to reach the destination is?
(A) 2 hrs
(B) 3 hrs
(C) 5 hrs
(D) 6 hrs
(E) 4 hrs
Rationale: A
Ratio of speeds = 3:4
Ratio of times taken = 4:3
Suppose A takes 4x hrs and B takes 3x hrs to reach the destination.
Then, 4x - 3x = 30/60 => x = 1/2
Time taken by A = 4x hrs = 4 * 1/2 = 2 hrs.
Answer: (A) 2 hrs
Question: In a workshop there are 4 kinds of beds, 2 kinds of closets, 2 kinds of shelves and 7 kinds of chairs. In how many ways can a person decorate his room if he wants to buy in the workshop one shelf, one bed and one of the following: a chair or a closet?
(A) 168.
(B) 80.
(C) 56.
(D) 48.
(E) 72.
Rationale: ways to select one shelf = 2
ways to select one bed = 4
ways to select one of the following: a chair or a closet = 7+2 = 9
ways to select all of them together = 2*4*9 = 72
Hence, E is the answer.
Answer: (E) 72.
Question: What is the average of first 21 multiples of 6 ?
(A) A)66
(B) B)77
(C) C)79
(D) D)81
(E) E)82
Rationale: Required average = 6(1+2+....+21) / 21
(6/21)X ( (21x22) / 2 ) (because sum of first 21 natural numbers)
= 66
A
Answer: (A) A)66