divelab/Sys2Bench huggingface dataset:
Question: Paige had a nature collection. She had 25 acorns, 16 dried seed pods, and 8 feathers. She
divided the acorns into 5 equal groups, the seed pods into 4 equal groups and the feathers into 2
equal groups. She gave her mother one group of each kind. How many separate items did her
mother get?
Options:
A)23 items
B)33 items
C)13 items
D)3 items
E)43 items
Rationale: 25 ÷ 5 = 5 acorns in a group
16 ÷ 4 = 4 seed pods in a group
8 ÷ 2 = 4 feathers in a group
5 + 4 + 4 = 13 items given to Mom
correct answer C
Answer: C
Question: Find 40 % of 440
Options:
A)96
B)94
C)86
D)176
E)110
Rationale: We know that R % of m is equal to R/100 × m.
So, we have 40 % of 440
40/100 × 440
= 176
Answer:D
Answer: D
Question: The value of (10^8-10^2)/(10^4-10^3) is closest to which of the following?
Options:
A)1
B)10
C)10^2
D)10^3
E)10^4
Rationale: Because the question asks for what value isclosestthe question invites approximation.
Let's look at the numerator:
10^8 - 10^2
10^8 is HUGE compared to 10^2.
So 10^8 - 10^2 is very close to 10^8 itself. (Just as 100 - 0.0001 is very close to 100 itself).
Likewise, 10^4 is HUGE compared to 10^3.
So 10^4 - 10^3 is very close to 10^4.
So we have:
10^8/10^4
or 10^(8-4) = 10^4.
Choose E.
Answer: E
Question: John started driving on a highway at a constant speed of R miles per hour at 13:00. Then, 2 hours later, Tom started driving on the same highway at a constant speed of 5R/3 miles per hour at 15:00. If both drivers maintained their speed, how many miles had John driven on the highway when Tom caught up with John?
Options:
A)3R
B)5R
C)8R
D)9R
E)10R
Rationale: In 2 hours, John drove 2R miles.
Tom can catch John at a rate of 5R/3 - R = 2R/3 miles per hour.
The time it takes Tom to catch John is 2R / (2R/3) = 3 hours.
In 3 hours, John can drive another 3R miles for a total of 5R miles.
The answer is B.
Answer: B
Question: Can you replace the question mark with the number to complete the series, provided the pair of numbers exhibits a similar relationship ?
? : 4623 :: 9 : 647
Options:
A)?= 17
B)18
C)13
D)10
E)20
Rationale: A
17
The relationship holds for below formula :
pow(x,3) - pow(x,2) - 1
=> 9*9*9 - 9*9 - 1
=> 729 - 81 - 1
=> 647
Similarly,
17*17*17 - 17*17 - 1
=> 4913 - 289 - 1
=> 4623
Answer: A
Question: Jonathan’s grandparents lend $1,000 to Jonathan at a simple annual interest rate of 10%. He pays them back 5 years later. How much do they receive?
Options:
A)1,000∗0.1^5
B)1,000∗0.5
C)1,000∗1.5
D)1,000∗1.1^5
E)(1,000∗0.1)^5
Rationale: 1>Simple Interest Vs Compound interest (there are answers options with compounded interest)
S.I = P x R x T formula in school the question is asking for Amount in 5 years. so (c) 1,000∗ 1.5
Ans : C
Answer: C
Question: Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 4 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is?
Options:
A)60 gallons
B)100 gallons
C)120 gallons
D)160 gallons
E)130 gallons
Rationale: Work done by the waste pipe in 1 minute = 1/15 - (1/20 + 1/24) = - 1/40
Volume of 1/40 part = 4 gallons\
Volume of whole = 4 * 40 = 160 gallons.
ANSWER:D
Answer: D
Question: The sum of the present ages of a father and his son is 62 years. Six years ago, father's age was four times the age of the son. After 6 years, son's age will be:
Options:
A)12 years
B)14 years
C)18 years
D)20 years
E)22 years
Rationale: Let the present ages of son and father be x and (62 - x) years respectively.
Then, (62 - x) - 6 = 4(x - 6)
56 - x = 4x - 24
x = 16
The son's age after 6 years will be 22.
The answer is E.
Answer: E
Question: A sum of money is put out at compound interest for 2 years at 20%. It would fetch Rs.482 more if the interest were payable half-yearly, then it were pay able yearly. Find the sum?
Options:
A)2099
B)6086
C)2976
D)2000
E)3862
Rationale: P(11/10)4 - P(6/5)2
= 482
P = 2000
Answer:D
Answer: D
Question: Sonika deposited Rs.6000 which amounted to Rs.9200 after 3 years at simple interest. Had the interest been 2% more. She would get how much?
Options:
A)9680
B)2277
C)2999
D)9560
E)1212
Rationale: (6000*3*2)/100 = 360
9200
--------
9560
Answer:D
Answer: D
Question: In each series, look for the degree and direction of change between the numbers. In other words, do the numbers increase or decrease, and by how much
Look at this series: 1.5, 2.0, 2.5, 3.0, ... What number should come next?
Options:
A)4.7
B)3.5
C)4.9
D)5.0
E)4.4
Rationale: 3.5
In this simple addition series, each number increases by 0.5
Answer : B
Answer: B
Question: The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical A present and inversely proportional to the concentration of chemical R present. If the concentration of chemical R is increased by 100 percent, which of the following is closest to the percent change in the concentration of chemical A required to keep the reaction rate unchanged?
Options:
A)100% decrease
B)50% decrease
C)40% decrease
D)40% increase
E)50% increase
Rationale: Let A and R be the concentratrations of the individual chemicals.
Rate of chemical reaction = A^2/R
Since new R is increased by 100%
Rate = A^2/(2R)
For the rate to be constant, new value of A should be square root(2)
So new value of A = 1.414A
That means A is increased by 41.4%
Nearest solution is D
Answer: D
Question: Applying VBODMAS rule
Options:
A)31/120
B)31/129
C)31/1276
D)31/122
E)31/111
Rationale: Answer:A
Answer: A
Question: P and Q started a business investing Rs. 85,000 and Rs. 15,000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively?
Options:
A)17:5
B)17:0
C)17:8
D)17:1
E)17:3
Rationale: P:Q = 85000 : 15000
= 17:3.
Answer: E
Answer: E
Question: If the equation x^2−6x=-2k has at least one solution, which of the following must be true?
Options:
A)k > 9
B)k < −9
C)k = 9
D)k ≤ 9/2
E)k ≥ −9
Rationale: x^2−6x=-2k
=> x^2−6x + 2k = 0
For a quadratic equation to have at least one solution, its discriminant (b^2-4ac) should be non-negative.
b^2-4ac ≥0
=> 36 - 4*1*(2k) ≥0
=> 36 - 8k ≥0
=> k ≤ 9/2
Answer D
Answer: D
Question: A, B and C, each working alone can complete a job in 6, 8 and 12 days respectively. If all three of them work together to complete a job and earn $2200, what will be C's share of the earnings?
Options:
A)$488.9
B)$480.9
C)$588.9
D)$680.9
E)$788.9
Rationale: The dollars earned will be in the same ratio as amount of work done
1 day work of C is 1/12 (or 2/24)
1 day work of the combined workforce is (1/6 + 1/8 + 1/12) = 9/24
C's contribution is 2/9 of the combined effort
Translating effort to $ = 2/9 * 2200 = $488.9
hence:A
Answer: A
Question: When positive integer G is divided by positive integer B, the result is 4.35. Which of the following could be the reminder when G is divided by B?
Options:
A) 13
B) 14
C) 15
D) 16
E) 17
Rationale: the remainder will be obtained from the decimal part when G is divided by B i.e. 0.35
0.35 = 35/100 = 7/20 so possible remainders are 7,14,21,28. Only option B-14 satisfies this
PS: for B-14 G=174 and B=40
Answer: B
Question: A student scored an average of 80 marks in 3 subjects: Physics, Chemistry and Mathematics. If the average marks in Physics and Mathematics is 90 and that in Physics and Chemistry is 70, what are the marks in Physics?
Options:
A)27
B)26
C)218
D)80
E)18
Rationale: Given M + P + C = 80 * 3 = 240 --- (1)
M + P = 90 * 2 = 180 --- (2)
P + C = 70 * 2 = 140 --- (3)
Where M, P and C are marks obtained by the student in Mathematics, Physics and Chemistry.
P = (2) + (3) - (1) = 180 + 140 - 240 = 80
Answer: D
Answer: D
Question: (?) - 19657 - 33994 = 9999
Options:
A)63630
B)63620
C)63670
D)63650
E)63690
Rationale: D
63650
19657+33994=53651
Let x - 53651 = 9999
Then, x = 9999 + 53651 = 63650
Answer: D
Question: P can do a work in the same time in which Q and R together can do it. If P and Q work together, the work can be completed in 10 days. R alone needs 15 days to complete the same work. then Q alone can do it in
Options:
A)20
B)22
C)25
D)27
E)60
Rationale: Work done by P and Q in 1 day = 1/10
Work done by R in 1 day = 1/15
Work done by P, Q and R in 1 day = 1/10 + 1/15= 1/6
But Work done by P in 1 day = Work done by Q and R in 1 day . Hence the above equation can be written as Work done by P in 1 day Ã— 2 = 1/6
=> Work done by P in 1 day = 1/12
=> Work done by Q and R in 1 day = 1/12
Hence work done by Q in 1 day = 1/12 â€“ 1/15 = 1/60
So Q alone can do the work in 60 days
Answer is E.
Answer: E
Question: Because he’s taxed by his home planet, Mork pays a tax rate of 40% on his income, while Mindy pays a rate of only 30% on hers. If Mindy earned 3 times as much as Mork did, what was their combined tax rate?
Options:
A)32.5%
B)34%
C)35%
D)36%
E)37.5%
Rationale: Say Morks income is - 100
So tax paid will be 40
Say Mindy's income is 3*100 = 300
So tax paid is 30% * 300 = 90
Total tax paid = 40+90 = 130.
Combined tax % will be 130/100+300 = 32.5%
ANSWER:A
Answer: A
Question: The speed of a boat in still water is 15 km/hr and the rate of current is 3 km/hr. The distance travelled downstream in 12 minutes is
Options:
A)1.2 km
B)1.8 km
C)2.4 km
D)3.6 km
E)None
Rationale: Solution
Speed downstreams	=(15 + 3)kmph
= 18 kmph.
Distance travelled	(18 x 12/60)km
= 3.6km.
Answer D
Answer: D
Question: In how many ways can 10 books be arranged on a shelf such that a particular pair of books should always be together?
Options:
A)9! x 2!
B)5!
C)3!
D)9!
E)2!
Rationale: We have a total of 10 books.
Given that a particular pair of books should always be together. Hence, just tie these two books together and consider as a single book.
Hence we can take total number of books as 9. These 9 books can be arranged in 9P9 =9!=9! ways.
We had tied two books together. These books can be arranged among themselves in 2P2 =2!=2! ways.
Hence, required number of ways
=9!×2!
Ans: A
Answer: A
Question: In a BCCI meeting there are ten people. All shake hands with each other once. How many handshakes will be there altogether?
Options:
A)28
B)9
C)H
D)H19
E)181
Rationale: Answer:B
Answer: B
Question: 16 is what % of 90?
Options:
A)16
B)17.78
C)17
D)18.5
E)18.23
Rationale: We assume that 90 is 100%
assume 'x' is value we looking for
here,
90 = 100% and
x% = 16
therefore,
100/x = 90/16
100/x = 5.625
x = 17.78
B
Answer: B
Question: The speed of a boat in still water is 70kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
Options:
A)22 kmph
B)40 kmph
C)78 kmph
D)50 kmph
E)23 kmph
Rationale: Speed downstream = 70 + 20 = 90 kmph
Speed upstream = 70 - 20 = 50 kmph
Answer:D
Answer: D
Question: A delegation of 5 members has to be formed from 3 ladies and 5 gentlemen. In how many ways the delegation can be formed, if 2 particular ladies are always included in the delegation?
Options:
A)20
B)28
C)29
D)49
E)48
Rationale: There are three ladies and five gentlemen and a committee of 5 members to be formed.
Number of ways such that two ladies are always included in the committee =
6C3= (6 * 5 * 4)/6 = 20.
Answer:A
Answer: A
Question: The average age of a class of 24 students is 23 years. The average increased by 1 when the teacher's age also included. What is the age of the teacher?
Options:
A)40
B)41
C)48
D)52
E)43
Rationale: Total age of all students =24Ã—23
Total age of all students + Age of the teacher =25Ã—24
Age of the teacher
=25Ã—24âˆ’24Ã—23=24(25âˆ’23)=24Ã—2=48
Answer is C.
Answer: C
Question: Shipment --- No. of Defective Chips/shipment --- Total Chips in shipment
S1 ---------------------- 2 ------------------------------------------ 5,000
S2 ---------------------- 5 ------------------- ---------------------- 12,000
S3 ---------------------- 5 ------------------------------------------ 15,000
S4 ---------------------- 4 ------------------------------------------ 16,000
A computer chip manufacturer expects the ratio of the number of defective chips to the total number of chips in all future shipments to equal the corresponding ratio for shipments S1, S2, S3, and S4 combined, as shown in the table above. What’s the expected number of defective chips in a shipment of 60,000 chips?
Options:
A)14
B)20
C)22
D)24
E)25
Rationale: for a total of 51000 chips (adding S1,S2,S3,S4) total number of defective chips is 17 ((adding defective chips of S1,S2,S3,S4) so ratio is 16/48000 or 1 every 3000 chips.
Keeping this ratio constant for 60000 chips number of defective chips will be (1/3000) * 60000 = 20
B
Answer: B
Question: 10 2 = 0.3010, the value of log10 80 is:
Options:
A)1.602
B)1.903
C)2.903
D)3.903
E)4.903
Rationale: log10 80	= log10 (8 x 10)
= log10 8 + log10 10
= log10 (23 ) + 1
= 3 log10 2 + 1
= (3 x 0.3010) + 1
= 1.9030.
Answer: Option B
Answer: B
Question: Steve traveled the first 5 hours of his journey at 40 mph and the last 3 hours of his journey at 80 mph. What is his average speed of travel for the entire journey?
Options:
A)53.33 mph
B)88 mph
C)60 mph
D)64 mph
E)66.67 mph
Rationale: Average Speed = Total distance/ Total time = (40 * 5 + 80 * 3)/(5 + 3) = 440/5 = 88
Answer: B
Answer: B
Question: A wheel that has 24 cogs is meshed with a larger wheel of 48 cogs. When the smaller wheel has made 12 revolutions, then the number of revolutions mad by the larger wheel is:
Options:
A)6
B)5
C)3
D)7
E)4
Rationale: A
6
Let the required number of revolutions made by larger wheel be x.
Then, More cogs, Less revolutions (Indirect Proportion)
48 : 24 :: 12 : x <-> 48 x x = 12 x 24
x = (12x 24)/48
x = 6
Answer: A
Question: 2+4
Options:
A)8
B)13
C)28
D)6
E)2
Rationale: D
Answer: D
Question: (1.00001)(0.99999) - (1.00004)(0.99996) =
Options:
A)0
B)10^-10
C)3(10^-10)
D)15(10^-10)
E)3(10^-5)
Rationale: (1.00001*0.99999)-(1.00004*0.99996)
= (1+0.00001)(1-0.00001) - (1+0.00004)(1-0.00004)
= 1 - (0.00001)^2 - 1 + (0.00004)^2
= -(0.0000000001) + (0.0000000016)
= 0.00000000015=15(10^-10)
Answer D
Answer: D
Question: In a village of 100 households, 75 have at least one DVD player, 80 have at least one cell phone, and 55 have at least one MP3 player. If x and y are respectively the greatest and lowest possible number of households that have all three of these devices, x – y
Options:
A)55
B)45
C)65
D)35
E)25
Rationale: x= (75+55+80-100-z)/2 for z=0 ->55
y=the same for z=100 ->10
Therefore x-y=45
ANSWER:B
Answer: B
Question: A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 78000, then the share of B is?
Options:
A)A)34500
B)B)36099
C)C)36000
D)D)38007
E)E)42000
Rationale: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6
Total profit = Rs. 78000
Share of B = 6/13 (78000)
= Rs. 36000
Answer:C
Answer: C
Question: A man can row 36 kmph in still water. It takes him thrice as long to row up as to row down the river. Find the rate of the stream?
Options:
A)14 kmph
B)12 kmph
C)18 kmph
D)1 kmph
E)None of these
Rationale: Explanation:
Let man's rate upsteam be X kmph
Then his rate of downstream = 3X kmph
Rate still water = 1/2 (3X + X) = 2X
2X = 36
X = 18
Rate of upstream = 18
Rate of downstream = 54
Rate of stream 1/2 ( 54 - 18) = 18 kmph
Answer: Option C
Answer: C
Question: Sides of a rectangular park are in the ratio 3: 2 and its area is 4704 sq m, the cost of fencing it at 50 ps per meter is?
Options:
A)287
B)1287
C)140
D)988
E)271
Rationale: 3x * 2x = 4704 => x = 28
2(84 + 56) = 280 m
280 * 1/2 = Rs.140
Answer: C
Answer: C
Question: At what rate percent on simple interest will Rs.750 amount to Rs.900 in 16 years?
Options:
A)6.25%
B)1.25%
C)4%
D)5%
E)3.25%
Rationale: 150 = (750*16*R)/100
R = 1.25%
Answer: B
Answer: B
Question: A group of 8 students bought movie tickets in one row next to each other. If Bob and Lisa are in this group, what is the probability that Bob and Lisa will each sit next to only one of the seven other students from the group?
Options:
A)5.67%
B)3.57%
C)15.17%
D)2.07%
E)2.57%
Rationale: The question basically asks about the probability that Bob and Lisa sit at the ends.
The total # of sitting arrangements is 8!.
Desired arrangement is either BUVWXYZL or LUVWXYZB. Now, UVWXYZ can be arranged in 6! ways, therefore total # of favorable arrangements is 2*6!.
P=(favorable)/(total)=(2*6!)/8!=1/28.
Answer: B.
Answer: B
Question: Train A left Centerville Station, heading toward Dale City Station, at 3: 00 p.m. Train B left Dale City Station, heading toward Centerville Station, at 1: 20 p.m. on the same day. The trains rode on straight tracks that were parallel to each other. If Train A traveled at a constant speed of 30 miles per hour and Train B traveled at a constant speed of 10 miles per hour, and the distance between the Centerville Station and Dale City Station is 90 miles, when did the trains pass each other?
Options:
A)3: 10 p.m.
B)5: 00 p.m.
C)5: 20 p.m.
D)5: 35 p.m.
E)6: 00 p.m.
Rationale: the distance travelled by the train A in first 20 minutes will be 10.
The distance which will be remaining is 80.
Now both trains are running in opposite direction.Their speed will be added so 40.
Time at which they will meet =80/40=2
time of train B will be 1:20 +2=3:20
Hence answer is A.Hope i am correct
Answer: A
Question: Hockey Stick and ball cost $50. If the Stick cost $49 more than the ball.
what is the cost of each ?
Options:
A)Hockey Stick $48.50 & ball $1.50
B)Hockey Stick $49.00 & ball $1.00
C)Hockey Stick $48.00 & ball $2.00
D)Hockey Stick $49.50 & ball $0.50
E)Hockey Stick $41.50 & ball $8.50
Rationale: D
Hockey Stick $49.50 & ball $0.50
Answer: D
Question: A single discount equivalent to the discount series of 20%, 12% and 5% is?
Options:
A)33.12
B)31.1
C)31.6
D)31.2
E)31.9
Rationale: Explanation:
100*(80/100)*(88/100)*(95/100) = 66.88
100 - 66.88 = 33.12
Answer: A
Answer: A
Question: The banker's gain on a sum due 6 years hence at 12% per annum is Rs. 684. What is the banker's discount?
Options:
A)1240
B)1120
C)1190
D)1634
E)None of these
Rationale: Explanation :
TD = (BG ×100)/TR = (684×100)/(6×12) = Rs. 950
BG = BD – TD
=> 684= BD - 950
=> BD = 684 + 950 = 1634 Answer : Option D
Answer: D
Question: There are 5 marbles in a bag - 2 are orange and 3 are blue. If two marbles are pulled from the bag, what is the probability that at least one will be orange?
Options:
A)7/10
B)3/5
C)2/5
D)3/10
E)1/10
Rationale: Probability of the first ball being orange = 2/5
The first all is not replaced, hence the total number of balls for the second pick = 1/4
Therefore the total probability is 2/5 x 1/4 = 1/10
Hence E
Answer: E
Question: The average weight of 20 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg. Find the average weights of all the boys in the class.
Options:
A)48.79286
B)42.25
C)50.87364
D)51.25
E)52.25474
Rationale: Explanation:
Average weight of 20 boys = 50.25
Total weight of 20 boys = 50.25 × 20
Average weight of remaining 8 boys = 45.15
Total weight of remaining 8 boys = 45.15 × 8
Total weight of all boys in the class = (50.25 × 20)+ (45.15 × 8)
Total boys = 20 + 8 = 28
Average weight of all the boys = (50.25×20)+(45.15×8)/28
=
Answer: Option A
Answer: A
Question: How many factors of 880 are odd numbers greater than 1?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: When factorized, 880 has 6 prime factors. Of these prime factors 2 are odd and 4 are even. Hence total number of odd factors is 2*2(4), which includes 4. The total number of odd factors greater than 1 are 3.(option A)
Answer: A
Question: The average of six number is 3.95. The average of two of them is 3.4, while the average of the other two is 3.85. what is the average of the remaining four number ?
Options:
A)2.3
B)4.6
C)4.7
D)4.8
E)None of these
Rationale: solution:
Sum of the remaining four numbers = (3.95 × 6) - [(3.4 × 2) + (3.85 ×2)]
=23.70 -(6.8 + 7.7) = 23.70 - 14.5 = 9.20.
∴ Required average =9.2/4 = 2.3 Answer A
Answer: A
Question: The operation # is defined for all nonzero q and y by #y = q + q/y. If a>0, then 1#(1#a) =
Options:
A)a
B)a+1
C)a/(a+1)
D)(a+2)/(a+1)
E)(2a+1)/(a+1)
Rationale: q#y = q + q/y. If a>0, then 1#(1#a) =
You can see that a stands for y and 1 stands for q. I like to work with numbers so I did q=1 a=2 and a=y so y=2
1#a= 1+(1/2)=1.5 so now a is 1.5 --> 1+(1/1.5)=1 2/3 = 5/3
So now you can check by filling in a, which is 2:
A. a --> 2
B. a+1 --> 2+1=3
C. a/(a+1)-->2/(2+1)=2/3
D. (a+2)/(a+1)-->(2+2)/(2+1)=4/3
E. (2a+1)/(a+1)-->(2*2+1)/(2+1)=5/3
So E is the answer.
Answer: E
Question: Find the value of x: x² + 4x + 4.
Options:
A)2
B)4
C)-2
D)-4
E)0
Rationale: That quadratic is factored as follows:x² + 4x +4 = (x+2)(x+2).Lesson 17.Now, it is easy to see that the second factor will be 0 when x = -2.The solution is:x	=	-2 C
Answer: C
Question: A clerk multiplied a number by ten when ten should have divided it. The answer he got was 100.what should the ans have been?
Options:
A)3
B)1
C)2
D)4
E)5
Rationale: let the number be x
actually form = x/10
but x*10=100
=>x=10
means the number the should be divided is 10
=>the answer would have been (10/10)=1
ANSWER:B
Answer: B
Question: The sale price at which a store sells an article is 25% more than its cost price. If the sale price is an integer, which of the following cannot be the cost price?
Options:
A)$12
B)$16
C)$31
D)$56
E)$92
Rationale: Sale Price = (5/4)*(Cost Price)
If the sale price is an integer, then the cost price must be divisible by 4.
The answer is C.
Answer: C
Question: The speed of a boat in still water is 60kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
Options:
A)80,47 kmph
B)80,80 kmph
C)80,42 kmph
D)80,40 kmph
E)83,40 kmph
Rationale: Speed downstream = 60 + 20 = 80 kmph
Speed upstream = 60 - 20 = 40 kmph.Answer:D
Answer: D
Question: If 24 men can do a piece of work in 25 hours, in how many hours will 15 men
do it ?
Options:
A)40 hours
B)45 hours
C)50 hours
D)55 hours
E)60 hours
Rationale: Let the required number of hours be x. Then,
Less men, More hours	(Indirect Proportion)
15 : 24 : : 25 : x<=>(15 x x) =(24 x 25)<=>(24 x 25)/15 = 40
Hence, 15 men can do it in 60 hours
Answer is A.
Answer: A
Question: There are two sets A and B. The range of set A is 7, and the range of set B is 13. If the two sets are combined and get a new set R, which cannot be the range of the set R?
Options:
A)8
B)B.11
C)C.14
D)D.17
E)E.21
Rationale: Let Set A has 1,8 as elements
B has 1,14 as elements.. So Range for Combined set R becomes 14-1=13
For range to be 14,
A = 1,8
B= 2,15 (Range=14)
For range to be 17
A=1,8
B= 5,18
For range to be 21:
A=1,8
B= 9 ,22
So we are left with A and B.
Now consider A has elements A= -1,-8 and Thus Range =-1-(-8) =7
So for Range of combined set to be 11, B needs to have largest elementxso that x- (-8)=11 or x=3...But if x=3, the largest element in Combined Set then smallest element in the combined set will be 3-y=13 or y=-10....And the range of combined set 3-(-10)=13...
Consider Option A
A=-1,-8
B= y,x where y and x are smallest and largest element in Set B
Elements of Combined Set: -8,-1,y and x
Now x-(-8)=8 or x=0, then x-y=13 or y=-13...
Range of Combined Set: 0-(-13)= 13...
I don't see how range can be 8 or 11...Can you please post the source and explanation for the OA in spoiler...=B
Answer: B
Question: If the radius of the sphere is 14 m. then its total surface area is
Options:
A)2644
B)2446
C)2464
D)6442
E)6424
Rationale: Sphere Total surface area
= 4πr(power2) = 4 × 22/7 × 14 × 14 = 2464
Answer is C.
Answer: C
Question: The average age of a class of 22 students is 21 years. The average increased by 1 when the teacher's age also included. What is the age of the teacher?
Options:
A)40
B)41
C)44
D)42
E)43
Rationale: Total age of all students =22×21
Total age of all students + Age of the teacher =23×22
Age of the teacher
=23×22−22×21=22(23−21)=22×2=44
Answer is C.
Answer: C
Question: Find the value of
((0.1)3 + (0.6)3 + (0.7)3 − (0.3)(0.6)(0.7))/((0.1)2 + (0.6)2 + (0.7)2 − 0.006 − 0.42 − 0.07)
Options:
A)14/10
B)14/23
C)15/31
D)13/15
E)None
Rationale: ((0.1)3 + (0.6)3 + (0.7)3 − (0.3)(0.6)(0.7))/((0.1)2 + (0.6)2 + (0.7)2 − 0.006 − 0.42 − 0.07)
=> (0.1 + 0.6 + 0.7)3/(0.1 + 0.6 + 0.7)2
=> 0.1 + 0.6 + 0.7 => 1.4 = 14/10
A)
Answer: A