divelab/Sys2Bench huggingface dataset:
Question: In a 500 m race, the ratio of the speeds of two contestants A and B is 3 : 4. A has a start of 140 m. Then, A wins by:
Options:
A)20 m
B)40 m
C)60 m
D)45 m
E)55 m
Rationale: To reach the winning post A will have to cover a distance of (500 - 140)m, i.e., 360 m.
While A covers 3 m, B covers 4 m.
while A covers 360 m B covers (4/3*360) = 480 m
when A reaches the winning post B covers 480 m and 20 m behind
ANSWER A
Answer: A
Question: A manufacturer of a certain product can expect that between 0.2 percent and 0.5 percent of the units manufactured will be defective. If the retail price is $2,500 per unit and the manufacturer offers a full refund for defective units, how much money can the manufacturer expect to need to cover the refunds on 20,000 units?
Options:
A) Between $15,000 and $25,000
B) Between $30,000 and $50,000
C) Between $60,000 and $100,000
D) Between $100,000 and $250,000
E) Between $300,000 and $500,000
Rationale: Number of defective units is between = .2 % of 20000 and .5% of 20000
= 40 and 100
Retail Price per unit = 2500 $
Expected price of refund is between = 2500 x 40 and 2500 x 100
=1,00,000 and 2,50,000 dollars
Answer D
Answer: D
Question: The difference of the areas of two squares drawn on two line segments in 32 sq. cm. Find the length of the greater line segment if one is longer than the other by 2 cm
Options:
A)9 cm
B)8 cm
C)7 cm
D)6 cm
E)5 cm
Rationale: Explanation:
Let the lengths of the line segments be x and x+2 cm
then,
(x+2)2−x2=32x2+4x+4−x2=324x=28x=7cm
Option C
Answer: C
Question: A man's speed with the current is 20 kmph and speed of the current is 4 kmph. The Man's speed
against the current will be
Options:
A)11 kmph
B)12 kmph
C)14 kmph
D)17 kmph
E)None of these
Rationale: Explanation:
Speed with current is 20,
speed of the man + It is speed of the current
Speed in sƟll water = 20 - 4 = 16
Now speed against the current will be
speed of the man - speed of the current
= 16 - 4 = 12 kmph
Answer: B
Answer: B
Question: At a certain university, the ratio of the number of teaching assistants to the number of students in any course must always be greater than 3:50. At this university, what is the maximum number of students possible in a course that has 4 teaching assistants?
Options:
A)63
B)64
C)65
D)66
E)67
Rationale: (4/3)*50=66 plus remainder
The answer is D.
Answer: D
Question: The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square?
Options:
A)482
B)268
C)260
D)480
E)632
Rationale: Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively.
4a = 2(l + b)
2a = l + b
l . b = 480
We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found .
Area of the square cannot be found.
Answer: D
Answer: D
Question: Zachary is helping his younger brother, Sterling, learn his multiplication tables. For every question that Sterling answers correctly, Zachary gives him 3 pieces of candy. For every question that Sterling answers incorrectly, Zachary takes away two pieces of candy. After 8 questions, if Sterling had answered 2 more questions correctly, he would have earned 31 pieces of candy. How many of the 8 questions did Zachary answer correctly?
Options:
A)6
B)7
C)8
D)9
E)10
Rationale: i got two equations:
3x-2y=25
x+y=8
3x-2(8-x)=25
3x-16+2x=25
5x=41
x=8.2 or between 8 and 9. 9ANS C)
Answer: C
Question: The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum (in Rs. ) is?
Options:
A)625
B)298
C)269
D)200
E)267
Rationale: Let the sum be Rs. x. Then,
[x (1 + 4/100)2 - x] = (676/625 x - x) = 51/625 x
S.I. = (x * 4 * 2)/100 = 2x/25
51x/625 - 2x/25 = 1 or x = 625.Answer: A
Answer: A
Question: What is the probability that a man flipping ten fair coins flips at least two heads?
Options:
A)1
B)1/2
C)1/512
D)1013/1024
E)1023/1024
Rationale: There is a 1/1024 chance of flipping no heads, and a 10/1024 chance of flipping 1 head. This means the chance of flipping two or more heads is 1 - (1/1024 + 10/1024) = 1013/1024, so the answer is D.
Answer: D
Question: Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is
Options:
A)5/6
B)5/9
C)5/3
D)5/1
E)5/2
Rationale: No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways.
Thus 6 * 5 * 4 = 120 favourable cases.
The total cases are 6 * 6 * 6 = 216.
The probability = 120/216 = 5/9.
Answer: B
Answer: B
Question: If k,m ,and n are positive real numbers such that k(m+n) = 152, m(n+k) =162 , and n(k+m) = 170, then kmn is
Options:
A)a) 672
B)b) 688
C)c) 704
D)d) 720
E)e) 750
Rationale: km+kn = 152 --------------------------------------1)
mn+mk = 162---------------------------------------2)
kn+nm = 170---------------------------------------3)
Re-writing equation 3 as follows: kn+nm = 162 + 8 kn+nm= mn+mk + 8
kn = mk + 8 ............... (4)
Adding (1)(4)
2kn = 160
kn = 80
kmn has to be multiple of 80, only 720 fits in
Answer = D
Answer: D
Question: Arjun started a business with Rs. 5,000 and is joined afterwards by Anoop with Rs.10, 000. After how many months did Anoop join if the profits at the end of the year are divided equally?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: Suppose Anoop joined after 3 months.
Then, 5000 * 12 = 10000 * (12 – x)
=> x = 6.
ANSWER:D
Answer: D
Question: The average of 1st 3 of 4 numbers is 16 and of the last 3 are 15. If the sum of the first and the last number is 13. What is the last numbers?
Options:
A)9
B)8
C)5
D)4
E)3
Rationale: A + B + C = 48
B + C + D = 45
A + D = 13
A – D = 3
A + D = 13
2D = 10
D = 5
Answer: C
Answer: C
Question: The ratio of the volumes of two cubes is 216 : 343. What is the ratio of their total surface areas?
Options:
A)81:12
B)31:36
C)81:22
D)8:19
E)1:11
Rationale: Ratio of the sides = ³√216 : ³√343
= 6 : 7
Ratio of surface areas = 62:72
= 31:36
Answer: B
Answer: B
Question: Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Five years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?
Options:
A)Can't be determined
B)40
C)27
D)24
E)None of these
Rationale: Explanation:
Let the present ages of Sameer and Anand be 5x years and 4x years respectively.
Then, (5x+5)/(4x+5)=11/9
⇒ 45x + 45 = 44x + 55⇒ 9(5x + 5) = 11(4x + 5)
⇒ 45x - 44x = 55 - 45
⇒ x = 10.
Anand's present age = 4x = 40 years.
Answer: B
Answer: B
Question: If n is an integer, f(n) = f(n-1) - n and f(4)=14. What is the value of f(6)?
Options:
A)3
B)0
C)1
D)2
E)4
Rationale: Since f(n)=f(n-1)-n then: f(6)=f(5)-6 and f(5)=f(4)-5.
As given that f(4)=14 then f(5)=14-5=9 --> substitute the value of f(5) back into the first equation: f(6)=f(5)-6=9-6=3.
Answer: A.
Questions on funtions to practice:
Answer: A
Question: Two men Amar and Bhavan have the ratio of their monthly incomes as 6:5. The ratio of their monthly expenditures is 3:2. If Bhavan saves one-fourth of his income, find the ratio of their monthly savings?
Options:
A)3:17
B)3:10
C)3:26
D)3:19
E)3:16
Rationale: Let the monthly incomes of Amar and Bhavan be 6x and 5x respectively.
Let the monthly expenditures of Amar and Bhavan be 3y and 2y respectively.
Savings of Bhavan every month = 1/4 (5x)
=(his income) - (his expenditure) = 5x - 2y
=> 5x = 20x - 8y => y = 15x/8
Ratio of savings of Amar and Bhavan
= 6x - 3y : 1/4 (5x) = 6x - 3(15x/8) : 5x/4
= 3x/8 : 5x/4 => 3:10
Answer: B
Answer: B
Question: If the area of a square with sides of length 9 centimeters is equal to the area of a rectangle with a width of 3 centimeters, what is the length of the rectangle, in centimeters?
Options:
A)4
B)27
C)12
D)16
E)18
Rationale: Let length of rectangle = L
9^2 = L*3
=> L = 81/3 = 27
Answer B
Answer: B
Question: Last year Department Store X had a sales total for December that was 6 times the average (arithmetic mean) of the monthly sales totals for January through November. The sales total for December was what fraction of the sales total for the year?
Options:
A)6/17
B)4/15
C)1/3
D)4/11
E)4/5
Rationale: Let avg for 11 mos. = 10
Therefore, Dec = 60
Year total = 11*10 + 60 = 170
Answer = 60/170 = 6/17 = A
Answer: A
Question: If r is even and s is odd, which of the following is odd?
Options:
A)rs
B)5rs
C)6(r^2)s
D)5r + 6s
E)6r + 5s
Rationale: Just checking options (In case you have difficulty then choose values of r=2 and t=1)
r = even
s= Odd
A. rs = Even*Odd = EvenINCORRECT
B. 5rs = Odd*Even*Odd = EvenINCORRECT
C. 6(r^2)s = 6*(Even^2)*Odd = EvenINCORRECT
D. 5r + 6s = 5*Even + 6*Odd = Even+Even = EvenINCORRECT
E. 6r + 5s = 6*Even + 5*Odd = Even+Odd = OddCORRECT
Answer: option E
Answer: E
Question: During 2001, a stock lost 80 percent of its value. During the following year, the stock's value increased by 100 percent. Which of the following is the percent change in the stock's value during those two years?
Options:
A)60 percent decrease
B)40 percent decrease
C)20 percent increase
D)60 percent increase
E)140 percent increase
Rationale: Let the value of the stock in 2000 be 100, then in 2001 its value would be 100*(1-80/100)=100*0.2=20 and in 2002 its value would be 20*(1+100/100)=40. Hence during those two years the value of the stock decreased from 100 to 40, so by 60%.
Answer: A.
Answer: A
Question: One night a certain hotel rented 3/4 of its rooms. including 2/3 of their air conditioned rooms. if 3/5 of its rooms were air conditioned, what percent of the rooms that were not rented were air conditioned?
Options:
A)20
B)33 1/3
C)35
D)40
E)80
Rationale: Consider total # of rooms to be 100;
As 3/5 of the rooms are air conditioned then # of rooms that are air conditioned is 3/5*100=60;
3/4 rooms were rented --> 1/4*100=25 were NOT rented;
2/3 of air conditioned rooms were rented --> 1/3*60=20 air conditioned room were NOT rented;
20/25=4/5=80%.
Answer: E.
Answer: E
Question: In Town X, 64 percent of the population are employed, and 46 percent of the population are employed males. What percent of the employed people in Town X are females?
Options:
A)16%
B)27%
C)32%
D)40%
E)52%
Rationale: answer b
male-employed - 64%
female-employed-18%
Total employed 64%
means total unemployed = 36%
therefore d and e are not correct because female unemployed has to be less than 36%
female-unemployed = 32% male unemployed = 4%
48% + 4% = 52%
16% + 32% = 48%
plug in a and b in place of 32% and the sum is not 100%
18/64 =27 B
Answer: B
Question: The age of father 6 years ago was four times the age of his son. Five years hence, father's age will be twice that of his son. The ratio of their present ages is:
Options:
A)55 : 23
B)43 : 23
C)51 : 23
D)53 : 23
E)56 : 23
Rationale: Let the ages of father and son 6 years ago be 3x and x years respectively.
Then, (4x + 6) + 5= 2[(x + 6) + 5]
4x + 11 = 2x + 22
x = 5.5.
Required ratio = (4x + 6) : (x + 6) = 28 : 11.5 =56 : 23.
Answer: Option E
Answer: E
Question: The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?
Options:
A)1
B)2
C)3
D)4
E)None
Rationale: Let the ten's digit be x and unit's digit be y.
Then, (10x + y) - (10y + x) = 36
9(x - y) = 36
x - y = 4.
Option D
Answer: D
Question: Little Texas Drilling Company has three wells, each producing oil at a constant rate. Well A produces one barrel every two minutes. Well B produces one barrel every three minutes. Well C produces one barrel every four minutes. How many hours does it take Little Texas Drilling Company to produce 205 barrels of oil?
Options:
A)2
B)3
C)4
D)18
E)180
Rationale: Well A produces 1/2 a barrel per minute.
Wells B and C produce 1/3 + 1/4 = 7/12 (a little more than half) a barrel per minute.
So all three wells combined produce a little more than 1 barrel per minute.
So for 205 barrels they will take a bit less than 205 mins which will be more than 3 hrs but less than 4 hrs.
Answer (C)
Answer: C
Question: A man takes 5 hours 45 min in walking to a certain place and riding back. He would have gained
2 hours by riding both ways. The time he would take to walk both ways is
Options:
A)11 hrs
B)8 hrs 45 min
C)7 hrs 45 min
D)9 hrs 20 min
E)10 hrs
Rationale: Given that time taken for riding both ways will be
2 hours lesser than the time needed for waking one way and riding back.
Therefore,
time needed for riding one way = time needed for waking one way -
2 hours
Given that time taken in walking one way and riding back
=5 hours 45 min
Hence, the time he would take to walk both ways
5 hours 45 min + 2 hours =7 hours 45 min
ANSWER C
Answer: C
Question: four mobsters have arrived at the theater for the premiere of the film “Goodbuddies.” One of the mobsters, Frankie, is an informer, and he's afraid that another member of his crew, Joey, is on to him. Frankie, wanting to keep Joey in his sights, insists upon standing behind Joey in line at the concession stand, though not necessarily right behind him. How many ways can the four arrange themselves in line such that Frankie’s requirement is satisfied?
Options:
A)24
B)28
C)32
D)36
E)42
Rationale: 4 mobsters can stand in 4! ways = 24
in half of the cases one person will be ahead and in the other person in the other half.
thus 24 cases.
A
Answer: A
Question: What amount does Kiran get if he invests Rs.4500 at 10% p.a. compound interest for three years, compounding done annually?
Options:
A)2999
B)2787
C)2097
D)5989
E)2886
Rationale: A= P{1 + R/100}n
=> 4500{1 + 10/100}3
= Rs.5989
Answer: D
Answer: D
Question: Radha started a business, investing 75,000. After 3 months, Sunidhi joined her with an amount of 1,25,000 and after another six months Neha joined them with an amount of 1,50,000. Profit earned at the end of three years from when Radha started the business should be distributed in what ratio among Radha, Sunidhi and Neha respectively?
Options:
A)36 : 55 : 54
B)18 : 28 : 27
C)35 : 54 : 55
D)Cannot be determined
E)None of these
Rationale: Ratio of their profits (Radha’s : Sunidhi’s : Neha’s)
= 75 × 36 : 125 × 33 : 150 × 27
= 3 × 36 : 5 × 33 : 6 × 27
= 3 × 12 : 5 × 11 : 6 × 9
= 36 : 55 : 54
Answer A
Answer: A
Question: A number when divided by a divisor leaves a remainder of 24.
When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?
Options:
A)37
B)39
C)42
D)44
E)45
Rationale: Let the original number be 'a'
Let the divisor be 'd'
Let the quotient of the division of aa by dd be 'x'
Therefore, we can write the relation as a/d = x and the remainder is 24.
i.e., a=dx+24 When twice the original number is divided by d, 2a is divided by d.
We know that a=dx+24. Therefore, 2a = 2dx + 48
The problem states that (2dx+48)/d leaves a remainder of 11.
2dx2dx is perfectly divisible by d and will therefore, not leave a remainder.
The remainder of 11 was obtained by dividing 48 by d.
When 48 is divided by 37, the remainder that one will obtain is 11.
Hence, the divisor is 37.
A
Answer: A
Question: A, Band C enter into partnership. A invests 3 times as much as B and B invests two-third of what C invests. At the end of the year, the profit earned is Rs. 3300. What is the share of B ?
Options:
A)1100
B)800
C)1400
D)600
E)None of them
Rationale: Let C's capital = Rs. x. Then, B's capital = Rs. (2/3)x
A’s capital = Rs. (3 x (2/3).x) = Rs. 2x.
Ratio of their capitals = 2x : (2/3)x :x = 6 : 2 : 3.
Hence, B's share = Rs. ( 3300 x (2/11))= Rs.600
Answer is D.
Answer: D
Question: A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 24 seconds. What is the length of the goods train?
Options:
A)230 m
B)240 m
C)260 m
D)270 m
E)None of these
Rationale: Explanation:
Speed =[ 72 x (5/18) ]m/sec= 20 m/sec.
Time = 24 sec.
Let the length of the train be x metres.
Then,[ (x+250)/24 ]= 20
=> x + 250 = 480
=> x = 230. Answer: A
Answer: A
Question: The ratio of two numbers is 3:4 and their sum is 49. The greater of the two numbers is?
Options:
A)12
B)14
C)16
D)17
E)28
Rationale: 3:4
Total parts = 7
= 7 parts --> 49 (7 Ã— 7 = 49)
= 1 part ---->7 (1 Ã— 7 = 7)
= The greater of the two number is = 4
= 4 parts ----> 28 (7 Ã— 4 = 28)
E
Answer: E
Question: The unit digit in the product (624 * 708 * 913 * 463) is:
Options:
A)2
B)5
C)6
D)8
E)10
Rationale: Explanation:
Unit digit in the given product = Unit Digit in (4*8*3*3) = 8
ANSWER: D
Answer: D
Question: (51+ 52 + 53 + ... + 100) = ?
Options:
A)3775
B)3795
C)3800
D)3900
E)4000
Rationale: This is an A.P. in which a = 51, l = 100 and n = 50.
Sum = n (a + l) = 50 x (51 + 100) = (25 x 151) = 3775.
2 2
A)
Answer: A
Question: In an electric circuit, two resistors with resistances A and B are connected in parallel. In this case, if r is the combined resistance of these two resistors, then the reciprocal of C is equal to the sum of the reciprocals of A and B. What is C in terms of A and B?
Options:
A)(A-B)/AB
B)(A+B)/AB
C)A+B
D)AB
E)AB/(A + B)
Rationale: The wording is a bit confusing, though basically we are told that 1/C= 1/A + 1/B, from which it follows that C=AB/(A + B).
Answer: E
Answer: E
Question: A library has an average of 570 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is:
Options:
A)250
B)276
C)280
D)295
E)None
Rationale: Since the month begins with sunday,to there will be five sundays in the month
Average required = (570x5 + 240x25) /30) = 295
Answer: Option D
Answer: D
Question: If x-y=8, which of the following must be true?
I. If x is negative, y must be negative
II. Both x and y are positive
III. If x is positive, y must be positive
Options:
A)I only
B)II only
C)III only
D)I and II
E)II and III
Rationale: If x-y=8, which of the following must be true?
I. Both x and y are positive
II. If x is positive, y must be positive
III. If x is negative, y must be negative
1. x and y can be negative, for instance, -2 - (-10) = 8 =>Eliminate A and D
2. x can be positive and y can be negative, for instance, 2 - (-6) = 8 => Eliminate B and E
A) I only
B) II only
C) III only
D) I and II
E) II and III
Answer A
Answer: A
Question: Ajay had purchased a second hand scooter for 18,000 and spent Rs.1800 for repairs. After one year he wanted to sell the scooter. At what price should he sell it to gain 100/9%, if 100/11% is to be deducted at the end of every year on account of deprecation?
Options:
A)Rs.18000
B)Rs.19800
C)Rs.20000
D)Rs.22500
E)Rs.23500
Rationale: Cost Price =Rs.18000.
Cost on Reparing = Rs. 1800.
So, Total cost = 18000 +1800 = 19800.
Depreciation = 100/11% = 9.09%.
Gain = 100/9% = 11.11%.
After depreciation, the cost price would be = 19800 - 9.09% of 19800 = Rs. 18000
SP to gain 11.11% = 18000 + 11.11% of 18000 = 18000 + 1999.8 = Rs. 20,000.
ANSWER : C
Answer: C
Question: Find compound interest on Rs. 8000 at 15% per annum for 2 years 4 months, compounded annually
Options:
A)3358
B)8952
C)3309
D)3109
E)3528
Rationale: Time = 2 years 4 months = 2(4/12) years = 2(1/3) years.Amount = Rs'. [8000 X (1+(15/100))^2 X (1+((1/3)*15)/100)]=Rs. [8000 * (23/20) * (23/20) * (21/20)]= Rs. 11109. .:. C.I. = Rs. (11109 - 8000) = Rs. 3109. Answer : D
Answer: D
Question: At Company K, 15 percent of the employees are secretaries and 60 percent are salespeople. If there are 45 other employees of Company K, how many employees does Company K have?
Options:
A)160
B)180
C)190
D)200
E)400
Rationale: Secretaries = 15 %
Salespeople = 60%
Percentage of employee other than Secretaries and Salespeople = 25%
Let total number of employees of company K = N
(25/100)* N = 45
=>N=180
Answer B
Answer: B
Question: A ship 77 km from the shore, springs a leak which admits to 9/4 tonnes of water in 11/2 minutes. 92 tonnes of water would sink it. But the pumps can throw out 12 tonnes of water per hour. Find the average rate of sailing so that the ship may just reach the shore as it begins to sink.
Options:
A)10.5
B)11
C)12
D)13
E)15
Rationale: Leak admits 9/4 tonnes water in 11/2 min
=11/2 * 4/9 = 22/9
leak admits 9/22 tonne of water in 5 min
in 1 min in thrws 1/5 tonne of water = 9/22 - 1/5 = 23/110
92/23/11 min = 440 min
22/3 min=7/22/22/3 => 10.5 km/hr
ANSWER A
Answer: A
Question: On dividing a number by 56, we get 29 as remainder. On dividing the same number by 8, what will be the remainder ?
Options:
A)4
B)5
C)6
D)8
E)9
Rationale: Explanation:
Formula: (Divisor*Quotient) + Remainder = Dividend.
Soln:
(56*Q)+29 = D -------(1)
D%8 = R -------------(2)
From equation(2),
((56*Q)+29)%8 = R.
=> Assume Q = 1.
=> (56+29)%8 = R.
=> 85%8 = R
=> 5 = R.
Answer B
Answer: B
Question: Total dinning bill for 5 people was $211.00.If they add 15% tip and divided the bill evenly ,approximate.What was each persons find share
Options:
A)$30.14
B)48.53
C)34.66
D)32.29
E)33.16
Rationale: 211*15=3165/100=31.65
211+31.65=242.65
242.65/5=48.53
ANSWER:B
Answer: B
Question: he probability that a number selected at random from the first 50 natural numbers is a composite number is ?
Options:
A)17/25
B)4/25
C)21/25
D)8/25
E)9/25
Rationale: Explanation:
The number of exhaustive events = ⁵⁰C₁ = 50.
We have 15 primes from 1 to 50.
Number of favourable cases are 34.
Required probability = 34/50 = 17/25.
A)
Answer: A
Question: If the positive integer x is a multiple of 7 and the positive integer y is a multiple of 6, then xy must be a multiple of which of the following?
I. 8
II. 12
III 18
Options:
A)II only
B)I and II only
C)I and III only
D)II and III only
E)I, II and III
Rationale: Ans A
From question x/4 is an integer.
x/4 = 2*2*q/4 ---> where q is the integer
Also y/6 = p => y/6 = 2*3*p/6
So, xy = 2*2*2*3 *pq
Thus 2*2*2 = 8 and 2*3*2 = 12 satisfy
Answer: A
Question: A grocer stacked oranges in a pile. The bottom layer was rectangular with 4 rows of 8 oranges each. In the second layer from the bottom, each orange rested on 4 oranges from the bottom layer, and in the third layer, each orange rested on 4 oranges from the second layer. Which of the following is the maximum number of oranges that could have been in the third layer?
Options:
A) 14
B) 12
C) 10
D) 7
E) 4
Rationale: Bottom Layer = 8 x 4 = 32
IInd Layer = (8-1) x (4-1) = 21
IIIrd Layer = (7-1) x (3-1) = 12
Answer = 12 = B
Answer: B
Question: A trumpet section includes four musicians. If they hold an audition to determine chair order within the section, and there are to be no ties, how many distinct chair orders can result?
Options:
A)240
B)125
C)120
D)100
E)24
Rationale: We have a word problem using permutations. We must identify the number of total items in the group. There are four possible musicians who could be placed in the first chair, three possible musicians for the second, two for the third, one for the fourth. To determine the number of possible orderings, we multiply these numbers, which we can express as 4!. Now 4! = (4)(3)(2)(1) = 24=E
Answer: E
Question: A room is 6 meters 24 centimeters in length and 4 meters 32 centimeters in Width. Find the least number of square tiles of equal size required to cover the entire floor of the room.
Options:
A)017
B)117
C)127
D)137
E)147
Rationale: Let us calculate both the length and width of the room in centimeters.
Length = 6 meters and 24 centimeters = 624 cm
width = 4 meters and 32 centimeters = 432 cm
As we want the least number of square tiles required, it means the length of each square tile should be as large as possible.Further,the length of each square tile should be a factor of both the length and width of the room.
Hence, the length of each square tile will be equal to the HCF of the length and width of the room = HCF of 624 and 432 = 48
Thus, the number of square tiles required = (624 x 432 ) / (48 x 48) = 13 x 9 = 117 Answer: B
Answer: B
Question: How many days will there be from 28th January,1996 to 15th May,1996(both days included)?
Options:
A)102
B)103
C)111
D)109
E)121
Rationale: Explanation:
Number of days from 28-Jan-1996 to 15-May-1996 (both days included)
= 4(Jan) + 29(Feb) + 31 (Mar) + 30(Apr)+ 15(May) = 109
Answer: Option D
Answer: D