divelab/Sys2Bench huggingface dataset:
Question: A store sells chairs and tables. If the price of 2 chairs and 1 table is 60% of the price of 1 chair and 2 tables, and the price of 1 table and 1 chair is $60, what is the price, in dollars, of 1 table? (Assume that every chair has the same price and every table has the same price.)
Options:
A)105/2
B)45
C)44
D)52
E)50
Rationale: LET C= CHAIR ; T =TABLE
2C+1T = 0.6 (1C + 2T) OR C( 2-0.6) = 1.2T -1T OR 1.4C = 0.2 T THEREFORE C= 0.2/1.4 T = 1/7 T
IC +1T =60 OR 1/7T + 1T =60 THEREFORE T= 60*7/8 = 105/2
A
Answer: A
Question: Which one of the following is not a prime number?
Options:
A)31
B)61
C)71
D)91
E)101
Rationale: 91 is divisible by 7. So, it is not a prime number.
answer :D
Answer: D
Question: Bobby has 23 Pokemon cards and he would like to give four friends his
cards. How many cards will each friend get? Will there be any cards left
over?
Options:
A)5 cards-3 left over
B)6 cards-4 left over
C)7 cards-5 left over
D)8 cards-6 left over
E)9 cards-7 left over
Rationale: 23/4 = 5 R 3 Each friend will get 5 cards and there will be 3 cards left
over.
correct answer A
Answer: A
Question: A batsman scored 210 runs which included 3 boundaries and 8 sixes. What % of his total score did he make by running between the wickets
Options:
A)40%
B)50%
C)65%
D)71.4%
E)75%
Rationale: Number of runs made by running = 210 - (3 x 4 + 8 x 6)
= 210 - (60)
= 150
Now, we need to calculate 60 is what percent of 120.
=> 150/210 * 100 = 71.4 %
D
Answer: D
Question: Jamshid and Irwin decided to make up their own version of basketball. In addition to being able to score 2-point baskets, they created ways to score 5-, 11-, and 13-point baskets. If at halftime the product of the point values of Irwin’s baskets was 2,420, how many 11-point baskets E did Irwin score?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: First thing I noticed was that all these numbers are prime...
Prime factorization gives the following
Step 1:2*1210
Step 2:2*11*110
Step 4:2*11*11*10
Step 5:2*11*11*2*5
So he scored E=2 11-point baskets in my opinion.
Answer C
Answer: C
Question: A bakery currently has 9 pies and 2 cakes in its inventory. The bakery’s owner has decided to display 5 of these items in the bakery’s front window. If the items are randomly selected, what is the probability that the display will have exactly 3 pies?
Options:
A)3/5
B)4/7
C)5/7
D)2/11
E)3/11
Rationale: The total number of ways to choose 5 from 11 is 11C5 = 462.
The number of ways that include 3 pies is 9C3*2C2 = 84*1 = 84
P(exactly 3 pies) = 84/462 = 2/11
The answer is D.
Answer: D
Question: David and Rachel are getting married. The extended family wants to have its picture taken, but David's father is unwilling to stand next to Rachel's mother. How many options does the photographer have to arrange the 15 family members in a row for the picture?
Options:
A)15!
B)14×13!
C)13×14!
D)14!/2!
E)13!
Rationale: The number of ways to arrange 15 people is 15!
We need to subtract the arrangement when these two people are together.
Let's think of these two people as a single unit so there are 14 units.
The number of ways to arrange 14 units is 14!
We need to multiply this by 2 since these two people could switch places.
The total number of valid arrangements is 15! - 2*14! = 14!*(15-2) = 13x14!
The answer is C.
Answer: C
Question: If two dice are thrown simultaneously, find the probability that the numbers appeared are equal?
Options:
A)2/6
B)1/6
C)3/6
D)4/6
E)5/6
Rationale: The numbers appeared are equal.
Therefore, the required events are (1, 1), (2, 2), (3, 3), (4, 4), (5, 5) and (6, 6).
Therefore, n(E) = 6
Therefore, the required probability = n(E)/n(S) = 6/36
= 1/6
ANSWER:B
Answer: B
Question: A sum of money becomes triple itself in 5 years at simple interest. How many years will it become four times at the same rate?
Options:
A)12 Â½ years
B)62 Â½ years
C)8 Â½ years
D)72 Â½ years
E)12 Â½ years
Rationale: 100 ---- 200 ---- 5
200 ---- 5
100 ---- 2 1/2
------------------
400 ---- 8 Â½ years
Answer:C
Answer: C
Question: A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5 according to the following constraints. The first digit cannot be 0 or 1, the second digit must be 0 or 1, and the second and third digits cannot both be 0 in the same code. How many different codes are possible?
Options:
A)144
B)152
C)160
D)44
E)176
Rationale: The first digit can be filled in 4 ways
For second digit , it can either be 0 or 1
Case 1 -
If second digit is 1 ,Third digit can take 6 values
number of codes = 4 * 1 * 6 = 24
Case 2 -
If second digit is 0,Third digit can take 5 values ( Third digit can't be zero)
number of codes = 4 * 1 * 5= 20
Total number of codes =44
Answer D
Answer: D
Question: Ira and Jake will throw three dice each. The score is the sum of points on all three dice. If Ira scores 4 in her attempt, what is the probability that Jake will outscore Ira in his attempt?
Options:
A)5/6
B)17/18
C)26/27
D)35/36
E)53/54
Rationale: The total number of ways the dice can land is 6*6*6=216.
There is only 1 way to get a score of 3 = 1+1+1
There are only 3 ways to get a score of 4 = 1+1+2
Jake wins for any other outcome.
P(Jake wins)=1-4/216=53/54
The answer is E.
Answer: E
Question: Machine A produces pencils at a constant rate of 9000 pencils per hour, and machine B produces pencils at a constant rate of 7000 pencils per hour. If the two machines to gather must produce 100,000 pencils and if each machine can operate for at most 8 hours, what is the least amount of time E, in hours, that machine B must operate?
Options:
A)4
B)4 2/3
C)5 1/3
D)6
E)6 1/4
Rationale: Machine A produces pencils at a constant rate of 9,000 pencils per hour, and machine B produces pencils at a constant rate of 7,000 pencils per hour. If the two machines together must produce 100,000 pencils and if each machine can operate for at most 8 hours, what is the least amount of time E, in hours, that machine B must operate?
a) 4
b) 4 and 2/3
c) 5 and 1/3
d) 6
e) 6 and 1/4
To minimize the time that machine B must operate we must maximize the time machine A can operate, so make it operate 8 hours. In 8 hours machine A will produce 8*9,000=72,000 pencils, so 100,000-72,000=28,000 pencils are left to produce, which can be produced by machine B in 28,000/7,000=4 hours.
Answer: A.
Answer: A
Question: What is the remainder when 12987^(65987036) is divided by 5?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: We need to find the units digit of the number.
The units digit of powers of seven repeats 7, 9, 3, and 1 cyclically.
Since 65987036 has the form 4a, the units digit is 1.
Then the remainder when dividing by 5 is 1.
The answer is B.
Answer: B
Question: In a factory, each day the expected number of accidents is related to the number of overtime hour by linear equation. Suppose that on one day there were 1000 overtime hours logged and 8 accidents reported and on another day there were 400 overtime hours logged and 5 accidents. What is the expected number of accidents when no overtime hours are logged?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: Explanation :
Let, the number of over time hours be x and expected number of accidents be y.
We will use the equation y = mx + c , where m and c are constant.
Now,according to the question,
if x =1000, then y=8
i.e 8=1000x + c ----(i)
And, if x=400, then y=5
i.e 5=400x + c. ----(ii)
On solving these equations, we get
m=1/200 and c=3.
Hence, in case, no overtime is there i.e x=0, then the number of expected accident will be 3.
Answer : B
Answer: B
Question: A voltage will influence current only if the circuit is:
Options:
A)2
B)7
C)6
D)889
E)1
Rationale: Answer:B
Answer: B
Question: A typist uses a sheet measuring 20cm by 30cm lengthwise. If a margin of 2 cm is left on each side and a 3 cm margin on top and bottom, then percent of the page used for typing is
Options:
A)40
B)60
C)64
D)72
E)None
Rationale: Solution
Area of the sheet	= (20 x 30 ) cm²
= 600 cm²
Area used for typing	= [(20 - 4) x (30 - 6)] cm²
= 384 cm²
Required percentage	= (384 / 600 x 100)%
=64%.
Answer C
Answer: C
Question: A is two years older than B who is twice as old as C. The total of the ages of A, B and C is 27. How old is B?
Options:
A)25
B)20
C)15
D)10
E)5
Rationale: Let age of C =x. Then,
Age of B =2x
Age of A =2+2x
Total age of A,B and C =27
⇒(2+2x)+2x+x=27⇒5x=25⇒x=255=5
B's age =2x=2×5=10
Answer is D.
Answer: D
Question: How many three-element subsets of {5,6,7,8,9} are there that do not contain the pair of elements 6 and 9?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: Required subsets are = {5,6,7},{5,7,8},{5,8,9},{6,7,8}, {7,8,9}= 5
Answer: E
Answer: E
Question: A shopkeeper sells his goods at cost price but uses a faulty meter that weighs 940 grams. Find the profit percent.
Options:
A)7.38
B)5.38
C)4.38
D)6.38
E)3.38
Rationale: Explanation:
(100 + g) / (100 + x) = True measure / Faulty measure
x = 0
true measure = 1000
faulty measure = 940
100 + g / 100 + 0 = 1000 / 940
100+g = 100/94*100
g = 6.38
ANSWER: D
Answer: D
Question: The numbers in which of the following pairs do NOT have a pair of distinct prime divisors in common?
Options:
A)10 and 20
B)12 and 18
C)24 and 16
D)21 and 63
E)22 and 88
Rationale: 16 has only the prime 2 (16=2^4) in its prime factorization, so it can not have a PAIR of distinct prime divisors in common with ANY of the numbers.
The answer is C.
Answer: C
Question: If a and b are positive even integers, and the least common multiple of a and b is expressed as a*b/q, which of the following statements could be false?
Options:
A)n is a factor of both a and b
B)(a*b)/n < ab
C)ab is multiple of 2.
D)(a*b)/n is a multiple of 2.
E)q is a multiple of 4.
Rationale: If we divide bynand get a multiple ofaand ofb, thennmust be a common factor. Answer A must be true.
If a and b are even integers, dividing by a factor (also an integer) results in something smaller than the productab. Answer B must be true.
If eitheraorbis even, thenabmust be even. Answer C must be true.
If both are even, the smallest either number can be is 2. Thus, the smallest common factor must be 2. Answer D must be true.
Ifbis 6 andais 2,nwould be 6, which is not 4. E can be false.
Answer: E
Question: Find The Odd One Out ?
Options:
A)BACK
B)SNIP
C)TRAP
D)DRAW
E)FLOW
Rationale: A
BACK
All the others can also be read backwards as proper words.
Answer: A
Question: The number of singles that a baseball player hit increased 11 percent from her first season to her second season, and the number of doubles that she hit in the same time period decreased by 1 percent. If the total number of singles and doubles that she hit increased 2 percent from her first season to her second season, what is the ratio of the number of singles she hit in her first season to the number of doubles she hit in her first season?
Options:
A)1:3
B)9:11
C)1:1
D)2:1
E)11:3
Rationale: Soln:-
1.11S + 0.99D = 1.02[S + d]
0.09S = 0.03D
S/D = 1/3
ANSWER:A
Answer: A
Question: The average monthly salary of laborers and supervisors in a factory is Rs.1250 per month; where as the average monthly salary of 6 supervisors is Rs.2450. If the average monthly salary of the laborers is Rs.950 find the number of laborers?
Options:
A)12
B)42
C)66
D)88
E)10
Rationale: 5x 6x 2x
50 25 100
250x + 150x + 200x = 4200
600x = 4200
x = 7 => 6x = 42
Answer: B
Answer: B
Question: A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 1500. The difference between the profit shares of A and C is?
Options:
A)288
B)266
C)155
D)600
E)441
Rationale: Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6
And also given that, profit share of B is Rs. 1500
=> 5 parts out of 15 parts is Rs. 1500
Now, required difference is 6 - 4 = 2 parts
Required difference = 2/5 (1500) = Rs. 600
Answer:D
Answer: D
Question: Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in
Options:
A)1×13/17 hours
B)2×8/11 hours
C)3×9/17 hours
D)4×1/2 hours
E)None
Rationale: Solution
Net part filled in 1 hour	= (1/5 + 1/6 -1/12)
= 17/60.
Therefore, the tank will be full in 60/17 hrs.	‹=› 3×9/17 hrs.
Answer C
Answer: C
Question: By selling 12 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%?
Options:
A)8
B)9
C)12
D)16
E)15
Rationale: Explanation:
80% --- 12
120% --- ?
80/120 * 12 = 8
ANSWER IS A
Answer: A
Question: Amit and Ananthu can do a work in 15 days and 45 days respectively. Amit started the work and left after 3 days. Ananthu took over and completed the work. In how many days was the total work completed?
Options:
A)28 days
B)30 days
C)33 days
D)35 days
E)39 days
Rationale: Amit’s one day’s work= 1/15
Amit’s 3 day’s work = 1/15 *3 = 1/5
Work left= 1-1/5 = 4/5
Ananthu’s one day’s work= 1/45
Ananthu can do work in = 4/5 *45 = 36 days
So total days = 36+3 = 39 days
ANSWER:E
Answer: E
Question: Solution X is 10 percent alcohol by volume, and solution Y is 30 percent alcohol by volume. How many milliliters of solution Y must be added to 300 milliliters of solution X to create a solution that is 18 percent alcohol by volume?
Options:
A)100
B)150
C)200
D)250
E)300
Rationale: 18% is 8%-points higher than 10% but 12%-points lower than 30%.
Thus there should be 3 parts of solution X for 2 parts of solution Y.
We should add 200 ml of solution Y.
The answer is C.
Answer: C
Question: Income and expenditure of a person are in the ratio 9 : 8. If the income of the person is Rs. 18000, then find his savings?
Options:
A)Rs.3600
B)Rs.3603
C)Rs.2000
D)Rs.3632
E)Rs.3602
Rationale: Let the income and the expenditure of the person be Rs. 9x and Rs. 8x respectively.
Income, 9x = 18000 => x = 2000
Savings = Income - expenditure = 9x - 8x = x
So, savings = Rs.2000
Answer:C
Answer: C
Question: The cost per pound of tea and milk powder were the same in June. In July, the price of milk powder shot up by 200% and that of tea dropped by 80%. If in July, a mixture containing equal quantities of tea and milk powder costs $4.80 for 3lbs, how much did a pound of tea cost in July?
Options:
A)$4
B)$0.2
C)$1
D)$3
E)$1.65
Rationale: Lets assume price of Coffee in June =100x
Price of Tea in June =100x
Price of milk powder in July = 300x (because of 200% increase in price)
Price of Tea in July = 20x (because of 80% Decrease in price)
Price of 1.5 pound milk powder 1.5 pound of Tea in July will be = 450x + 30x = 480x
As per question
480x= 4.80$
x = 0.01S
So the Price of Tea in July = 20x = 20 x 0.01 = 0.2$/pound
Answer B
Answer: B
Question: If a is the sum of m consecutive positive integers and b is the sum of n consecutive positive integers. For which of the following values of m and n is it impossible that a = b?
Options:
A)m = 2; n = 6
B)m = 3; n = 6
C)m = 10; n = 4
D)m = 7; n = 9
E)m = 10; n = 7
Rationale: I approached this in a different way, although may be longer but it's certainly more intuitive
It is impossible that a = b if one of them is necessarily even while the other is necessarily odd
for two consecutive integers the sum is necessarily odd
for six consecutive integers the sum is necessarily odd (sum of 3two consecutive integerswhich are all odd)
Thus A is incorrect.
The sum of 3 consecutive integers can be even or odd (an odd integer from the first 2 + an additional integer which can be even or odd). Thus B is incorrect. You can do a similar approach for D and E (it follows that the sum of a specified odd number of consecutive integers can be odd or even).
Leaving us with C to be the only not-wrong answer. To confirm, you can easily deduce that the sum of 4 consecutive integers (sum of 2 odd integers) is necessarily even while the sum of 10 consecutive integers (sum of 5 odd integers) is necessarily odd. Thus C is the right answer.
Answer: C
Question: A five digit number is to be formed using each of the digits 1, 2, 3, 4 and 5 ONLY ONCE. How many numbers can be formed when 3 and 4 are not together ?
Options:
A) 48
B) 36
C) 60
D) 72
E) 120
Rationale: Reqd ways = (Total No. of ways - cases when both 3 and 4 are together)
5 numbers can be arranged in 5 places in 5! ways. Now tie 3 and 4 together so effectively there are 4 nos. they can be arranged in 4! ways. 1 and 2 can be arranged within themselves in 2!ways.
Reqd. Answer = 5! - 4!2! = 120 - (24*2) = 72
Answer: D
Answer: D
Question: A car averages 30 miles per hour for the first 6 hours of a trip and averages 46 miles per hour for each additional hour of travel time. If the average speed for the entire trip is 34 miles per hour, how many hours long is the trip?
Options:
A)8
B)10
C)12
D)14
E)16
Rationale: Let T be the total time of the trip.
30*6 + 46(T-6) = 34T
12T = 276-180
T = 8
The answer is A.
Answer: A
Question: A 1100 m long train crosses a tree in 110 sec, how much time will It take to pass a platform 700 m long?
Options:
A)288
B)190
C)188
D)180
E)12
Rationale: L = S*T
S= 1100/110
S= 10 m/Sec.
Total length (D)= 1800 m
T = D/S
T = 1800/10
T = 180 Sec
Answer:D
Answer: D
Question: The area of a square field is 625 km2. How long will it take for a horse to run around at the speed of 25 km/h ?
Options:
A)12 h
B)10 h
C)8 h
D)4 h
E)None of these
Rationale: Explanation Area of field = 625 km2. Then, each side of field = √625=25km Distance covered by the horse = Perimeter of square field = 25 × 4 = 100 km ∴ Time taken by horse = distances/peed=100/25=4h Answer D
Answer: D
Question: For any triangle T in the xy–coordinate plan, the center of T is defined to be the point whose x–coordinate is the average (arithmetic mean) of the x–coordinates of the vertices of T and whose y–coordinate is the average of the y–coordinates of the vertices of T. If a certain triangle has vertices at the points (0,0) and (9,0) and center at the point (3,3), what are the coordinates of the remaining vertex?
Options:
A)(3,4)
B)(3,6)
C)(0,9)
D)(6,4)
E)(9,6)
Rationale: Let (a,b) be the remaining vertex.
x: 0 + 9 + a = 3*3. Then a = 0.
y: 0 + 0 + b = 3*3. Then b = 9.
The answer is C.
Answer: C
Question: The total of the ages of Amar, Akbar and Anthony is 80 years. What was the total of their ages three years ago ?
Options:
A)71 years
B)72 years
C)74 years
D)77 years
E)79 years
Rationale: The total of the ages of Amar, Akbar and Anthony is 80 years.
total of their ages three years ago = 80-3*3= 71 yrs
ANSWER:A
Answer: A
Question: Mangala completes a piece of work in 10 days, Raju completes the same work in 40 days. If both of them work together, then the number of days required to complete the work is?
Options:
A)5 days
B)6 days
C)7 days
D)8 days
E)9 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 10 × 40/50 = 8 days.
D)
Answer: D
Question: The number of diagonals of a polygon of n sides is given by the formula z=n(n-3)/2. If a polygon has twice as many diagonals as sides, how many sides does it have?
Options:
A) 3
B) 5
C) 6
D) 7
E) 8
Rationale: z=n(n-3)
z=2*n
2n=n(n-3)
=>2=n-3
=>n=5
Answer B
Answer: B
Question: The ratio of the ages of three people is 4:6:7. Eight years ago, the sum of their ages was 61. Find their present ages.
Options:
A)12,18,21
B)16,24,28
C)20,30,35
D)24,36,42
E)28,42,49
Rationale: Let the present ages be 4x, 6x, 7x.
(4x-8) + (6x-8) + (7x-8) = 61
17x = 85
x = 5
Their present ages are 20, 30, and 35.
The answer is C.
Answer: C
Question: In the accounting branch of a commercial institute, the percentage of male and female workers is 48% and 52% respectively. In this branch, 40% of males and 20% of females are age 25 or older. If one of the workers is selected at random, what is the probability E that the worker is under 25 years old?
Options:
A) 0.30
B) 0.25
C) 0.45
D) 0.70
E) 0.90
Rationale: Percentage of male worker = 48
Percentage of female worker = 52
Let total number of workers = 1000
number of male workers= 480
number of female workers = 520
Number of male age 25 or older = (4/10)*480 = 192
Number of female age 25 or older =(2/10)*520 = 104
Total number of workers 25 or older = 192+104 = 296
Total number of workers under 25 = 1000 - 296 = 704
Probability that a worker randomly selected is under 25 years old = 704/1000 = .704
Alternatively , since the answer options are not close , we can use estimation here .
Percentage of male worker 25 or older = (4/10)*48 = 20 % approx
Percentage of female worker 25 or older = (2/10)*52 = 10 % approx
Percentage of total worker 25 or older = 30 %
Percentage of total worker under 25 = 70 %
Probability that a worker randomly selected is under 25 years old E= .7
Answer D
Answer: D
Question: When you multiply a number by 4 and
then subtract 3, the result is the same as
if you first subtracted 7 from the same
number and then multiplied by 9. What
is the number?
Options:
A)A)23
B)B)13
C)C)19
D)D)12
E)E)10
Rationale: Let x equal the number and then change the words into an equation and solve for x:
4x – 3 = 9(x – 7)
4x – 3 = 9x – 63
60 = 5x
12 = x
correct answer D)12
Answer: D
Question: One half of the workers at the biscuit company is technician,quarter is clerk,one-fifth are administrative and the other 25 are supervisors. How many workers total are there in the biscuit company?
Options:
A)250
B)366
C)400
D)500
E)2500
Rationale: 1/2x + 1/4x +1/5x = 19/20x
Remaining 1/20 x= 25
x= 25*20= 500
D is the answer.
Answer: D
Question: In Chess game, one player throws two fair, six-sided die at the same time. If the player receives at least a five or a one on either die, that player wins. What is the probability that a player wins after playing the game once?
Options:
A)1/3
B)4/9
C)5/9
D)2/3
E)3/4
Rationale: In Chess game,Probably the easiest approach would be to find the probability of the opposite event and subtract it from 1:
P(win) = 1- P(not win) = 1 - 4/6*4/6 = 5/9.
Answer: C.
Answer: C
Question: A garrison of 400 men had a provision for 31 days. After 28 days 280 persons re-enforcement leave the garrison. Find the number of days for which the remaining ration will be sufficient?
Options:
A)22
B)88
C)10
D)99
E)27
Rationale: 400 --- 31
400 --- 3
120 --- ?
400*3 = 120*x => x =10 days
Answer: C
Answer: C
Question: Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 36 kmph. Of how many minutes does the train stop per hour?
Options:
A)16
B)17
C)12
D)18
E)12
Rationale: T = 9/45 * 60
= 12
Answer: C
Answer: C
Question: The instructions state that Cheryl needs 2 square yards of one type of material and 1/2 square yards of another type of material for a project. She buys exactly that amount. After finishing the project, however, she has 5/10 square yards left that she did not use. What is the total amount of square yards of material Cheryl used?
Options:
A)1/12
B)1/9
C)2
D)1 1/9
E)2 1/9
Rationale: total bought = 2+1/2
left part 5/10--->1/2
so used part 2+1/2-1/2=2
Ans C
Answer: C
Question: The number of students enrolled at school XX this year is 7 percent more than it was last year. The number of students enrolled at school YY this year is 3 percent more than it was last year. If school XX grew by 40 more students than school YY did, and if there were 4000 total enrolled students last year at both schools, how many students were enrolled at school YY last year?
Options:
A)480
B)1600
C)1920
D)2080
E)2400
Rationale: Given Info:
No. of students enrolled in school X is= 7% more than previous year's strength= 7X/100
No. of students enrolled in school Y is= 3% more than previous year's strength= 3Y/100
Given that "THIS YEAR" school X have 40 students more than school Y. So the increase in strength can be written as
7X/100= 40 + 3Y/100
7X= 4000 + 3Y....................(1)
And total students on previous year are X + Y=4000......................(2)
Equating & Solving we get, Y=2400
ANS is E
Answer: E
Question: In how many ways can live boys and three girls sit in a row such that all boys sit together?
Options:
A)2888
B)2885
C)2880
D)2876
E)2224
Rationale: Treat all boys as one unit. Now there are four students and they can be arranged in 4! ways. Again five boys can be arranged among themselves in 5! ways.
Required number of arrangements = 4! * 5! = 24 * 120 = 2880.
Answer:C
Answer: C