divelab/Sys2Bench huggingface dataset:
Question: There is certain numbers of toys in the box. They are divided into such a way that the person who gets 1/4 of the whole gets thrice of what the others get on an average. Find the number of people amongst whom the toys are distributed?
Options:
A)8
B)10
C)12
D)9
E)4
Rationale: Explanation:
If the person who gets 1/4 of the whole gets thrice of what the others get on an average,
each one will get =1/3×1/4=112 of the whole.
Therefore, if there are k persons other than the person who gets one-fourth, then
1/4 + k/12 = 1
⇒ k=9
Hence, total number of people = 10.
Answer: B
Answer: B
Question: In what ratio water be mixed with milk costing Rs.12 per liter to obtain a mixture worth of Rs.8 per litre?
Options:
A)2:7
B)1:2
C)2:9
D)2:2
E)2:6
Rationale: Answer with Explanation: By the rule of allegation, i. C.P of 1 liter of water = 0 ii. C.P of 1 liter of milk = 12 iii. Mean price (p) = 8 iv. d – m = 12-8 = 4 v. m – c = 8-0 = 8  Ratio of water and milk = 4 : 8 = 1 : 2
Answer:B
Answer: B
Question: 9, 16, 20, 25, 36,49
Options:
A)9
B)16
C)20
D)25
E)36
Rationale: Each of the numbers except 20, is perfect square.
Answer: Option C
Answer: C
Question: The average of 7 numbers is 23. If each number be multiplied by 5. Find the average of new set of numbers?
Options:
A)A)110
B)B)122
C)C)120
D)D)115
E)E)145
Rationale: Explanation:
Average of new numbers = 23 * 5 = 115
Answer: Option D
Answer: D
Question: Tom read a book containing 100 pages by reading the same number of pages each day. If he would have finished the book 10 days earlier by reading 30 pages a day more, how many days did Tom spend reading the book?
Options:
A)7
B)7.68
C)8
D)9
E)10
Rationale: Actually u can set up 2 equation
P--stands for the pages
D--stands for the days
1) P*D=100 (we want to find the Days, soP=100/D)
2) (P+30)(D-10)=100 => PD-10P+30D-300=100
as the 1) stated u can put 1) into 2)
=> 100-10P+30D-300=100 => 30D-10P=100
put the bold one into it => 30D-10(100/D)=100
the we get the final equation 30D^2-1000=100D (divide 16)
=> D^2-5D-150=0
(D-15)(D+10)=0 so D=7.68 days. Ans:( B)
Answer: B
Question: Annie has 100 cards numbered 1 through 100. If she deals four cards to Alex, without replacing any of them, what is the probability that Alex will get five consecutive numbers?
Options:
A)95!/100!
B)96!/100!
C)(95! X 5!)/100!
D)(96! X 5!)/100!
E)(97! X 4!)/100!
Rationale: Alex to get 4 consecutive cards in ascending order, to have 4 consecutive at the end is good enough.
There are 97 consecutive numbers in 100: {1, 2, 3, 4, }, {2, 3, 4, 5}, ..., { 97, 98, 99, 100};{4!*97!}{100!}.
Answer: E.
Answer: E
Question: Two persons A and B take a field on rent. A puts on it 21 horses for 3 months and 15 cows for 2 months; B puts 15 cows for 6months and 40 sheep for 7 1/2 months. If one day, 3 horses eat as much as 5 cows and 6 cows as much as 10 sheep, what part of the rent should A pay?
Options:
A)1/3
B)1/5
C)1/4
D)1/2
E)1/1
Rationale: 3h = 5c
6c = 10s
A = 21h*3 + 15c*2
= 63h + 30c
= 105c + 30c = 135c
B = 15c*6 + 40s*7 1/2
= 90c + 300s
= 90c + 180c = 270c
A:B = 135:270
27:52
A = 27/79 = 1/3
Answer: A
Answer: A
Question: How many cubes of 4cm edge can be cut out of a cube of 28cm edge
Options:
A)343
B)232
C)216
D)484
E)None of these
Rationale: Explanation:
number of cubes=(28 x 28 x 28) / (4 x 4 x 4) = 343
Answer: A
Answer: A
Question: When the price of an article was reduced by 25% its sale increased by 80%. What was the net effect on the sale?
Options:
A)35% increase
B)44% decrease
C)60% increase
D)66% increase
E)66% decrease
Rationale: if n items are sold for $p each, revenue is $np. If we reduce the price by 25%, the new price is 0.75p. If we increase the number sold by 80%, the new number sold is 1.8n. So the new revenue is (0.75p)(1.8n) = 1.35np, which is 1.35 times the old revenue, so is 35% greater.
ANSWER:A
Answer: A
Question: The number of positive integers which can be formed by using any number of digits from 0,1,2,3,4,5 without repetition.
Options:
A)1200
B)1500
C)1600
D)1630
E)None
Rationale: Solution: One digit positive numbers = 5.
Two digit positive numbers = 25.
Three digit positive numbers = 100.
4 digit positive numbers = 300.
5 digit positive numbers = 600.
Six digit positive numbers = 600.
Total positive numbers,
= 5+25+100+300+600+600
= 1630.
Answer: Option D
Answer: D
Question: A sum of money at simple interest amounts to Rs. 855 in 3 years and to Rs. 854 in 4 years. The sum is:
Options:
A)s. 650
B)s. 690
C)s. 738
D)s. 700
E)s. 718
Rationale: S.I. for 1 year = Rs. (854 - 815) = Rs. 39.
S.I. for 3 years = Rs.(39 x 3) = Rs. 117.
Principal = Rs. (855 - 117) = Rs. 738.
Answer: Option C
Answer: C
Question: In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?
Options:
A)1
B)2/7
C)1/7
D)2/5
E)2
Rationale: P (getting a prize) = 10/(10 + 25) = 10/35
= 2/7
Hence Answer is B
Answer: B
Question: To fill an art exhibit, the ladies in an art course are assigned to create one piece of artwork each in the following distribution: 1/3 are sculptures, 1/8 are oil paintings, 1/2 are watercolors, and the remaining 10 pieces are mosaics. How many ladies are in the art class?
Options:
A)80
B)120
C)240
D)320
E)400
Rationale: Let the total number of ladies in the art class = s
Distribution of artwork is as
1/3 are sculptures
1/8 are oil paintings
1/2 are watercolors, and the remaining 10 pieces are mosaics
(1/3)s +(1/8)s +(1/2)s + 10 = s
Since remaining 10 pieces are mosaics , (1/24)s = 10
s = 240
Answer C
Answer: C
Question: A rectangular field has area equal to 150 sq m and perimeter 50 m. Its length and breadth must be?
Options:
A)12 m, 10 m
B)13 m, 12 m
C)14 m, 11 m
D)15 m, 10 m
E)15 m, 12 m
Rationale: lb = 150
2(l + b) = 50 => l + b = 25
l – b = 5
l = 15 b = 10
ANSWER:D
Answer: D
Question: A train 200m long passes a standing man in 18 seconds. What is the speed of the train?
Options:
A)30km/hr
B)40km/hr
C)42km/hr
D)50km/hr
E)32km/hr
Rationale: Speed of the train = 200/18* 18/5 = 40km/hr
Answer is B
Answer: B
Question: Hiralal gave a loan of Rs. 20 to Ramlal and recovered it at the rate of Rs 3.50 for eight months, commencing from the end of 1st month. What is the effective rate of simple interest?
Options:
A)60%
B)80%
C)20%
D)90%
E)none
Rationale: Explanation:
Principal = Rs 20
Amount = Rs 3.50 x 8 = Rs 28
Interest = Rs 28 - Rs 20 = Rs 8
Time = 8 months = 8/12 years
8 = 20×8×r/12×100
r = 12×100/20 = 60% p.a.
Answer A
Answer: A
Question: A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is
Options:
A)720
B)900
C)1200
D)1800
E)None
Rationale: Solution
2(15 + 12) ×h	= 2(15 x 12)
‹=›h= 180/27 m
= 20/3m
Volume	= (15×12×20/3)m3
‹=›1200 m3.
Answer C
Answer: C
Question: Find a number such that when 15 is subtracted from 7 times the number, the results is more than twice the number?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: Solution
Let the number be x.	= Then, 7x-15 = 2x+10
= 5x = 25
‹=›x = 5.
Hence the required number is 5.
Answer D
Answer: D
Question: Given that a “6-inch pizza” means circular pizza with a diameter of 12 inches, changing from an 4-inch pizza to a 6-inch pizza gives you approximately what percent increase in the total amount of pizza?
Options:
A)33
B)50
C)67
D)80
E)125
Rationale: area of 4 inch pizza= 2*2*pi=4 pi
area of 6 inch pizza =3*3*pi=9 pi
5/4*100=125% increase
hence answer is E
Answer: E
Question: The figure above shows the dimensions of a semicircular cross section of a one-way tunnel. The single traffic lane is 12 feet wide and is equidistant from the sides of the tunnel. If vehicles must clear the top of the tunnel by at least ½ foot when they are inside the traffic lane, what should be the limit Y on the height of vehicles that are allowed to use the tunnel?
Options:
A)5½ ft
B)7½ ft
C)8 ½ ft
D)9½ ft
E)10 ft
Rationale: Let's label the midpoint of the circle O. Since the base of the semi-circle is 20, we know that the diameter is 20 and, accordingly, the radius is 10.
We also know that the traffic lane is 12 feet long and there's an equal amount of space on either side, so the traffic lane extends 6 feet on either side of O. Let's call the leftmost point on the base of the traffic lane A. So, the distance OA is 6.
Now draw a line straight up from A to the top of the tunnel. Let's label the point at which the line intersects the circle B. The answer to the question will, therefore, be the height AB - .5 feet (we need to leave .5 feet of clearance).
Here's the key to solving the question: if we draw a line from O to B, that line is a radius of the circle and, therefore, has length 10. We now have right triangle OAB (the right angle is at point A), with leg OA=6 and hypotenuse OB=10. We can now solve for leg AB=8 (either by applying the pythagorean theorum or by applying the 3/4/5 special right triangle ratio).
Finally: AB=8, so the correct answer YBis 8 - .5 = 7.5... choose (B)!
From a strategic guessing point of view, as soon as we realize that the height of the tunnel is 10 in the middle, we should quickly eliminate (D) and (E) as too big; worse case you have a 1/3 shot at picking up the points.B
Answer: B
Question: A rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?
Options:
A)2288
B)2779
C)2779
D)3900
E)2781
Rationale: Area = (l + b – d) d
(80 + 60 – 10)10 => 1300 m2
1300 * 3 = Rs.3900
Answer:D
Answer: D
Question: In doing a division of a question with zero remainder,a candidate
took 12 as divisor instead of 21.The quotient obtained by him was 35.
The correct quotient is?
Options:
A)12
B)21
C)20
D)35
E)10
Rationale: Dividend=12*35=420.
Now dividend =420 and divisor =21.
Therefore correct quotient =420/21=20.
ANSWER C 20
Answer: C
Question: A car drives 90 miles on local roads at 30 mph, and 75 miles on the highway at 60 mph, what is the average speed of the entire trip?
Options:
A)36 mph
B)40 mph
C)39 mph
D)42 mph
E)38 mph
Rationale: So The Answer is Plainly C....
we have a general relation for speed , time and distance : v (velocity) * t ( time)= d (distance)
for first part we have d=90 miles , and v= 30 mph so we can obtain time : 30*t = 90 Or t= 90/30 = 3 hours the needed time to cover 90 miles
in the same way we should divide 75 to 60 to find the needed time to cover 75 miles ,so t= 1.25 hours
so the total time for covering total distance would be 3+1.25 = 4.25 hours and total distance is 90+75= 165 miles
Final stage : average speed is total distance divide to total time : 165/4.25 = 38.8 miles per hour rounded up to 39 MPH....
Answer: C
Question: What amount does Kiran get if he invests Rs. 18000 at 15% p.a. simple interest for four years?
Options:
A)Rs. 28800
B)Rs. 28810
C)Rs. 28820
D)Rs. 28880
E)Rs. 28890
Rationale: Simple interest = (18000 * 4 * 15)/100 = Rs. 10800
Amount = P + I = 18000 + 10800 = Rs. 28800
Option A
Answer: A
Question: The price of gasoline in the area where the Smith family lives is scheduled to increase by 5% next year. Since the Smith family cannot afford an increase in their fuel bill, how much will they have to reduce consumption to keep their cost the same?
Options:
A)6.14%
B)None
C)5%
D)2.45%
E)4.76%
Rationale: Solution: Let the current fuel expense be represented by Rs. 100.
The cost of gasoline rises 5%. So, to buy same amount of fuel, they need to increase their expense,
= (100 + 5% of 100) = Rs. 105.
But, they want to keep fuel expense the same, so they have to cut Rs. by 5 to keep it to Rs. =100.
The % decrease in consumption is,
(5/105)*100 = 4.76%.
Mental Calculation Method;
100-----5%↑---→105------X%↓---→100.
Here, X = (5/105)*100 = 4.76%.
Answer: Option E
Answer: E
Question: In how many ways can three consonants and two vowels be selected from the letters of the word "TRIANGLE"?
Options:
A)76 ways
B)30 ways
C)16 ways
D)15 ways
E)19 ways
Rationale: The word contains five consonants. Three vowels, three consonants can be selected from five consonants in ⁵C₃ ways, two vowels can be selected from three vowels in ³C₂ ways.
3 consonants and 2 vowels can be selected in ⁵C₂ . ³C₂ ways i.e., 10 * 3
= 30 ways.
Answer:B
Answer: B
Question: Sam invested Rs. 3000 @ 10% per annum for one year. If the interest is compounded half-yearly, then the amount received by Sam at the end of the year will be?
Options:
A)2554.0
B)3387.0
C)2503.0
D)3307.5
E)16537.11
Rationale: P = Rs. 3000 ; R = 10% p.a. = 5% per half-year; T = 1 year
= 2 half-year
Amount = [3000 * (1 + 5/100)2]
= (3000 * 21/20 * 21/20)
= Rs.3307.50
Answer:D
Answer: D
Question: In how many different ways can the letters of the word 'CORPORATMON' be arranged so that the vowels always come together?
Options:
A)40000
B)50000
C)50400
D)50700
E)60000
Rationale: The word 'CORPORATMON' has 11 letters. It has the vowels 'O','O','A','M','O' in it and
these 5 vowels should always come together. Hence these 5 vowels can be grouped
and considered as a single letter. that is, CRPRTN(OOAMO).
Hence we can assume total letters as 7. But in these 7 letters, 'R' occurs 2 times and
rest of the letters are different.
Number of ways to arrange these letters = 7!2! = (7×6×5×4×3×2×1)/(2×1) = 2520
In the 5 vowels (OOAMO), 'O' occurs 3 and rest of the vowels are different.
Number of ways to arrange these vowels among themselves = 5!3! = (5×4×3×2×1)/(3×2×1) = 20
Hence, required number of ways = 2520 x 20 = 50400
C
Answer: C
Question: A car traveled from San Diego to San Francisco at an average speed of 51 miles per hour. If the journey back took twice as long, what was the average speed of the trip?
Options:
A)24.
B)34.
C)36.
D)42.
E)44.
Rationale: Let the time taken be = x
One way distance = 51x
Total distance traveled = 2 * 51x = 102x
Total time taken = x + 2x = 3x
Average speed = 102x/3x = 34
Answer: B
Answer: B
Question: Analyze the number square carefully and find out what number fits in place of question mark.
35	20	14
9	17	42
2	8	?
Options:
A)12
B)6
C)18
D)2
E)42
Rationale: 20 fits in place of question mark.
This is because (number in first column) / (number in second column) * 8 = number in third column.
Here (left number / middle number) * 8 = right number
(6
2/ 8) * 8 = 2*1= 2
D
Answer: D
Question: Three times the first of three consecutive odd integers is 6 more than twice the third. The third integer is:
Options:
A)9
B)11
C)13
D)15
E)18
Rationale: Let the three integers be x, x + 2 and x+ 4.
Then,
3x = 2(x + 4) + 6
x = 14
Third integer = x + 4 = 18.
ANSWER:E
Answer: E
Question: The cross-section of a cannel is a trapezium in shape. If the cannel is 12 m wide at the top and 8 m wide at the bottom and the area of cross-section is 690 sq m, the depth of cannel is?
Options:
A)39
B)28
C)27
D)69
E)71
Rationale: 1/2 * d (12 + 8) = 690
d = 69
Answer: D
Answer: D
Question: If each digit in the set of A = {1,2,3,4,5,6} is exactly used once, in how many ways can the digits be arranged such that the 2 and 5 are not adjacent?
Options:
A)4*5!
B)6! - 5!
C)6! / 5!
D)6!* 5!
E)6! - 4!
Rationale: The answer should be the (total arrangements) - (arrangements when 2 and 5 are adjacent).
The number of ways to arrange 6 units is 6!
If we think of 2 and 5 as one single unit, the number of arrangements is 5!
Note that 2 and 5 can have two arrangements, so we multiply by 2 to get 2*5!
The total number of valid arrangements is 6! - 2*5! = 6*5! - 2*5! = 4*5!
The answer is A.
Answer: A
Question: A part of Rs. 38800 is lent out at 6% per 6 months. The rest of the amount is lent out at 5% per annum after 1 year. The ratio of interest after 3 years from the time when first amount was lent out is 5:4. Find the second part that was lent out at 5%.
Options:
A)28800
B)27800
C)29800
D)26500
E)55055
Rationale: Let the 1st part that is lent out be x at 6%. then 2nd part will be (38800-x) at 5%.then the S.I1 of 1st part is (p*r*t)/100 = (x*6*6)/100 [t=6 becoz we r calculating till 3yrs & der is six 6months in 3yrs]
similarly S.I2 of 2nd part = {(38800-x)*5*2}/100 [t=2 since the 5% rate is to be calculated after the 1st year & per annum, so no. of years left is 2]therefore, S.I1/S.I2=5/4, by calculating it we get x=10000So, 2nd part is 38800-10000=28800
ANSWER:A
Answer: A
Question: A ranch has both horses and ponies. Exactly 5/7 of the ponies have horseshoes, and exactly 2/3 of the ponies with horseshoes are from Iceland. If there are 4 more horses than ponies, what is the minimum possible combined number of horses and ponies on the ranch?
Options:
A)34
B)38
C)42
D)46
E)50
Rationale: 5/7*P are ponies with horseshoes, so P is a multiple of 7.
2/3*5/7*P = 10/21*P are Icelandic ponies with horseshoes, so P is a multiple of 21.
The minimum value of P is 21. Then H = P+4 = 25.
The minimum number of horses and ponies is 46.
The answer is D.
Answer: D
Question: Find The Missing Number in this sequence ?
1, 2, 6, 42, ? 3263442
Options:
A)2000
B)1806
C)4580
D)3546
E)1239
Rationale: B
1806
each number is multiplied by the number+1
1x2 = 2
2x3 = 6
6x7 = 42
42x43 = 1806
1806x1807 = 3263442
Answer: B
Question: It takes a boat 3 hours to travel down a river from point A to point B, and 5 hours to travel up the river from B to A. How long would it take the same boat to go from A to B in still water?
Options:
A)2 hours and 45 minutes.
B)5 hours and 45 minutes.
C)3 hours and 45 minutes.
D)4 hours and 45 minutes.
E)6 hours and 45 minutes.
Rationale: Let: S be the speed of the boat in still water, r be the rate of the water current and d the distance between A and B.
d = 3(S + r) : boat traveling down river
d = 5(S - r) : boat traveling up river
3(S + r) = 5(S - r)
r = S / 4 : solve above equation for r
d = 3(S + S/4) : substitute r by S/4 in equation B
d / S = 3.75 hours = 3 hours and 45 minutes.
correct answer C
Answer: C
Question: A boy is born when his father is 27 years old. How old will he be when he is exactly half his fathers' age?
Options:
A)23
B)24
C)25
D)27
E)39
Rationale: when son born:
son s=0
father f=27.
after x years:
son s=x
father f=f+x=27+x:
according to given condition
son age is exactly half his fathers' age...so
x=(27+x)/2---solve this
son age is 27
ANSWER:D
Answer: D
Question: A rectangular floor is covered by a rug except fo a strip p meters along each of the four edges. If the floor is m meters by w meteres, What is the area of the rug in square meters?
Options:
A)mn - p(m+n)
B)mn – 2p(m+n)
C)mn – p^2
D)(m - p)(n - p)
E)(m - 2p)(w - 2p)
Rationale: The answer must be E.
Plug in M 100
w 50
P 10.
Answer: E
Question: What is the sum of all the prime numbers from 20 to 40?
Options:
A)279
B)100
C)278
D)120
E)191
Rationale: Explanation:
23 + 29 + 31 + 37 = 120
Answer: D
Answer: D
Question: a company has 17 office tasks 8 outdoor tasks and 7 misc. tasks for workers each worker can complete 4 tasks max what is he minimum number of workers required
Options:
A)6
B)7
C)8
D)9
E)10
Rationale: Total subjects = 17+8+7=32
Max tasks by 1 worker = 4
So, min of workers required = 32/4 = 8
ANSWER:C
Answer: C
Question: Without stoppages, a train travels certain distance with an average speed of 80 km/h, and with stoppages, it covers the same distance with an average speed of 60 km/h. How many minutes per hour the train stops ?
Options:
A)15
B)18
C)10
D)16
E)None of these
Rationale: Due to stoppages, it covers 20 km less .
Time taken to cover 20 km = 20⁄80h = 1⁄4h
= 1⁄4 × 60 min = 15 min
Answer A
Answer: A
Question: Which values of ‘x’ satisfies the inequality
x2 - 3x + 2 > 2x - 4 ?
Options:
A)2< x < 3
B)x > 3 or x < 2
C)x ³ 3
D)x £ 2
E)None of these
Rationale: Given expression is
x2 – 3x + 2 – 2x + 4 > 0
or, x2 – 5x + 6 > 0
or, x2 – 3x – 2x + 6 > 0
or, x(x – 3) – 2(x – 3) > 0
or, (x – 3)(x – 2) > 0
or, x > 3 or, x < 2
Answer B
Answer: B
Question: How many terms are in the G.P. 3, 6, 12, 24, ......., 96 ?
Options:
A)6
B)9
C)67
D)5
E)2
Rationale: Explanation:
Here a = 3 and r = 6/3 = 2. Let the number of terms be n.
Then, t = 96 => a * r^(n-1) = 96
=> 3 * 2^(n-1) = 96 => 2^(n-1) = 32 = 2^(5)
=> n-1 = 5 => n = 6
Answer: A
Answer: A
Question: (x —1)(x + 3) > 0
(x +5)(x—4) < 0
Which of the following values of x satisfy both inequalities shown?
I. -6
II. -4
III. 2
IV. 3
Options:
A)I and II only
B)I and III only
C)II and III only
D)II and IV only
E)II, III, and IV
Rationale: (x - 1)(x + 3) > 0 --> x<-3 or x>1.
(x + 5)(x - 4) < 0 --> -5<x<4.
Among choices only -4 and 2 satisfy both inequalities.
Answer: E.
Answer: E
Question: The speed of a boat in still water is 60kmph and the speed of the current is 15kmph. Find the speed downstream and upstream?
Options:
A)80,47 kmph
B)75,55 kmph
C)80,42 kmph
D)80,40 kmph
E)83,40 kmph
Rationale: Speed downstream = 60 + 15 = 75 kmph
Speed upstream = 60 - 15 = 55 kmph.Answer:B
Answer: B
Question: If James has to pay 12 % interest per year on an amount of $60,000 for 12 year then what is total principal?
Options:
A)52000
B)24000
C)25000
D)27000
E)24590
Rationale: For simple interest, I = P * N * R / 100
let Principle P = x
I = x * 12 * 12 / 100
I = 1.44 * x
Amount = P + I
60000 = 1.44 x + x
x = 24590.16 = P
E
Answer: E
Question: At a constant Rate of flow, it takes 30 minutes to fill a swimming pool if a large hose is used and 45 minutes if a small hose is Used. At these constant rates, how many minutes will it take to fill the pool when both hoses are used simultaneously?
Options:
A)20
B)22
C)18
D)16
E)14
Rationale: time taken to fill the pool by Large Hose =30 minutes =L or 1/L=1/30 similarly 1/S=1/45
simultaneously it will take 1/L+1/S=1/30+1/45=5/90=18 minutes
Answer : C
Answer: C
Question: Working alone, A can complete a certain kind of job in 15 hours. A and D, working together at their respective rates, can complete one of these jobs in 10 hours. In how many hours can D, working alone, complete one of these jobs?
Options:
A) 20
B) 24
C) 26
D) 28
E) 30
Rationale: Let total time taken by D to complete the job = D
total time taken by A to complete the job = 15
Work done by A in an hour
1/A = 1/15
Working together A and D can complete the job in 10 hours
1/A + 1/D = 1/10
=>1/D = 1/10 - 1/15
= 1/10 - 1/15
= 1/30
=> D = 30 hours
Answer E
Answer: E
Question: The area of a parallelogram is 128sq m.Then the area of a triangle formed by its diagonal is ----------?
Options:
A)128m
B)64m
C)64m^2
D)128m^2
E)none
Rationale: b*h/2=128/2=64m. Ans:(B)
Answer: B
Question: If X and Y are two different prime numbers, which of the following cannot be true?
Options:
A)XY is odd.
B)X + Y is even.
C)X + Y is odd.
D)XY is even.
E)X/Y is an integer
Rationale: A prime number is a positive integer with exactly two distinct positive divisors: 1 and itself. So, a prime number cannot be a multiple of another prime number. Which makes option E not possible (X/Y=integer means that X is a multiple of Y).
All other options are possible:
A. XY is odd --> X=3 and Y=5;
B. X + Y is even --> X=3 and Y=5;
C. X + Y is odd -->X=2 and Y=3;
D. XY is even --> X=2 and Y=3;
Answer: E.
Answer: E
Question: A trailer carries 3, 4 and 6 crates on a trip. Each crate weighs no less than 120 kg. What is the maximum weight of the crates on a single trip?
Options:
A)1250
B)625
C)600
D)7500
E)720
Rationale: Max No. of crates=6.
Max Weight=120Kg
Max. weight carried = 6*120=720Kg=E
Answer: E
Question: A 4-letter code word consists of letters H, I, and J. If the code includes all the three letters, how many such codes are possible?
Options:
A)72
B)48
C)18
D)24
E)36
Rationale: Note that the correct answer to this question is 36, not 72.
H-HIJ can be arranged in 4!/2!=12 ways;
I-HIJ can be arranged in 4!/2!=12 ways;
J-HIJ can be arranged in 4!/2!=12 ways;
Total: 12+12+12=36.
Answer: E
Answer: E