divelab/Sys2Bench huggingface dataset:
Question: In a mixture 60 litres, the ratio of milk and water 2 : 1. If the this ratio is to be 1 : 2, then the quanity of water to be further added is
Options:
A)20 liters
B)30 liters
C)50 liters
D)60 liters
E)None of these
Rationale: Explanation:
Quantity of Milk = 60*(2/3) = 40 liters
Quantity of water = 60-40 = 20 liters
As per question we need to add water to get quantity 2:1
=> 40/(20+x) = 1/2
=> 20 + x = 80
=> x = 60 liters
Option D
Answer: D
Question: A boy rides his bicycle 10 km at an average speed of 12 km/hr and again travels 12 km at an average speed of 10 km/hr. His average speed for the entire trip is approximately.
Options:
A)10.2 km/hr
B)10.4 km/hr
C)10.6 km/hr
D)10.8 km/hr
E)None of these
Rationale: Explanation :
Total distance traveled = (10+12) km = 22 km
Total time taken = [10/12 + 12/10] hrs = 61/30 hrs
Average speed = [22*30/61] km/hr = 10.8 km/hr.
Answer : D
Answer: D
Question: What distance (in meters) will be covered by a bus moving at 72 km/hr in 40 seconds?
Options:
A)740
B)800
C)860
D)920
E)980
Rationale: 72 km/hr = 72 * 5/18 = 20 m/s
distance = 20 * 40 = 800 meters
The answer is B.
Answer: B
Question: In a certain game there are 6 steps, referred to as step 1, step 2, and so on with the final step being step 6. The steps are played one after the other. In each step a score of 1, 2, 3, 4, or 5 is obtained. Roslin played the game, getting at least one score of each of 1, 2, 3, 4, and 5, and never getting the same score in consecutive steps. What is the greatest possible score that Roslin could have gotten?
Options:
A)30
B)25
C)20
D)15
E)10
Rationale: There are two conditions:
1. Roslin got at least one score of each of 1, 2, 3, 4, and 5.
2. She never got the same score in consecutive steps.
Taking that into account, the greatest possible score that Roslin could have gotten is 5 + 1 + 5 + 2 + 5 + 3 + 5 + 4 = 30.
Answer: A.
Answer: A
Question: How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
Options:
A)200
B)300
C)500
D)600
E)700
Rationale: Let length of tunnel is x meter
Distance = 800+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
800+x = (65/3) * 60
800+x = 20 * 65 = 1300
x = 1300 - 800 = 500 meters
Answer: Option C
Answer: C
Question: At a local beach, the ratio of little dogs to average dogs to enormous dogs is 2:5:8. Late in the afternoon, the ratio of little dogs to average dogs doubles and the ratio of little dogs to enormous dogs increases. If the new percentage of little dogs and the new percentage of average dogs are both integers and there are fewer than 30 total dogs at the beach, which of the following represents a possible new percentage of enormous dogs?
Options:
A)25%
B)40%
C)50%
D)55%
E)70%
Rationale: Little Dogs(L), Average Dogs(A) and Enormous Dogs (E)
The initial ratio for L:A:E :: 2:5:8
Initial Total dogs = 15X ( x assumed; 2+5+8= 15), Since the total dogs are less than 30 therefore initial total value has to be 15
L = 2, A = 5 E = 8
L:A= 2:5
This ratio doubles
Hence New Dog count is
L= 4 , A = 5 E= X: Also 4+5+x<30
We need to Find X*100/(4+5+X)
Now it says that new percentage of little dogs and Average dogs is an integer
%L = 4*100/(9+x) %A = 5*100/(9+x); Only Value for X is 11 ; 9+x<30 and % integer
Therefore, Enormous Dogs % is = 11*100/(20) = 55%
ANSWER:D
Answer: D
Question: The perimeter of a rhombus is 52 units. One of its diagonal is 24 units. What is its second diagonals length?
Options:
A)5
B)10
C)15
D)20
E)25
Rationale: When the perimeter of a triangle is 52 units each side is 13 units
Next, the diagonal of a rhombus bisect each other at 90 degree
Thus the half of the diagonal is 12 units
Now in a right angle triangle so formed, the perpendicular is 12 and the hypptenuse is 13(that is the side of the triangle)
Finding the base(which is half of the other diagonal):
13^2-12^2 =25
Thus half of the diagonal is 5 and the diagonaL IS 10UNITS
ANSWER:B
Answer: B
Question: In order to obtain an income of Rs. 500 from 30% stock at Rs. 90, one must make an investment of
Options:
A)Rs.1550
B)Rs.1430
C)Rs.1450
D)Rs.1400
E)Rs.1500
Rationale: Explanation :
Market Value = Rs. 90
Required Income = Rs. 500.
Here face value is not given. Take face value as Rs.100 if it is not given in the question
To obtain Rs.30 (ie,30% of the face value 100), investment = Rs.90
To obtain Rs.15000, investment = 90/30Ã—500=Rs.1500
Answer : Option E
Answer: E
Question: An ice cream store received shipments of ingredients on Tuesday and Wednesday. Tuesday's shipment had 3 different packages, with an average (arithmetic mean) of 10 and 2/3 pounds. Wednesday's shipment included 7 packages, weighing an average of 8 and 3/7 pounds. What was the average package weight, in pounds, of the shipments received on both days?
Options:
A)9 pounds
B)10 and 1/10 pounds
C)10 and 2/5 pounds
D)11 pounds
E)11 and 1/7 pounds
Rationale: Solution: Average weight = Total weight/number of packages. The total weight on Tuesday was 3 * (10 and 2/3 pounds), or 35 pounds. The total weight on Wednesday was 7 * (8 and 3/7 pounds), or 66 pounds. The sum of the weights for both days is 59 + 32, or 101 pounds. The average is 91 pounds/10 packages, or 9 pounds per package.
Correct answer: A
Answer: A
Question: A box contains nine slips that are each labeled with one number: 1, 2, 3, 5, 8, 21, 34 and 55. Two of the slips are drawn at random from the box without replacement. What is the probability that the sum of the numbers on the two slips is equal to one of the numbers left in the box?
Options:
A)7/72
B)1/6
C)1/7
D)15/36
E)21/36
Rationale: Probability = No: of desired outcomes / Total No: of outcomes.
You are picking two slips out of 8 slips. So
Total No: of outcomes = 8C2 = 28
Desired outcome : sum of the numbers on the two slips is equal to one of the numbers left in the box. How many such outcomes are there?
If you look at the numbers closely, you will see that the following pair of numbers will give you the desired outcome.
(1,2) (2,3) (3,5) (21,34) . There are 4 such pairs. If the two numbers which I pick is from any of these 4 pairs, then I get my desired outcome.
So No: of desired outcomes = 4
Probability = 4/28=1/7
Answer :C
Answer: C
Question: A truck uses 60-gallon fuel tank wants to travel to Cleveland, which is 480 miles away. The driver recognizes that the current engine, which can travel only 10 miles per gallon, will not get him there. By how many miles per gallon of fuel efficiency be improved to make the truck to Cleveland possible?
Options:
A)2
B)6
C)8
D)5
E)4
Rationale: Actual miles/gallon is = 480/60 = 8 miles/gallon.
Current engine miles/gallon is 10 miles/gallon.
Additional 2 miles/gallon is required to match the actual mileage.
ANSWER:A
Answer: A
Question: The entire contents of a full sack of flour can be used to make 15 cupcakes and 8 pizzas. The same full sack of flour can be used to make 6 cupcakes and 14 pizzas. If a full sack of flour is used to make only pizzas, how many pizzas can be made?
Options:
A)18 1/4
B)18 1/2
C)18 3/4
D)18
E)19 1/4
Rationale: 15x+8y=6x+14y
x=2/3y. Answer D
Answer: D
Question: How much is 65% of 40 is greater than 4/5 of 25?
Options:
A)29
B)776
C)66
D)12
E)6
Rationale: (65/100) * 40 – (4/5) * 25
26 - 20 = 6
Answer: E
Answer: E
Question: A and B together have Sterling 1250. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does B have?
Options:
A)Sterling 460
B)Sterling 484
C)Sterling 500
D)Sterling 664
E)None
Rationale: Explanation: 4/15A = 2/5B
A = (2/5 x 15/4)B
A = 3/2 B
A/B = 3/2
A : B = 3 : 2.
B's share = Sterling (1250 x 2/5) = Sterling 500.
Answer: Option C
Answer: C
Question: At a party, there were two times as many females as males and same times as many adults as children. Which of the following could NOT be the number of people at the party?
Options:
A)384
B)258
C)216
D)121
E)72
Rationale: Five times as many females as males --> F = 2M.
Three times as many adults as children --> (F + M) = C.
The number of people at the party = F + M + C = C + C = 2C.
The number of people at the party must be a multiple of 2. The only answer choice which is NOT a multiple of 4 is 2.
Answer: D.
Answer: D
Question: A cistern can be filled by a tap in 5 hours while it can be emptied by another tap in 10hours. If both the taps are opened simultaneously then after how much time will the cistern get filled?
Options:
A)20hr
B)10hr
C)5hr
D)4hr
E)15hr
Rationale: Net part filled in 1 hour 1/5 - 1/10 = 1/10
The cistern will be filled in 10hr
Answer is B
Answer: B
Question: Tom is having a cookout. 9 people want steak, 27 people want grilled chicken breast, and 13 people want bratwurst. Each steak cost $21.00, each chicken breast cost $3.24, and each bratwurst cost $4.30. What is the average price per piece of meat Tom paid?
Options:
A)$332.38
B)$6.78
C)14.74
D)28.54
E)9.51
Rationale: Explanation:
9 27 13
$21.00 $3.24 $4.30
$189.00 + $87.48 + $55.90 = $332.38/49 = $6.78
B
Answer: B
Question: If the sum of three consecutive positive integers is A, then the sum of the next five consecutive integers in terms of A is:
Options:
A)3A+5
B)3A/5
C)3A/5 + 12
D)5A/3
E)5A/3 + 20
Rationale: In Case of Consecutive Integers or Integers in Arithmetic Progression Mean = Median
I.e. Median = A/3 = Mean = Second Integer
First Integer = A/3 - 1
Second Integer = A/3
Third Integer = A/3 + 1
I.e.
Fourth Integer = A/3 + 2
Fifth Integer = A/3 + 3
Sixth Integer = A/3 + 4
Seventh Integer = A/3 + 5
Eighth Integer = A/3 + 6
Now Mean of next 5 Integers = Median = A/3 + 4
i.e. Sum of Next 5 integers = (A/3 + 4)*5 = 5A/3 +20
Answer: option E
Answer: E
Question: Jim’s Taxi Service charges an initial fee of $2.35 at the beginning of a trip and an additional charge of $0.35 for each 2/5 of a mile traveled. What is the total charge for a trip of 3.6 miles?
Options:
A)$3.15
B)$4.45
C)$4.80
D)$5.5
E)$5.40
Rationale: Let the fixed charge of Jim’s Taxi Service = 2.35 $
and charge per 2/5 mile(.4 mile) = .35$
Total charge for a trip of 3.6 miles = 2.35 + (3.6/.4) * .35
= 2.35 + 9*.35
= 5.5 $
Answer D
Answer: D
Question: Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
Options:
A)9
B)10
C)12
D)16
E)20
Rationale: Due to stoppages, it covers 9 km less.
Time taken to cover 9 km = 9/54	x 60	min	= 10 min.
Answer: B
Answer: B
Question: Four staff members at a certain company worked on a project. The amounts of time that the four staff members worked on the project were in the ratio 2 to 3 to 5 to 6. If one of the four staff members worked on the project for 90 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project?
Options:
A)720
B)480
C)288
D)192
E)240
Rationale: Four members worked in ration 2:3:5:6, hence as everyone mentioned, individual work could be taken as 2x, 3x,5x, and 6x. Also this gives us total work as 16x.
But we are told that one of these individual works is 90hrs. hence, possible scenarios, if
(1)2x =90 => 16x = 720 (2) 3x =90 => 16x = 480 (3) 5x =90 => 16x = 288 (4) 6x =90 => 16x = 240
Hence Answer is D 192 which can not be any of these.
Answer: D
Question: Man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:
Options:
A)20
B)22
C)12
D)15
E)17
Rationale: consider x = x+24
x+24 + 2 = 2(x+2)
x+26=2x+4
x=22
ANSWER B
Answer: B
Question: UBA Capital recently bought Brand new vehicles for office use. UBA capital only went for Toyota and Honda and bought more of Toyota than Honda at the ratio of 4:6. If 40% of the Toyota bought and 60% of the Honda bought were SUVÃ¢â‚¬â„¢s. How many SUVÃ¢â‚¬â„¢s did UBA capital buy in the aforementioned purchase?
Options:
A)66%
B)64%
C)68%
D)69%
E)52%
Rationale: let total no of Vehicles bought be 100, Toyota 40 and Honda 60, so total number of SUV's bought for Toyota and Honda respectively 40* 40/100=16 and 60* 60/100=36
so total 52 SUV's were bought out of 100 Vehicles bought..so required % is 52%
ANSWER:E
Answer: E
Question: In what time will a railway train 60 m long moving at the rate of 36 kmph pass a telegraph post on its way?
Options:
A)5 sec
B)4 sec
C)3 sec
D)6 sec
E)1 sec
Rationale: T = 60/36 * 18/5 = 6 sec
Answer: D
Answer: D
Question: A can do a work in 6 days , B can do a work in 8 days and C can do it in 12 days. B left work after 2 days. For how many number of days should A and C should work together to complete the remaining work ?
Options:
A)1/2
B)2/3
C)1/3
D)4/3
E)5/2
Rationale: b work 1/8 * 2=1/4
remaining work =1-1/4=3/4
a and c work together =1/6+1/12=3/12=1/4
take reciprocal 3/4 * remaining work =4/3 *1/4=1/3
ANSWER:C
Answer: C
Question: There are some pigeons and hares in a zoo. If heads are counted, there are 200. If legs are counted, there are 680. The number of hares in the zoo is?
Options:
A)90
B)99
C)77
D)140
E)221
Rationale: 200*2 = 400
680
-----
280
1----2
?----280 =140
Answer:D
Answer: D
Question: Find the sum of first 89 odd numbers
Options:
A)7921
B)4800
C)7900
D)4980
E)4960
Rationale: Explanation:
n2 = 892 = 7921
Answer: Option A
Answer: A
Question: What number should replace the question mark?
123, 124, 126, 132, 133, 136, 142, 143, 147, ?
Options:
A)154
B)634
C)165
D)134
E)164
Rationale: A
154
Add the first digit to arrive at the second number i.e. 123 + 1 = 124, then the second digit i.e. 124 + 2 = 126, then the third digit etc.
Answer: A
Question: Statement: An amount of money was lent for 3yrs. What will be the difference between the simple and the CI earned on it at the same rate?
Conclusion:
1) The rate of interest was 8 p.c.p.a.
2) The total amount of simple interest was Rs. 1200
Options:
A)I alone sufficient while II alone not sufficient to answer
B)II alone sufficient while I alone not sufficient to answer
C)Either I or II alone sufficient to answer
D)Both I and II are not sufficient to answer
E)Both I and II are necessary to answer
Rationale: Given: T = 3 years.
I. gives: R = 8% p.a.
II. gives: S.I. = Rs. 1200.
Thus, P = Rs. 5000, R = 8% p.a. and T = 3 years.
Difference between C.I. and S.I. may be obtained.
So, the correct answer is (E).
Answer: E
Question: A mobile battery in 1 hour charges to 20 percent.How much time (in minute) will it require more to charge to 50 percent.
Options:
A)145
B)150
C)175
D)160
E)130
Rationale: 1 hr =20 percent.Thus 15 min=5 percent .Now to charge 50 percent 150 min.Answer:B
Answer: B
Question: The annual interest rate earned by an investment increased by 8 percent from last year to this year. If the annual interest rate earned by the investment this year was 27 percent, what was the annual interest rate last year?
Options:
A)22%
B)20%
C)25%
D)23%
E)21%
Rationale: let i = interest rate
i(this year) = i(last year) + 0.08i(last year) = 1.08i(last year)
27 = 1.08 x i(last year)
i(last year) = 27/1.08= 2700/108 = 25%
Answer : C
Answer: C
Question: A start walking from a place at a uniform speed of 6 kmph in a particular direction. After half an hour, B starts from the same place and walks in the same direction as A at a uniform speed and overtakes A after 1 hour 48 minutes. Find the speed of B.
Options:
A)4.7 kmph
B)6.6 kmph
C)4 kmph
D)7 kmph
E)5.3 kmph
Rationale: Distance covered by A in 30 min = 1 Km
B covers extra 1km in 1 hour 48 minutes (9/5 hr)
i.e. Relative speed of B over A = 1/(9/5) = 5/9
So the speed of B = Speed of A + 5/9
= 6 + 5/9
= 6.55
Answer B
Answer: B
Question: A circle graph shows how the MegaTech corporation allocates its Research and Development budget: 14% microphotonics; 19% home electronics; 10% food additives; 24% genetically modified microorganisms; 8% industrial lubricants; and the remainder for basic astrophysics. If the arc of each sector of the graph is proportional to the percentage of the budget it represents, how many degrees of the circle are used to represent basic astrophysics research?
Options:
A)8°
B)90°
C)18°
D)36°
E)52°
Rationale: 14% microphotonics;
19% home electronics;
10% food additives;
24% genetically modified microorganisms;
8% industrial lubricants;
100-(14+19+10+24+8)=25% basic astrophysics.
25% of 360° is 90°.
Answer: B.
Answer: B
Question: The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
Options:
A)65 cm2
B)85 cm2
C)11 cm2
D)15 cm2
E)35 cm2
Rationale: Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 2.5 * 28/2
= 35 cm2
Answer: E
Answer: E
Question: Three numbers are in the ratio 1:2:4 and their H.C.F is 6. The numbers are?
Options:
A)6, 12, 30
B)6, 12, 32
C)6, 18, 24
D)6, 12, 28
E)6, 12, 24
Rationale: Let the required numbers be x, 2x and 4x. Then, their H.C.F = x. So, x = 6.
The numbers are 6, 12, 24.
Answer: E
Answer: E
Question: A train 180 m long is running with a speed of 54 km per hour. In what time will it pass a telegraph post?
Options:
A)11 s
B)10 s
C)7 s
D)12 s
E)None of these
Rationale: We know from the formula Time = Distance/ Speed
Thus, Time = 180/ 54 x 5/18
or, Time = 12 sec.
ANSWER:D
Answer: D
Question: The income of a company increases 30% per annum. If its income is Rs 26,64,000 in the year 1999, what was its income in the year 1997?
Options:
A)Rs.15,68,542
B)Rs.16,55,423
C)Rs.15,76,331
D)Rs.16,76,331
E)none of these
Rationale: We have P = 2664000, R = 30 and n = 2
Therefore Company’s income in 1977
= P/(1 + (R/100))n = 2664000/(1 + (30/100))2
= Rs 15,76,331.
ANSWER:C
Answer: C
Question: A certain number of horses and an equal number of men are going somewhere. Half of the owners are on their horses' back while the remaining ones are walking along leading their horses. If the number of legs walking on the ground is 50, how many horses are there ?
Options:
A)10
B)12
C)14
D)16
E)18
Rationale: legs 10*4 = 40
now half on their horses so remaining on the walk so 5 men
5 men has 10 legs
so, 10+ 40 = 50 legs walking
ANSWER:A
Answer: A
Question: There are 44 students in a hostel, due to the administration, 15 new students has joined. The expense of the mess increase by Rs. 33 per day. While the average expenditure per head diminished by Rs. 3, what was the original expenditure of the mess ?
Options:
A)Rs. 612
B)Rs. 611
C)Rs. 610
D)Rs. 616
E)Rs. 615
Rationale: Let the average expenditure per head be Rs. p
Now, the expenditure of the mess for old students is Rs. 44p
After joining of 15 more students, the average expenditure per head is decreased by Rs. 3 => p-3
Here, given the expenditure of the mess for (44+15 = 59) students is increased by Rs. 33
Therefore, 59(p-3) = 44p + 33
59p - 177 = 44p + 33
15p = 210
=> p = 14
Thus, the expenditure of the mess for old students is Rs. 44p = 44 x 14 = Rs. 616.
Answer: D
Answer: D
Question: The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1.30 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost?
Options:
A)399
B)272
C)865.8
D)277
E)311
Rationale: Answer: Option C
Explanation:
a2 = 3136 => a = 56
56 * 4 * 3 = 672 â€“ 6 = 666 * 1.3 = 865.8 Answer: C
Answer: C
Question: A library has an average of 510 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is:
Options:
A)250
B)276
C)280
D)285
E)295
Rationale: Explanation:
Since the month begins with a Sunday, to there will be five Sundays in the month.
Required average = (510 × 5 + 240 × 25/30)
= 8550/30
= 285
Answer: D
Answer: D
Question: A group of 6 children and 10 adults are going to the zoo. Child tickets cost $10, and adult tickets cost $16. How much will the zoo tickets cost in all?
Options:
A)$220
B)$340
C)$150
D)$100
E)$120
Rationale: Step 1: Find the cost of the children's tickets.
6 × $10 = $60
Step 2: Find the cost of the adults' tickets.
10 × $16 = $160
Step 3: Find the total cost.
$60 + $160 = $220
The zoo tickets will cost $220.
Answer is A.
Answer: A
Question: A cistern has three pipes, A, B and C. The pipes A and B can fill it in 3 and 4 hours respectively and C can empty it in 2 hours. If the pipes are opened in order at 1, 2 and 3 A.M. When will the cistern be empty?
Options:
A)1 PM
B)5 PM
C)4 PM
D)3 PM
E)2 PM
Rationale: 1 to 2 = 1/3
2 to 3 = 1/3 + 1/4 = 7/12
After 3 AM = 1/3 + 1/4 - 1/2 = 1/12
1/3 + 7/12 = 11/12
1 h ---- 1/12
? ----- 11/12
11 hours ==> 2 PM
Answer:E
Answer: E
Question: what is a percent of b divided by b percent of a?
Options:
A)100
B)10
C)1
D)a
E)b
Rationale: a percent of b=>ab/100
b percent of a=>ba/100
a percent of b divided by b percent of a=>(ab/100)/(ba/100)
=>1
ANSWER:C
Answer: C
Question: A and B invests Rs.3000 and Rs.6500 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit?
Options:
A)8:8
B)9:8
C)9:6
D)9:5
E)9:13
Rationale: (3*6 + 6*6): (6.5*12)
54:78 => 9:13
Answer: E
Answer: E
Question: If 1/a^2 + a^2 represents the diameter of circle O and 1/a + 2a = 3, which of the following best approximates the circumference of circle O?
Options:
A)28
B)22
C)20
D)16
E)12
Rationale: Given that (1/a)+a =3
Square both sides of the equation:
We get,
[(1/a)^2 + a^2 + 2*(1/a)*a] = 9
=> (1/a)^2 + a^2 + 2 = 9
=> (1/a)^2 + a^2 = 7 ----------------- (1)
Diameter D = (1/a)^2 + a^2
= 7 (From (1))
So Radius = D/2 = 7/2
Circumference = 2*Pi*r
= 2*(22/7)*(7/2)
=16
So the answer should be D.
Answer: D
Question: The contents of a certain box consist of 48 apples and 30 kiwis. How many kiwis must be added to the box so that exactly 30% of the pieces of fruit in the box will be apples?
Options:
A)90
B)72
C)82
D)54
E)65
Rationale: apple = (apple + kiwi + x)*0.3
48 = (30 + 48 + x)*0.3
x = 82
Answer: C
Answer: C
Question: 3 letters have to be put into their 3 respective envelopes. If the letters are inserted randomly into the envelopes, what is the probability that all the letters go into their respective envelopes?
Options:
A)1/30
B)1/6
C)1/120
D)1/240
E)3/5
Rationale: A-B-C-D-E (envelopes)
a-b-c-d-e (letters)
3 letters (a, b, c, d, and e) can be assigned to 3 envelopes (arranged) in 3! ways, out of which only one will be correct, thus the probability is 1/3! = 1/6.
Answer: B.
Answer: B
Question: A number is said to be prime saturated if the product of all the different positive prime factors of a is less than the square root of a. What is the greatest two digit prime saturated integer ?
Options:
A)99
B)98
C)97
D)96
E)95
Rationale: Clearly D A number is said to be prime saturated if the product of all the different positive prime factors of a is less than the square root of a.
96 has more number of smaller prime factor thats the clue !!=D
Answer: D
Question: If x-1 – 1 is divided by x - 1 the quotient is:
Options:
A)1
B)1/(x-1)
C)- 1/(x-1)
D)1/x,
E)– 1/x
Rationale: Solution:
x-1 – 1 is divided by (x – 1)
= x-1 – 1 × 1/(x-1)
= 1/x – 1 × 1/(x-1)
= (1 – x/x) × 1/(x-1)
= - (1 – x)/x × 1/(x-1)
= – 1/x [cancel x – 1 from the numerator and denominator].
Answer: E
Answer: E
Question: Two trains of equal are running on parallel lines in the same direction at 44 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is?
Options:
A)40 m
B)72 m
C)80 m
D)82 m
E)84 m
Rationale: Let the length of each train be x m.
Then, distance covered = 2x m.
Relative speed = 44 - 36 = 8 km/hr.
= 8 * 5/18 = 20/9 m/sec.
2x/36 = 20/9 => x = 40.
ANSWER:A
Answer: A
Question: If two sides of a triangle are 5 and 12, respectively, which of the following could NOT be the area of this triangle?
Options:
A)1
B)6
C)38
D)29
E)17
Rationale: For this question it would be helpful to know the largest area that this triangle could be, given the two sides of 5 and 12.
We know that the area of a triangle will be maximized when two sides are perpendicular to each other (consult Bunuel's drawing above). Thus we have a max area being equal to one half the base times the height, either (.5)12 * 5 -or- (.5)5 * 12 will result in a maximum area of 30 for the triangle; therefore, the triangle could never have an area of 38.
C
Answer: C