divelab/Sys2Bench huggingface dataset:
Question: 16 balls are numbered 1 to 16. A ball is drawn and then another ball is drawn without replacement. What is the probability that both balls have even numbers?
Options:
A)4/11
B)5/17
C)6/25
D)7/30
E)8/37
Rationale: P(1st ball is even) = 8/16
P(2nd ball is also even) = 7/15
P(both balls are even) = 8/16 * 7/15 = 7/30
The answer is D.
Answer: D
Question: The wages earned by Robin is 35% more than that earned by Erica. The wages earned by Charles is 60% more than that earned by Erica. How much % is the wages earned by Charles more than that earned by Robin?
Options:
A)25.92%
B)18.75%
C)30%
D)50%
E)100%
Rationale: Explanatory Answer
Let the wages earned by Erica be $100
Then, wages earned by Robin and Charles will be $135 and $160 respectively.
Charles earns $35 more than Robin who earns $135.
Therefore, Charles' wage is 35/135*100 = 25.92%.
The correct choice is (A)
Answer: A
Question: A four-character password consists of one letter of the alphabet and three 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)5,040
B)18,720
C)26,000
D)37,440
E)52,000
Rationale: 4 character password: DLDD
First digit can be chosen in 10 ways.
The letter can be chosen in 26 ways.
Next digit can be chosen in 9 ways.
Next digit can be chosen in 8 ways.
This gives us 10*26*9*8ways
Now, the letter can also be DDLD so there will be another 10*9*26*8 ways
Total = 10*26*9*8*2 = 37,440 ways
ANS:D
Answer: D
Question: A can do a work in 20days, B in 30days. A alone start the work after 10days he left work. In how many days B can finish the work?
Options:
A)30days
B)25days
C)20days
D)10days
E)15days
Rationale: 10days work of A = 10/20 = 1/2
remaining work = 1-1/2 = 1/2
B can finish 1/2 work = 30*1/2 = 15days
Answer is E
Answer: E
Question: If a is a positive integer, and if the units digit of a^2 is 9 and the units digit of (a+1)^2 is 4, what is the units U digit of (a+2)^2?
Options:
A)1
B)3
C)5
D)6
E)C. 14
Rationale: I also got A. By punching in numers:
U...7^2=...9
...8^2=...4
...9^2=...1.A
Answer: A
Question: How many of the positive divisors G of 120 are also multiples of 4 not including 120?
Options:
A)3.
B)4.
C)5.
D)7.
E)8.
Rationale: 4,8,12,20,24,40,60. (7) is the answer
Other way : factors of 120 = 2^3 * 3*5
Separate 2^2 ( which means 4)
Now, calculate the number of other factors.
G=2*3*5 = total positive factors are 2*2*2 = 8
This 8 factors include 120
So subtract 1 from 8
Ans is 7=D
Answer: D
Question: Look at this series: 439,404, 369, 334, 299, 264 ... What number should come next?
Options:
A)206
B)208
C)206
D)229
E)204
Rationale: 229
This is a simple subtraction series. Each number is 35 less than the previous number.
D
Answer: D
Question: The side of a square is increased by 25% then how much % does its area increases?
Options:
A)56.75 %
B)56.25 %
C)53.85 %
D)57.25 %
E)56.21 %
Rationale: a = 100 a2 = 10000
a = 125 a2 = 15625
----------------
10000 --------- 5625
100 -------? => 56.25 %
Answer:B
Answer: B
Question: A, B, C subscribe Rs. 50,000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 35,000, A receives:
Options:
A)Rs. 8400
B)Rs. 11,900
C)Rs. 13,600
D)Rs. 14,700
E)Rs. 14,900
Rationale: Let C = x.
Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.
So, x + x + 5000 + x + 9000 = 50000
3x = 36000
x = 12000
A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.
A's share = Rs.(35000 x21/50) = Rs. 14,700.
Answer:D
Answer: D
Question: A number x is multiplied with itself and then added to the product of 4 and x. If the result of these two operations is -3, what is the value of x?
Options:
A)-4
B)-1 and -3
C)2
D)4
E)Cannot be determined.
Rationale: A number x is multiplied with itself --> X^2
added to the product of 4 and x --> X^2+4X
If the result of these two operations is -3 --> X^2+4X=-3
i.e X^2+4X+3=0 is the Quadratic equation which needs to be solved.
(X+1)(X+3) = 0
Hence X=-1. X=-3
IMO B
Answer: B
Question: When y is divided by 276, the remainder is 44. What is the remainder when the same y is divided by 23?
Options:
A)19
B)20
C)21
D)22
E)23
Rationale: y = 276*a + 44 = (23*12)*a + 23 + 21
The answer is C.
Answer: C
Question: If the average of 5 positive integers is 45 and the difference between the largest and the smallest of these 5 numbers is 10, what is the maximum value possible for the largest of these 5 integers?
Options:
A)50
B)53
C)49
D)48
E)44
Rationale: Sum of 5 Integer (a, b, c, d, e) = 5*45 = 225
e - a = 10
i.e. e = a+10
For e to be maximum remaining 4 MUST be as small as possible
Since smallest of 5 numbers is a so to minimize other numbers we can take them equal to the smallest of 5 numbers
i.e. a+a+a+a+(a+10) = 225
i.e. 5a = 215
i.e. a = 43
i.e. Largest e = 43+10 = 53
Answer: option B
Answer: B
Question: From a total of 5 boys and 6 girls, how many 4-person committees can be selected if the committee must have exactly 2 boys and 2 girls?
Options:
A)16
B)24
C)60
D)120
E)150
Rationale: Answer=E=150
No of 4 person committees that can be formed=5C2*6C2=150
Answer E
Answer: E
Question: Mary can divide his herd into 5 equal parts and also to 6 equal parts, but not to 9 equal parts. What could be the number of cows Mary has in his herd?
Options:
A)120
B)155
C)456
D)180
E)336
Rationale: On first look B,C,E are not divisible either by 5 or 6 - ruled out.
D,A divisible by both 5,6, but 180 is divisible by 9.
Answer : A
Answer: A
Question: An order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter. Find the ratio of the areas of the carpets in both the ?
Options:
A)8:6
B)8:7
C)8:1
D)8:2
E)8:4
Rationale: Let the length and breadth of the carpet in the first case be 3x units and 2x units respectively.
Let the dimensions of the carpet in the second case be 7y, 3y units respectively.
From the data,.
2(3x + 2x) = 2(7y + 3y)
=> 5x = 10y
=> x = 2y
Required ratio of the areas of the carpet in both the cases
= 3x * 2x : 7y : 3y
= 6x2 : 21y2
= 6 * (2y)2 : 21y2
= 6 * 4y2 : 21y2
= 8:7
Answer:B
Answer: B
Question: If 3 (A's capital) = 8 (B's capital) = 10 (C's capital). Then the ratio of their capitals is?
Options:
A)40:15:15
B)40:15:18
C)40:15:12
D)40:15:14
E)40:15:11
Rationale: 3A = 8B = 10 C
A:B:C = 1/3:1/8:1/10
= 40:15:12
Answer: C
Answer: C
Question: 3889 + 12.543 - ? = 3854.002
Options:
A)A)47.095
B)B)47.752
C)C)47.932
D)D)47.541
E)of the above
Rationale: Let 3889 + 12.543 - x = 3854.002.
Then x = (3889 + 12.543) - 3854.002
= 3901.543 - 3854.002
= 47.541.
Answer = D
Answer: D
Question: Yesterday's closing prices of 2,200 different stocks listed on a certain stock exchange were all different from today's closing prices. The number of stocks that closed at a higher price today than yesterday was 20 percent greater than the number that closed at a lower price. How many of the stocks closed at a higher price today than yesterday?
Options:
A) 484
B) 726
C) 1,200
D) 1,320
E) 1,694
Rationale: Lets consider the below -
The number of stocks that closed at a higher price = H
The number of stocks that closed at a lower price = L
We understand from first statement -> H+L = 2200 ----(1)
We understand from second statement -> H = (120/100)L => H = 1.2L ----(2)
Solve eq (1)(2) to get H = 1200.
C is my answer.
Answer: C
Question: In a group of people, if 30 people were made to stand in each column, 16 columns could be formed. If 60 people were made to stand in a column, how many columns could be formed?
Options:
A)6
B)8
C)10
D)12
E)14
Rationale: 16*30 = 60*n
n = 8
The answer is B.
Answer: B
Question: A train running at the speed of 60 km/hr crosses a pole in 9 sec. What is the length of the train?
Options:
A)176 m
B)167 m
C)178 m
D)198 m
E)150 m
Rationale: Speed = 60 * 5/18
= 50/3 m/sec
Length of the train = speed * time
= 50/3 * 9
= 150 m
Answer:E
Answer: E
Question: Each Machine of type A has 3 steel parts and 2 chrome parts. Each machine of type B has 2 steel parts and 4 chrome parts. If a certain group of type A and type B machines has a total of 50 steel parts and 66 chrome parts, how many machines are in the group
Options:
A)11
B)21
C)31
D)61
E)51
Rationale: Look at the below representation of the problem:
Steel Chrome total
A 3 2 50 >>no. of type A machines=50/5=10
B 2 4 66 >>no. of type B machines=66/6=11
So the answer is 21 i.e B.
Hope its clear .
Answer: B
Question: A committee of 2 persons is to be formed from 3 company secretaries, 4 economists and 1 chartered accountant. What is the probability that each of the three professions is represented in the committee?
Options:
A)1/28
B)3/28
C)1/14
D)4/28
E)1/14
Rationale: 3/8*4/7*1/6*2! = 1/14. We are multiplying by 2! because we can choose secretary,economist, and accountant is several way: .
Answer: E.
Answer: E
Question: There are, in a certain league, 10 teams, and each team face another team for a total of 10 times. How many games are played in the season?
Options:
A)1000
B)450
C)720
D)180
E)400
Rationale: By using the formula, t[n(n - 1) / 2], where t = no. of games between two teams and n = total no. of teams, we get: 450
Option A.
Answer: A
Question: The profit earned by selling an article for Rs. 832 is equal to the loss incurred when the same article is sold for Rs. 448. What should be the sale price for making 60% profit?
Options:
A)220
B)230
C)1024
D)780
E)400
Rationale: C.P. = Rs. x.
Then, 832 - x = x - 448
2x = 1280 => x = 640
Required S.P. = 160% of Rs. 640 = 160/100 * 640 = Rs. 1024.
C
Answer: C
Question: The fourth proportional to 12, 14 and 18 is?
Options:
A)twenty one
B)66
C)77
D)88
E)12
Rationale: (14* 18) /12 = 21
Answer: A
Answer: A
Question: Uncle Bruce is baking chocolate chip cookies. He has 36 ounces of dough (with no chocolate) and 10 ounces of chocolate. How much chocolate is left over if he uses all the dough but only wants the cookies to consist of 20% chocolate?
Options:
A)2
B)4
C)6
D)3
E)1
Rationale: First, you must find the total weight of the mixture given that 80% of it will be dough.
80%*Total = 36 => (8/10)Total=36=> Total=360/8 => Total=45 oz,
From there, you must find 10% of the total 40 oz of the mixture.
20%*Total => (2/10)(45)= 9 oz choclate used,
Not forgetting that the question asks how much chocolate is left over we must subtract the chocolate used from the initial chocolate. 10-9 = 1 oz chocolate left over.
Answer : E
Answer: E
Question: Divide Rs. 1500 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?
Options:
A)s.360
B)s.400
C)s.375
D)s.500
E)s.900
Rationale: A+B+C = 1500
A = 1/3(B+C); B = 2/3(A+C)
A/(B+C) = 1/3
A = 1/4 * 1500 => 375
ANSWER:C
Answer: C
Question: Two pipes can separately fill a tank in 20 and 30 hours respectively. Both the pipes are opened to fill the tank but when the tank is full, a leak develops in the tank through which one-third of water supplied by both the pipes goes out. What is the total time taken to fill the tank?
Options:
A)22 hrs
B)16 hrs
C)77 hrs
D)99 hrs
E)65 hrs
Rationale: 1/20 + 1/30 = 1/12
1 + 1/3 = 4/3
1 --- 12
4/3 --- ?
4/3 * 12 = 16 hrs
Answer: B
Answer: B
Question: In a recent election, Ms. Robinson received 8000 voters cast by independent voters, that is, voters not registered with a specific political party. She also received 25 percent of the votes cast by those voters registered with a political party. IF N is the total number of votes cast in the election and 40 percent of the votes cast were cast by independent voters, which of the following represents the number of votes that Mrs. Robbins received?
Options:
A) 0.06N+3200
B) 0.1N+7200
C) 0.4N+7200
D) 0.15N+8000
E) 0.06N+8000
Rationale: 40% of N are independent voters, hence 60% of N are not independent voters. From this group she received 25% votes so, 0.25*0.6*N plus 8,000 votes from independents: total=0.25*0.6*N+8,000=0.15*N+8,000.
Answer: D.
Answer: D
Question: The parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places
Options:
A)34
B)35
C)56
D)67
E)23.57
Rationale: Let the side of the square be a cm.
Parameter of the rectangle = 2(16 + 14) = 60 cm Parameter of the square = 60 cm
i.e. 4a = 60
A = 15
Diameter of the semicircle = 15 cm
Circimference of the semicircle
= 1/2(∏)(15)
= 1/2(22/7)(15) = 330/14 = 23.57 cm to two decimal places
Answer: Option E
Answer: E
Question: Two trains of length 250 m and 120 m are 50 m apart. They start moving towards each other on parallel tracks, at speeds 64 kmph and 42 kmph. After how much time will the trains meet?
Options:
A)15/10
B)17/10
C)16/10
D)18/10
E)16/10
Rationale: They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (64 + 42)*5/18 = 7*5 = 29.4 mps.
The time required = d/s = 50/29.4 = 17/10 sec.
Answer:B
Answer: B
Question: The vertices of a rectangle in the standard (x,y) coordinate place are (0,0), (0,3), (6,0) and (6,3). If a line through (2,2) partitions the interior of this rectangle into 2 regions that have equal areas, what is the slope of this line?
Options:
A)1/2
B)2/5
C)4/7
D)1
E)7/4
Rationale: CONCEPT: The readers need to know that a rectangle can be divided into two equal area by a Straight line only when the straight line passes through the Centre of the Rectangle (Intersection of its two diagonals)Draw a figure and know it for yourself.
The point of Intersections of the diagonals will be the midpoint of any diagonal i.e. Midpoint of (0,0), and (6,3) OR Midpoint of (0,3) and (6,0)
i.e. Either [(0+6)/2, (0+3)/2] OR [(0+6)/2, (3+0)/2] =[3,1.5]
Slope of line passing through points (2,2) and (3,1.5) = (2-1.5)/(3-2) = 0.5/1 = 1/2
A
Answer: A
Question: The sum of ages of 5 children born at the intervals of 8 years each is 90 years. What is the age of the youngest child?
Options:
A)2
B)9
C)6
D)4
E)0
Rationale: Let the ages of children be x, (x +8), (x + 16), (x + 24) and (x + 32) years.
Then, x + (x + 8) + (x + 16) + (x + 24) + (x + 32) =90
5x = 10
x = 2.
Age of the youngest child = x = 2 years.
Answer:A
Answer: A
Question: Sally has a gold credit card with a certain spending limit, and a platinum card with twice the spending limit of the gold card. Currently, she has a balance on her gold card that is 1/3 of the spending limit on that card, and she has a balance on her platinum card that is 1/6 of the spending limit on that card. If Sally transfers the entire balance on her gold card to her platinum card, what portion of her limit on the platinum card will remain unspent?
Options:
A)2/3
B)29/60
C)17/30
D)19/30
E)11/15
Rationale: Let s assume the platinum card spending limit =x
Gold card spending limit will be =x/2
balance on gold card is =x/2*1/3=x/6
Platinum card unspent limit is= x-1/6x=5/6x
So if gold card balance is transferred then the rest unspent will be
5/6x-x/6=2/3x
So the ans is A
Answer: A
Question: The average age of a family of 6 members is 28 years.If the age of the youngest member is 7 years,what was the average age of the family at the birth of the youngest member?
Options:
A)15
B)18
C)21
D)12
E)19
Rationale: Present age of total members = 6 X 28 = 168
7 yrs back their ages were = 6 x 7 = 42
Ages at the birth of youngest member = 168 - 42 = 126
Therefore, avg age at the birth of youngest member = 126/6 = 21.
ANSWER:C
Answer: C
Question: There are some passengers riding on a bus. At the first stop, half the passengers get off and nobody gets on the bus. This pattern continues as the bus goes to the next stops. If only one passenger gets off at stop number 7, how many passengers were on the bus originally?
Options:
A)128
B)64
C)32
D)16
E)8
Rationale: Before stop 7, there were 2 passengers on the bus.
Before stop 6, there were 4 passengers on the bus.
etc...
Before stop x, there were 2^(8-x) passengers on the bus.
Before stop 1, there were 2^7 = 128 passengers on the bus.
The answer is A.
Answer: A
Question: If √2n = 64, then the value of n is :
Options:
A)6
B)12
C)24
D)48
E)NOne
Rationale: Sol.
√2n = 64 ⇔ (2n)1/2 ⇔ 2n/2 = 26 ⇔ n/2
= 6 ⇔ n = 12.
Answer B
Answer: B
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)18 m
B)17 m
C)26 m
D)27 m
E)15 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: A rectangular box measures internally 1.6 m long, I m broad and 60 cm deep.The number of cubical blocks each of edge 20 cm that can be packed inside the box is
Options:
A)30
B)53
C)60
D)120
E)None
Rationale: Solution
Number of blocks	= (160×100×60 / 20×20×20)
= 120.
Answer D
Answer: D
Question: Louie takes out a three-month loan of $1000. The lender charges him 30% interest per month compounded monthly. The terms of the loan state that Louie must repay the loan in three equal monthly payments. To the nearest dollar, how much does Louie have to pay each month?
Options:
A)A)333
B)B)663
C)C)402
D)D)433
E)E)483
Rationale: Here's the calculation for that case, assume monthly payment is X.
After 1st month: (1000)(1.3)-X = 1300-X
After 2nd month: (1300-X)(1.3)-X = 1690-2.21X
After 3rd month: (1690-2.21X)(1.3)-X = 2197-3.31X
Now, the amount after the last payment in 3rd month must bring the total to 0. Hence:
2197-3.31X = 0
X = 2197/3.31 = 663.74
Answer B
Answer: B
Question: On a certain transatlantic crossing, 20 percent of a ship’s passengers held round-trip tickets and also took their cars abroad the ship. If 20 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship’s passengers held round-trip tickets?
Options:
A)20%
B)25%
C)30%
D)35%
E)40%
Rationale: Let T be the total number of passengers.
Let x be the number of people with round trip tickets.
0.2T had round trip tickets and took their cars.
0.8x had round trip tickets and took their cars.
0.8x = 0.2T
x = 0.25T
The answer is B.
Answer: B
Question: If a committee of 4 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many such committees are possible?
Options:
A)20
B)40
C)50
D)80
E)120
Rationale: Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 4 couples (as there should be 4 members) each to send onerepresentativeto the committee: 5C4=5.
But these 4 chosen couples can send two persons (either husband or wife): 2*2*2=2^3=8.
Total # of ways: 5C3*2^3=40.
Answer: B.
Answer: B
Question: a is the hundreds digit of the three digit integer x, b is the tens digit of x, and c is the units digit of x. 2a = b = 4c, and a > 0.
What is the difference between the two greatest possible values of x?
Tip: Dont stop till you have exhausted all answer choices to arrive at the correct one.
Options:
A)124
B)241
C)394
D)421
E)842
Rationale: Ratio of a:b:c= 2:4:1
Two possible greatest single digit values for b are 8 and 4
if b is 8, then x= 482
if b is 4, then x= 241
difference= 482-241= 241
B is the answer
Answer: B
Question: Six cards numbered from 1 to 6 are placed in a cardboard box . First one card is drawn and then put back into the bowl; then a second card is drawn. If the cards are drawn at random and if the sum of the numbers on the cards is 10, what is the probability that one of the two cards drawn is numbered 5 ?
Options:
A)1/2
B)1/4
C)1/5
D)1/6
E)1/3
Rationale: (6,4) (4,6) (5,5) – only 3 possible scenarios for sum to be 10. One from this 5 has already happened.
From this three cases, only in one we have 5. So, the probability is 1 chances out of 3 that the one that occurred had 5: P=1/3.
Answer: E.
Answer: E
Question: There are 8 teams in a certain league and each team plays each of the other teams exactly once. If each game is played by 2 teams, what is the total number of games played?
Options:
A)15
B)16
C)28
D)56
E)64
Rationale: Number of ways 2 teams can be selected out of 8 teams:
C8/2=8∗7/2=28
Ans:"C"
Answer: C
Question: The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?
Options:
A)8%
B)4%
C)5%
D)3%
E)2%
Rationale: 65*(90/100)*((100-x)/100) = 56.16
x = 4%
Answer: B
Answer: B
Question: Average of 7 numbers is zero. At most how many numbers may be greater than zero
Options:
A)0
B)1
C)6
D)9
E)10
Rationale: Answer: Option C
Answer: C
Question: A line that passes through (–1, –4) and (5, k) has a slope = k. What is the value of k?
Options:
A) 3/4
B) 1
C) 4/5
D) 2
E) 7/2
Rationale: Slope = (y2-y1)/(x2-x1)
=> k = (k+4)/(5+1)
=> 6k = k+4
=> k =4/5
Ans C it is!
Answer: C
Question: n a 1000m race, if A gives B a start of 40m, A wing by 19sec. But if A gives B start of 30sec, B wins by 40m.
Find the time taken by B to run 3000m race?
Options:
A)300
B)350
C)375
D)400
E)425
Rationale: then 960/B -1000/A = 19 => 24/B - 25/A = 19/40
and 1000/B - 960/A = 30 => 25/B - 24/A = 30/40
solving equation A speed =8 and B=20/3
for 1000m b will take 3000/20/3= 375 sec
C
Answer: C
Question: Tom wants to buy items costing $25.35, $70.69, and $85.96. He earns $6.50 an hour doing
odd jobs. If ten percent of his income is put aside for other purposes, how many hours must he
work to earn the money he needs for his purchases? Round your answer to the nearest whole
hour.
Options:
A)8 hours
B)48 hours
C)31 hours
D)18 hours
E)28 hours
Rationale: $6.50 x .10 = $.65 is 10% of his hourly income
$6.50 - .65 = $5.85 hourly amount available to spend
$25.35 + $70.69 + $85.96 = $182 total needed
$182 ÷ $5.85 = 31.11... rounds to 31 hours
correct answer C
Answer: C
Question: A and B invested Rs.15000 and Rs.20,000 respectively in a business. How should a loss of Rs.2800 be divided between them at the end of year? (in rupees)
Options:
A)1500,1300
B)1200,1600
C)1300,1500
D)1600,1200
E)1700,1200
Rationale: Ratio btwn invest is == 3:4
loss==2800
so 2800/7==400
A==3*400==1200
B==4*400==1600
ANSWER:B
Answer: B
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is?
Options:
A)3/5
B)3/2
C)3/9
D)3/6
E)3/1
Rationale: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 23 ==> 27 x + 17 y = 23 x + 23 y ==> 4 x = 6 y ==> x/y = 3/2.Answer: B
Answer: B
Question: If 70% of a number exceeds 28% of it by 39.9, then find the number?
Options:
A)65
B)67
C)100
D)95
E)33
Rationale: Use the elimination method to find the correct option.
Of all the options only 95 fits
70% of 95 = 66.5
28% of 95 = 26.6
66.5 - 26.6 = 39.9
Required number is 95.
ANSWER:D
Answer: D
Question: Find the ratio in which rice at Rs. 7.30 a kg be mixed with rice at Rs. 5.70 a kg to produce a mixture worth Rs. 6.30 a kg
Options:
A)2:0
B)2:3
C)3:5
D)2:2
E)2:8
Rationale: By the rule of alligation:
Cost of 1 kg rice of 1st kind Cost of 1 kg rice of 2nd kind
Required ratio = 60 : 100 = 3 : 5
Answer: C
Answer: C
Question: If S + A < S - A < A - S, which of the following is correct?
Options:
A)A < S < 0.
B)S < A < 0.
C)S < 0 < A.
D)0 < B < A.
E)B > A > 0.
Rationale: Check first inequality
S + A < S - A
A<-A
A is -ve
Check another equality
S - A < A - S
-2A<-2S
A>S
Combining both 0>A>S
Option B fits only
Ans B
Answer: B
Question: A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Dollar 5400 interest only for the period. The principal amount borrowed by him was:
Options:
A)Dollar 2000
B)Dollar 10,000
C)Dollar 15,000
D)Dollar 20,000
E)None of these
Rationale: Explanation: Principal = Dollar (100 x 5400)/(12x3) = Dollar 15000.
Answer: Option C
Answer: C