divelab/Sys2Bench huggingface dataset:
Question: Seats for Mathematics, Physics and Biology in a school are in the ratio 5:7:8. There is a proposal to increase these seats by 40, 50 and 75 respectively. What will be the ratio of increased seats?
Options:
A)2:3:4
B)6:7:8
C)6:8:9
D)None of these
E)Cannot be determined
Rationale: Explanation :
Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively.
And, the number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x).
=>(140/100)×5x, (150/100)×7x, (175/100)×8x.
=>7x, 21x/2, 14x.
The required ratio :-
=>7x : 21x/2 : 14x.
=>14x : 21x : 28x.
=>2:3:4.
Answer : A
Answer: A
Question: A rectangular tank needs to be coated with insulation. The tank has dimensions of 3 feet, 6 feet, and 2 feet. Each square foot of insulation costs $20. How much will it cost to cover the surface of the tank with insulation?
Options:
A)$980
B)$1060
C)$1220
D)$1440
E)$1650
Rationale: The total surface area is 2(2*3 + 3*6 + 2*6) = 72 square feet
The total cost is 72*$20 = $1440
The answer is D.
Answer: D
Question: Baseball's World Series matches 2 teams against each other in a best-of-seven series. The first team to win four games wins the series and no subsequent games are played. If you have no special information about either of the teams, what is the probability Y that the World Series will consist of fewer than 7 games?
Options:
A) 12.5%
B) 25%
C) 31.25%
D) 68.75%
E) 75%
Rationale: Your explanation is very close toManhattan GMAT's official answer - it's quite uncanny:
"There are many other ways this could happen. Using the permutation formula, there are 6!/(3!)(3!) = 20 ways for the two teams to split the first 6 games (3 wins for each).
There are then 2 possible outcomes to break the tie in Game 7. Thus, there are a total of 202 = 40 ways for the World Series to last the full 7 games.
The probability that any one of these 40 ways occurs can be calculated from the fact that the probability of a team winning a game equals the probability of a team losing a game = 1/2.
Given that 7 distinct events must happen in any 7 game series, and that each of these events has a probability of 1/2, the probability that any one particular 7 game series occurs is.
Since there are 40 possible different 7 game series, the probability that the World Series will last exactly 7 games is: (1/2)^7 = 1/128
40*1/128 = 40/128 = 31.25%
Thus the probability Y that the World Series will last less than 7 games is 100% - 31.25% = 68.75%.
The correct answer is D."
Answer: D
Question: A and B complete a work in 6 days. A alone can do it in 10 days. If both together can do the work in how many days?
Options:
A)3.95 days
B)4.95 days
C)3.75 days
D)2.50 days
E)1.45 days
Rationale: 1/6 + 1/10 = 8/30 = 4/15
15/4 = 3.75 days
ANSWER:C
Answer: C
Question: Two varieties of wheat - A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3 : 7. If 5 kg of the mixture is sold at 25% profit, find the profit made?
Options:
A)Rs.16.90
B)Rs.16.59
C)Rs.16.60
D)Rs.16.50
E)Rs.18.50
Rationale: Let the quantities of A and B mixed be 3x kg and 7x kg.
Cost of 3x kg of A = 9(3x) = Rs. 27x
Cost of 7x kg of B = 15(7x) = Rs. 105x
Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x
Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66
Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 * 66 =Rs.16.50
Answer:D
Answer: D
Question: The average price of three items of furniture is Rs. 10000. If their prices are in the ratio 3:5:7, the price of the cheapest item is?
Options:
A)2379
B)2600
C)9288
D)9000
E)28311
Rationale: Let their prices be 3x, 5x and 7x.
Then, 3x + 5x + 7x = (10000 * 3) or x = 866.6.
Cost of cheapest item = 3x = Rs. 2600.
Answer: B
Answer: B
Question: R is the set of positive even integers less than 50, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain ?
Options:
A)None
B)Two
C)Three
D)Five
E)Seven
Rationale: squares < 50 {1,4,9,16,25,36,49 }
S = {1,4,16,36}
R = {2,.....48}
Hence C.
Answer: C
Question: The H.C.F. of two numbers is 12 and their L.C.M. is 600. If one of the number is 20, find the other?
Options:
A)100
B)360
C)120
D)200
E)150
Rationale: Other number = 12*600/20= 360
Answer is B
Answer: B
Question: The length of a rectangle is one - fourth of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
Options:
A)350 sq.units
B)250 sq.units
C)300 sq.units
D)200 sq.units
E)100 sq.units
Rationale: Given that the area of the square = 6400 sq.units
=> Side of square = √6400= 80 units
The radius of the circle = side of the square = 35 units Length of the rectangle = 1/4 * 80 = 20 units
Given that breadth = 10 units
Area of the rectangle = lb = 20 * 10 = 200 sq.units
Answer:D
Answer: D
Question: It takes Joey the postman 1 hours to run a 4 mile long route every day. He delivers packages and then returns to the post office along the same path. If the average speed of the round trip is 5 mile/hour, what is the speed with which Joey returns?
Options:
A)6 2/3
B)12
C)13
D)14
E)15
Rationale: let his speed for one half of the journey be 4 miles an hour
let the other half be x miles an hour
now,
avg speed =5 mile an hour
2*4*x/4+x=5
8x=5x+20=>3x=20=>x=6 2/3
A
Answer: A
Question: Find the ratio in which rice at Rs. 7.10 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)3:4
C)2:1
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 : 80 = 3 : 4
Answer: B
Answer: B
Question: Find the number which is nearest to 3105 and is exactly divisible by 21
Options:
A)1208
B)3108
C)241
D)217
E)3147
Rationale: On dividing 3105 by 21, we get 18 as remainder.
Number to be added to 3105 = (21 - 18) - 3.
Hence, required number = 3105 + 3 = 3108.
ANSWER B 3108
Answer: B
Question: The diameter of a cylindrical tin is 6cm and height is 5 cm. Find the volume of the cylinder?
Options:
A)28π cc
B)15π cc
C)4π cc
D)45π cc
E)27π cc
Rationale: Explanation:
r = 3 h = 5
π * 3 * 3 * 5 = 45 π cc
Answer: D
Answer: D
Question: R campers fished for 2 hours. If m of the campers caught 2 fish apiece and the rest caught a combined total of n fish, how many fish did the R campers catch per hour?
Options:
A)2m + n(R-m)
B)(2m + n(R-m))/3
C)(2m + n(m-R))/3
D)(2m + n)/2
E)(2m + n)/R
Rationale: m of the campers caught 2 fish apiece in 2 hours --> total fish caught by m campers = 2m;
The rest caught a combined total of n fish.
Total fish caught in 2 hours = 2m+n --> per hour (2m+n)/2.
Answer: D.
Answer: D
Question: A no.when divided by 221 gives a remainder 43, what remainder will be obtainedby dividingthe same no.17?
Options:
A)3
B)6
C)9
D)11
E)14
Rationale: 221 + 43 = 264/17 = 9 (Remainder)
C
Answer: C
Question: A man walks at a speed of 3 km/hr and runs at a speed of 7 km/hr. How much time will the man require to cover a distance of 10 1/2 km, if he completes half of the distance, i.e., (5 1/4) km on foot and the other half by running?
Options:
A)2 1/2
B)2 1/6
C)4 1/2
D)2 1/1
E)2 1/8
Rationale: Required time = (5 1/4)/3 + (5 1/4)/7 = 2 1/2 hours.
Answer: A
Answer: A
Question: 5 men and 12 boys finish a piece of work in 4 days, 7 men and 6 boys do it in 5 days. The ratio between the efficiencies of a man and boy is?
Options:
A)6:6
B)6:1
C)6:9
D)6:5
E)6:2
Rationale: 5M + 12B ----- 4 days
7M + 6B ------- 5 days
20M + 48B = 35M + 30B
18B = 15M => 5M = 6B
M: B = 6:5
Answer: D
Answer: D
Question: How many three letter words are formed using the letters of the word GAMER?
Options:
A)60
B)45
C)67
D)98
E)29
Rationale: The number of letters in the given word is four.
The number of three letter words that can be formed using these four letters is 5P3
= 5 * 4 *3 = 60.
Answer: A
Answer: A
Question: 2/5 of 3/7 of 23/11 of ? = 64 × 3
Options:
A)511
B)419
C)616
D)636
E)686
Rationale: Explanation:
2/5 &time; 3/7 &time; 20/11 &time; x = 192
X = 192 &time; 11 &time; 7 &time; 5/2 &time; 3 &time; 20 = 616
Answer: Option C
Answer: C
Question: Find the value of (2 − 1/3) (1 − 1/4)(1 − 1/5)……… (1 − 1/99)(1 − 1/100)
Options:
A)1/20
B)1/21
C)2/13
D)2/15
E)None
Rationale: (2 − 1/3) (1 − 1/4)(1 − 1/5)..... (1 − 1/99)(1 − 1/100)
5/3 × 3/4 × 4/5 × ....... 98/99 × 99/100 = 5/100 = 1/20
A)
Answer: A
Question: The average of first 10 natural numbers is?
Options:
A)5.6
B)5.5
C)5.9
D)5.4
E)5.1
Rationale: Sum of 10 natural no. = 110/2 = 55
Average = 55/10 = 5.5
Answer:B
Answer: B
Question: A and B participate in a 5000 m bicycle race which is being run on a circular track of 500 m. If the speed of A and B are 20 m/s and 10 m/s respectively, what is the distance covered by A when he passes B for the seventh time ?
Options:
A)2500
B)2800
C)4000
D)4500
E)situation not possible
Rationale: Track length = 500 m
Speed of A and B are 20m/s and 10 m/s respectively
Time taken by them to meet = length/ relative speed = 500/(20-10) 50 sec.
Time taken to meet for the 7th time = 7 *50 =350 sec ……..(1)
Total duration of race = total legth of race/ speed
= 500/20 = 250 sec ……..(2)
From (1) and (2) we can find out that 7th time meeting is not possible.
ANSWER:E
Answer: E
Question: A board 10ft. 9 inches long is divided into 3 equal parts . What is the length of each part?
Options:
A)3ft. 7 inches
B)6ft. 7 inches
C)4ft. 7 inches
D)2ft. 7 inches
E)1ft. 7 inches
Rationale: Length of board=10ft. 9 inches=(10*12+9)inches=129 inches.
Therefore, Length of each part = (129/3) inches = 43 inches = 3ft. 7 inches
Answer is A.
Answer: A
Question: I. Class A has a higher enrollment than Class B.
II. Class C has a lower enrollment than Class B.
III.Class A has a lower enrollment than Class C.
If the first two statements are true, the third statement is
Options:
A)true
B)false
C)uncertain
D)none
E)two
Rationale: Explanation:
From the first two statements, we know that of the three classes, Class A has the highest enrollment, so the third statement must be false.
Answer: B) false
Answer: B
Question: Amy's grade was 90th percentile of the 80 grades for her class. Of the 100 grades from another class, 19 were higher than Amy's, and the rest were lower. If no other grade was the same as Amy's grade, then Amy's grade was what percentile of the grades of the two classes of two classes combined?
Options:
A)72nd
B)80th
C)81st
D)85th
E)92nd
Rationale: Being in 90% percentile out of 80 grades means Amy was 73rd (from the least grade) in the class (as long as nobody had Amy's grades), she outscored 72.
In another class her grade would rank her 82 (from the least grade out of 101, 100+Amy), 81 had the grades lower than Amy.
So in combined classes she outscored 72+81=153. There are 180 students 153/180=0.85
Answer: D (85%)
Answer: D
Question: Two persons C & D started traveling from A and B which are 300 km apart, towards B and A respectively at 1.00 p.m. C travels at a constant speed of 30 kmph whereas D doubles his speed every hour. If D reaches A in 4 5/8 hours, at what time did C and D meet each other ?
Options:
A)4:30 p.m.
B)4:40 p.m.
C)5:00 p.m.
D)5:10 p.m.
E)5:20 p.m.
Rationale: Let speed of D in first hour = x
D’s speed = x+ 2x+ 4x+ 8x+ 16x*(5/8) = 25x
Given 25x=300 :. X = 12
At the end of four hours C traveled 120 (30 *4) kmph and D traveled 12 + 24+ 48 +96 = 180kmph
:. They meet each other after 4 hours ie at 5:00 p.m.
ANSWER:C
Answer: C
Question: A radio station has to choose one day of the seven in a week to broadcast a certain program, and that set will repeat each week. The program can be broadcast equally on any of the seven weekdays —- weekdays vs. weekends don’t matter at all —- nor does it matter whether the days the program airs are adjacent or not. Absolutely any three of the seven weekdays can be chosen. How many different three-day combinations of the seven weekdays can be constructed?
Options:
A)7
B)15
C)21
D)35
E)56
Rationale: Behind the story, we are really being asked to evaluate 7C1. We could use the factorial formula, but above we conveniently happen to have Pascal’s Triangle written out to the seventh row. We see that 7C1, the third entry of the seventh row, is 7. Answer = A.
Answer: A
Question: At what rate percent on simple interest will a sum of money double itself in 60 years?
Options:
A)3 1/3%
B)3 1/9%
C)1 2/3%
D)3 2/3%
E)3 6/3%
Rationale: P = (P*60*R)/100
R = 1 2/3%
Answer: C
Answer: C
Question: When positive integer Q is divided by 6 the remainder is 3. Which of the following CANNOT be an even integer?
Options:
A)a. k + 1
B)b. k -11
C)c. 4k + 2
D)d. (k-3)/3 +2
E)e. Q/3
Rationale: When positive integer Q is divided by 6 the remainder is 3
So, Q could equal 3, 9, 15, 21, etc
let's TEST Q =3
a.3+ 1 = 4 (EVEN)
b.3-11 = -8 (EVEN)
c. 4(3) + 2 = 14 (EVEN)
d. (3-3)/3 +2 = 2 (EVEN)
At this point, we can already see the answer must be E.
Let's check E forfun
e.3/3 = 1 (ODD)
Great!
Answer: E
Answer: E
Question: Find the compound ratio of (2:3), (3:4) and (1:4) is
Options:
A)1:2
B)2:3
C)1:8
D)4:5
E)3:2
Rationale: Required ratio = 2/3 * 3/4 * 1/4 = 1/8 = 1:8
Answer is C
Answer: C
Question: The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is
Options:
A)153550 m^2
B)153600 m^2
C)153700 m^2
D)153800 m^2
E)153900 m^2
Rationale: Explanation:
Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m.
60
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
Length = 480 m and Breadth = 320 m.
Area = (480 x 320) m2 = 153600 m^2.
Option B
Answer: B
Question: Let S be the set {1, 2, 3, . . . , n} consisting of the first n positive integers.
What is the maximum value of n for which every 100-element subset of
S contains two integers which differ by 25 ?
Options:
A)171
B)172
C)173
D)174
E)175
Rationale: Let n be as large as possible so that every 100-element subset of S contains two integers
differing by 25. Observe that the set
A = {1, 2, . . . , 25} [ {51, 52, . . . , 75} [ {101, 102, . . . , 125} [ {151, 152, . . . , 175}
has 100 elements no two of which differ by 25. So n 174. We show now that S = {1, 2, . . . , 174}
has the property that every 100-element subset of S contains two integers differing by 25. For
0 j 24, let Tj be the subset of S consisting of the integers from S that have a remainder of j
when we divide by 25. The sets Tj have no common elements. If S0 is a subset of S consisting of
exactly 100 elements, then there are exactly 74 elements of S not in S0. These must lie in the 25
sets Tj . One of the sets Tj contains at most 2 of these 74 elements of S not in S0 (by the pigeon-hole
principle). Fix such a j. Since Tj contains at least 6 elements, the intersection Tj \S0 contains two
consecutive elements of Tj , that is two elements of Tj that differ by 25. Thus, S has the property
that every 100-element subset of S contains two integers differing by 25
correct answer D
Answer: D
Question: A jar of 144 marbles is divided equally among a group of marble-players today. If 2 people joined the group in the future, each person would receive 1 marble less. How many people are there in the group today?
Options:
A)12
B)14
C)16
D)18
E)20
Rationale: 144 = 16*9 = 18*8
There are 16 people in the group today.
The answer is C.
Answer: C
Question: A set of football matches is to be organized in a “round-robin” fashion, i.e., every participating team plays a match against every other team once and only once. If 21 matches are totally played, how many teams participated?
Options:
A)6 teams
B)7 teams
C)5 teams
D)4 teams
E)2 teams
Rationale: For a match you need 2 teams.suppose there are totally ‘n ‘teams.Now you have to choose 2 teams out of ‘n’ teams.so answer =no of such choices=no. of possible combinations. So we’ve ans = nC2(ncombination2)=21;solve to get n=7.
Sol: n(n-1)/2=21. so n=7.if u don’t understand c the graph below each team plays no. of matches=no of teams ahead of it. One bar ” represents one team. ————7 6 5 4 3 2 1 0 ———–21last team is written as 0 matches because this team has already played with all other teams-hence sum of matches =6+5+4+3+2+1=21 which is correct only if no of teams =7
answer is :7 teams
Answer B
Answer: B
Question: Marketing executives for a certain chewing gum company projected a 20 percent increase in revenue this year over that of last year, but revenue this year actually decreased by 25%. What percent of the projected revenue was the actual revenue ?
Options:
A)53%
B)58%
C)62.5%
D)64%
E)75%
Rationale: Last year revenue = 100 (assume);
This year revenue = 75;
Projected revenue = 120.
Actual/Projected*100=75/120*100 = 62.5%.
Answer: C
Answer: C
Question: Bacteria reproduce in such a manner that every hour their number
doubles In a controlled experiment that started with a certain number of
bacteria in a jar at 12noon on Tuesday ,30 million were found at 12noon on
Wednesday .At what time were there 15 million bacteria ?
Options:
A)Midnight ,Tuesday
B)6 a.m on Wednesday
C)10 a.m Wednesday
D)9 a.m Wednesday
E)None of these
Rationale: at 12 pm ,bacteria was 30 million ,plus it is also given that quantity of bacteria gets double after every 1 hour
if 12pm(wednesday) bacteria was 30 million;
then at 11 am(wednesday) bacteria was 15 million
so answer is none of these
ANSWER:E
Answer: E
Question: One side of a rectangular field is 15 m and one of its diagonals is 17 m. Find the area of the field.
Options:
A)100 m^2
B)110 m^2
C)120 m^2
D)130 m^2
E)140 m^2
Rationale: Other side = ((17) 2- (15)2)(1/2)
= (289- 225)(1/2)
= (64)(1/2)
= 8 m.
Area = (15 x 8) m2 = 120 m2.
Option C
Answer: C
Question: Circular gears L and R start to rotate at the same time at the same rate. Gear L makes 20 complete revolutions per minute and gear R makes 60 revolutions per minute. How many seconds after the gears start to rotate will gear R have made exactly 8 more revolutions than gear L?
Options:
A)a) 6
B)b) 8
C)c) 10
D)d) 14
E)e) 12
Rationale: Gear L -- 20 rotations per 60 seconds -- 2 rotation per 6 seconds.
Gear R -- 60 rotations per 60 seconds -- 6 rotations per 6 seconds.
First 6 seconds -- Gear L makes 1 rotation. -- Gear R makes 4 rotations -- Net difference -- 4 rotations
Hence every 6 seconds the difference between the number of rotations of R and L gear is 4 units.
Required net difference should be 8 rotations => 2 (6 seconds later) ==> 12 seconds.
Answer: E
Answer: E
Question: 248:3::328:?
Options:
A)7
B)5
C)4
D)6
E)none of the above
Rationale: 248----24/8...3
328---32/8...4
answer C
Answer: C
Question: A starts business with Rs.3500 and after 6 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is Bâ€™s contribution in the Capital ?
Options:
A)24887
B)20778
C)23788
D)10500
E)2811
Rationale: Explanation:
A invested Rs.3500 for 12 months.
Let B joined with investment x. And he invested for 12 - 6 = 6 months.
So there profit ratio = (3500 Ã— 12) : (6x) = 2 : 3
â‡’ x = 10500
Answer: D
Answer: D
Question: In the x-y plane, point (x, y) is a lattice point if both x and y are integers. A square has a center at (0, 0) and side = 4. Some points, such as the center (0, 0), are inside the square, but a point such as (0, 2) is on the square but not in the square. How many lattice points are in the square?
Options:
A)10
B)9
C)8
D)5
E)12
Rationale: The lattice points that are in the square, that lie on the x and y axes, are (0, 0), (0, 1), (1, 0), (0, -1), and (-1, 0).The lattice points in the square and not on the x and y axes are (1, 1), (-1, 1), (1, -1), and (-1, -1).
There are a total of 9 lattice points in the square.
Answer: B
Answer: B
Question: In how many ways can 6 boys and 4 girls sit around a table in such a way that no two girls sit together?
Options:
A)43200
B)41100
C)48500
D)46500
E)49600
Rationale: The 6 boys can be seated around a table in 5! Ways. In between them there are 6 places.
The 4 girls can be placed in the 6 places in 6P4 ways.
Therefore, Required number of ways= 5!* 6P4
=120*360
=43200
ANSWER:A
Answer: A
Question: A sum of Rs. 125000 amounts to Rs. 15000 in 4 years at the rate of simple interest. What is the rate of interest?
Options:
A)3%
B)4%
C)5%
D)6%
E)7%
Rationale: S.I. = (15000 - 12500) = Rs. 2500\
Rate = (100 * 2500) / (12500 * 4) = 5%
ANSWER:C
Answer: C
Question: A man saves 10% of his monthly salary. If an account of dearness of things he is to increase his monthly expenses by 10%, he is only able to save Rs. 200 per month. What is his monthly salary?
Options:
A)Rs.22,000
B)Rs.21,000
C)Rs.20,000
D)Rs.23,000
E)Rs.24,000
Rationale: Income = Rs. 100
Expenditure = Rs. 90
Savings = Rs. 10
Present Expenditure 90+90*(10/100) = Rs.99
Present Savings = 100 – 99 =Rs. 1
If savings is Rs. 1, salary = Rs. 100
If savings is Rs.200, salary = 100/1*200 = 20000
Answer : C
Answer: C
Question: A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.200 when the rate to profit rises from 5 to 7 percent. Find the Capital of B?
Options:
A)2888
B)2777
C)2500
D)2999
E)2771
Rationale: A:B:C = 2/3:1/6:1/6 = 4:1:1
x * 2/100 * 2/3 = 200
B capital = 15000*1/6 = 2500
Answer: C
Answer: C
Question: Farm A had an average output of 300 kgs of wheat per acre. Farm B had an average output of 350 kgs of wheat per acre. It is known that Farm B's area is 20 acres less than Farm A's. It is also known that Farm B in total harvested 2000 kgs of wheat more than Farm A. What is the area of Farm A?
Options:
A) 130 acres
B) 135 acres
C) 145 acres
D) 160 acres
E) 180 acres
Rationale: The area of Farm A = x acres;
The area of Farm B = x-20 acres.
Total output of Farm A = 300x kgs;
Total output of Farm B = 350(x-20) kgs.
Farm B in total harvested 2000 kgs of wheat more than Farm A: 300x+2000=350(x-20) --> x=180 acres.
Answer: E.
Answer: E
Question: If n is a natural number, t hen 6n^2 + 6n is always divisible by?
Options:
A)6 only
B)6 and 12
C)12 only
D)18 only
E)20 only
Rationale: 6n^2 + 6n = 6n(n+1), which is always divisible by 6 and 12 both, since n(n+1) is always even.
Answer is B
Answer: B
Question: If a cube has a volume of 125, what is the surface area of one side?
Options:
A)5
B)25
C)50
D)150
E)625
Rationale: volume of a cube = side^3
125 = side^3
so side = 5
area of one side of the cube = side^2 = 5^2 = 25
correct answer - B
Answer: B
Question: What is the value of 10^7 - 6^5?
Options:
A)99,91,223
B)99,92,224
C)99,94,265
D)99,95,300
E)99,96,307
Rationale: As 10^n will always have last digit as 0 AND 6^n will always as last digit 6.. hence difference of such sum should always be ending with 4 and there is only on option ..
Answer B
Answer: B
Question: A man on tour travels first 160 km at 64 km/he and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is?
Options:
A)71.61 km/hr
B)71.11 km/hr
C)71.18 km/hr
D)77.11 km/hr
E)21.11 km/hr
Rationale: Total time taken = (160/64 + 160/8) = 9/2 hrs.
Average speed = 320 * 2/9
=71.11 km/hr.
Answer:B
Answer: B
Question: When the bus started from the first bus stop, the number of male passengers to the number of female passengers was 1 : 3. At the first stop, 16 passengers got down and 6 more female passengers got in. The ratio of the male to female passengers now became 1: 2. What was the total number of passengers in the bus when it started from the first stop?
Options:
A)64
B)48
C)54
D)46
E)Cannot be determined
Rationale: Let, initially the number of males and females in the bus be ’x’ and ’3x’ respectively.
At the first stop, suppose ’m’ males and ’f’ females left the bus.
Therefore at the first stop the number of males is ’x - m’ and the number of females is ’(3x - f) + 6’
Therefore (x - m)/[(3x - f) + 6] = 1/2
=> 2x - 2m = 3x - f + 6
Also m + f = 16
x = 26 - f
As we have 3 variable and 2 equations, a definite value cannot be determined.
ANSWER:E
Answer: E