divelab/Sys2Bench huggingface dataset:
Question: If a and b are positive integers such that a/b = 3.98, which of the following must be a divisor of a?
Options:
A)67
B)197
C)91
D)199
E)42
Rationale: 1) A and B are positive INTEGERS
2) A/B = 3.98
A = 398
B = 100
398/100 = 3.98
These values are NOT the smallest possible values though (since they're both even, we can divide both by 2)...
A = 199
B = 50
199/50 = 2.86
There is no other way to reduce this fraction, so A must be a multiple of 199 and B must be an equivalent multiple of 50. At this point though, the value of B is irrelevant to the question. We're asked for what MUST divide into A....
Since A is a multiple of 199, we have to 'factor-down' 199. This gives us only (199), excluding 1 itself. So this number MUST be a factor of A. You'll find the match in the answer choices.
Answer: D
Answer: D
Question: A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is?
Options:
A)180 m
B)1870 m
C)050 m
D)150 m
E)110 m
Rationale: Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 15 => y = x/15
x + 100 / 25 = x / 15
x = 150 m.
Answer:D
Answer: D
Question: 50 is divided into two parts such that the sum of their reciprocals is 1/ 12.Find the two parts.
Options:
A)27 and 23
B)25 and 25
C)10 and 40
D)35 and 15
E)30 and 20
Rationale: Let the two parts be x and (50 - x).
Then, 1 / x + 1 / (50 – x) = 1 / 12 => (50 – x + x) / x ( 50 – x) = 1 / 12
=> x2 – 50x + 600 = 0 => (x – 30) ( x – 20) = 0 => x = 30 or x = 20.
So, the parts are 30 and 20.
Answer is E.
Answer: E
Question: Calculate the amount that an investor needs to be invest to earn $1023 in interest in 24 months if the investor plans to invest x dollars in a savings account that pays interest at an annual rate of 12% compounded semi-annually?
Options:
A)3980
B)3600
C)3700
D)3800
E)3900
Rationale: the approach is substitution,
our interest requirement is $1023 after 24 months, 2 compounding period.
calculate the compound interest on each option and find out the one that yields $1023 in 24 months
3900 yielded $1023
using the formula
A = P(1 + r/n)nt
hence answer is E
Answer: E
Question: here's an easy question of averages, but let's try to see innovative ways of solving this.
A class has 12 boys and x girls. Average score of boys and girls is 80 and 92 respectively. the average of the whole class is 86, what is the value of x?
Options:
A)a) 6
B)b) 7
C)c) 8
D)d) 10
E)e) 12
Rationale: 12(80)+92x/12+x=86
960+92x/12+x=86
960+92x=86(12+x)
960+92x=1032+86x
X's one side, numbers one side we get,
92x - 86x=1032-960
6x=72
hence, x=12
Answer E
Answer: E
Question: Ranjit went to the market with Rs. 100. If he buys 3 pens and 6 pencils he uses up all his money. On the other hand, if he buys 3 pencils and 6 pens he would fall short by 20%. If he wants to buy equal number of pens and pencils, how many pencils can he buy?
Options:
A)222
B)277
C)267
D)100
E)221
Rationale: Let price of a pen = x and pencil = y
3x + 6y = 100 ....(i)
and 6x + 3y = 125 ....(ii)
Adding (i) and (ii)
9(x + y) = 225
x + y = 25
multiply by 4
4x + 4y = 100
He can by 4 pens and 4 pencils in Rs. 100.
Answer:D
Answer: D
Question: A movie buff buys movies on DVD and on Blu-ray in a ratio of 13:4. If she returns 2 Blu-ray movies, that ratio would change to 7:2. If she buys movies on no other medium, what was the original number of movies purchased?
Options:
A)22
B)28
C)77
D)99
E)119
Rationale: Now coming to the process m(D) = 13x and b(D) = 4x
now from the next line the new eqn becomes 13x/ (4x -2) = 7/2
Solving it 26x = 28x -14
x =7
which means m (d) = 91 and b(d) = 28
SO total initially is m(d) + b(d) = 119
E
Answer: E
Question: On a test, 15% of the students received an A, 60% of the remaining students received a below a B. What percentage of the students received a B?
Options:
A)15% of the students received a B.
B)60% of the students received a B.
C)51% of the students received a B.
D)66% of the students received a B.
E)None of these.
Rationale: Explanation:Let total number of students be 100,Then, number of students who received an A = 15.Number of students receiving below a B = 60% of 85 = 51.Total number of students arriving alone = 100 – (15 + 51) = 34.Thus, 34% of the students received a B.Answer: Option E.
Answer: E
Question: John tossed a fair coin 4 times. What is the probability that the coin landed heads up exactly twice?
Options:
A)0.15
B)0.25
C)0.3
D)0.35
E)0.4
Rationale: The probability is exactly same as the cion landed tail up once. That is 4*(1/2)^4 = 4/16 =0.25.
The answer is, therefore, (B).
Answer: B
Question: A garrison of 2000 men has provisions for 54 days. At the end of 15 days, a reinforcement arrives, and it is now found that the provisions will last only for 20 days more. What is the reinforcement?
Options:
A)2777
B)2565
C)9877
D)1900
E)1557
Rationale: 2000 ---- 54
2000 ---- 39
x ----- 20
x*20 = 2000*39
x = 3900
2000
-------
1900
Answer:D
Answer: D
Question: Amanda goes to the toy store to buy 1 ball and 3 different board games. If the toy store is stocked with 3 types of balls and 6 types of board games, how many different selections E of the 4 items can Amanda make?
Options:
A)9
B)12
C)14
D)15
E)60
Rationale: Amanda goes to the toy store to buy 1 ball and 3 different board games. If the toy store is stocked with 3 types of balls and 6 types of board games, how many different selections of the 4 items can Amanda make?
3! / 1!2! * 6! / 3!3!
E=3*20=60
E. 60
Answer: E
Question: Which of the following equations is NOT equivalent to 4a^2 = b^2 - 9 ?
Options:
A) 4a^2 + 9 = b^2
B) 4a^2 - b^2 = -9
C) 4a^2= (b + 3)(b - 3)
D) 2a = b - 3
E)a^2 = (b^2-9)/4
Rationale: 4a^2 = b^2 - 9
The basic rule when dealing with equations is that you can do ANYTHING to both sides of an equation as long as you do it EQUALLY to BOTH sides. Everything gets a bit more complex when you're dealing with variables in the denominator of a fraction and/or inequalities, but neither of those subjects is a factor in this prompt.
Looking at Answer D, we have....
2a = b - 3
While you COULD take the square root of both sides of the original equation, it's important to note that the square root of b^2 - 9 is NOT (b-3).
b^2 - 9 can be factored into (b-3)(b+3), but neither of these parentheses is the square root of b^2 - 9.
You can see the proof when you square either of the two parentheses:
(b-3)^2 = b^2 - 6a + 9
(b+3)^2 = Y^2 + 6a + 9
Thus, D is NOT equivalent to the prompt.
Answer: D
Question: A basketball player succeeds with 70% of her free throws. If she has a set of three free throws, what is the probability that she succeeds at least once?
Options:
A)0.952
B)0.964
C)0.973
D)0.985
E)0.992
Rationale: P(missing all 3 free throws) = 0.3^3 = 0.027
P(succeeding at least once) = 1 - 0.027 = 0.973
The answer is C.
Answer: C
Question: A car takes 8 hours to cover a distance of 540 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
Options:
A)10Kmph
B)45Kmph
C)60Kmph
D)55Kmph
E)30Kmph
Rationale: Time = 8
Distence = 540
3/2 of 8 hours = 8 * 3/2 = 12 Hours
Required speed = 540/12 = 45 Kmph
B)
Answer: B
Question: Two pipes A and B can separately fill a tank in 12 and 15 minutes respectively. A third pipe C can drain off 45 liters of water per minute. If all the pipes are opened, the tank can be filled in 15 minutes. What is the capacity of the tank?
Options:
A)590 liters
B)540 liters
C)740 liters
D)560 liters
E)580 liters
Rationale: 1/12 + 1/15 - 1/x
= 1/15
x = 12
12 * 45 = 540
Answer:B
Answer: B
Question: A sum of money invested at C.I. amounts to Rs. 800 in 3 years to Rs. 850 in 4 years. The rate of interest per annum is?
Options:
A)2 1/2 %
B)4%
C)5%
D)6 2/3 %
E)6 1/4%
Rationale: S.I. on Rs. 800 for 1 year = (850 - 800) = Rs. 50 Rate = (100 * 50)/(800 * 1) = 6 1/4%
ANSWER:E
Answer: E
Question: There are 133 employees in Company X. If the number of employees who birth in June is the greatest, what is the least possible number of the employees in the company who birth in June?
Options:
A)10
B)11
C)12
D)13
E)14
Rationale: IMO 12
Take each answer choice and substract it from 133 and the divided this with 11.
B
Answer: B
Question: L9Q,L36S,P81U,R144W,T225U,?
Options:
A)V434Y
B)U475Y
C)V472Z
D)V324Y
E)V361X
Rationale: L + Q = 9
L + S = 36
P + U = 81
R + W = 144
T + W = 225
3^2 , (3*2=6)^2 , (3*3)^2 , (3*4)^2 , (3*5)^2 ---> AS per this number sequence
=> next number = (3*6)^2 = 324
V + Y =324 => V324Y
ANSWER:D
Answer: D
Question: What is the place value of 7 in the numeral 7259
Options:
A)A)2700
B)B)2800
C)C)2900
D)D)7000
E)E)3000
Rationale: 7 * 1000 = 7000
D
Answer: D
Question: Which is the least number that must be subtracted from 1856 so that the remainder when divided by 7, 12, 10 is 4?
Options:
A)168
B)172
C)182
D)140
E)160
Rationale: First we need to figure out what numbers are exactly divisible by 7,12,10. This will be the set {LCM,LCMx2,LCMx3,...}
LCM(7,12,10) = 42*10 = 420
The numbers which will leave remainder 4 will be {420+4, 420x2 +4, ,...}
The largest such number less than or equal to 1856 is 420*4+4 or 1684
To obtain this you need to subtract 172.
B
Answer: B
Question: A train 150 m long running at 72 kmph crosses a platform in 20 sec. What is the length of the platform?
Options:
A)443 m
B)354 m
C)450 m
D)350 m
E)250 m
Rationale: E
250
E = 72 * 5/18 = 20 = 400 â€“ 150 = 250
Answer: E
Question: In a village of 2,700 people, 900 people are over 70 years old and 1200 people are female. It is known that 60 percent of the females are younger than 70 years old. If no one in the village is 70 years old, what is the probability that a person chosen at random is either a male or younger than 70 years old?
Options:
A)4/5
B)5/7
C)13/15
D)37/45
E)79/90
Rationale: The number of people younger than 70 years old is 2700-900 = 1800
The number of females older than 70 years old is 0.4*1200 = 480
The number of males older than 70 years old is 900-480 = 420
The number of people who are either male or younger than 70 is 1800+420 = 2220.
P(a person is younger than 70 or male) = 2220/2700 = 37/45
The answer is D.
Answer: D
Question: There are 2 sections A and B in a class, consisting of 60 and 70 students respectively. If the average weight of section A is 60kg and that of section B is 80kg, Find the average of the whole class?
Options:
A)50.78kg
B)49.32kg
C)70.76kg
D)69.15kg
E)70.89kg
Rationale: Total weight of 60+70 students = 60*60 + 70*80 = 3600+5600
Average weight of the class is = 9200/130 = 70.76 kg
Answer is C
Answer: C
Question: A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train?
Options:
A)65 Kmph
B)70 Kmph
C)72 Kmph
D)75 Kmph
E)78 Kmph
Rationale: Length = Speed * time
Speed = L/T
S = 400/20
S = 20 M/Sec
Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 72 Kmph
ANSWER:C
Answer: C
Question: Henry answered 3/5 of the questions he was given for homework in the first hour, 5/17 of the remaining questions in the second hour and the remaining x questions in the third hour where x is an integer. How many questions was Henry given for homework?
Options:
A)x
B)(85/12)*x
C)(85/24)*x
D)(85/36)*x
E)(85/48)*x
Rationale: Let Q be the number of homework questions.
Q = 3Q/5 + (5/17)(2Q/5) + x
Q = 51Q/85 + 10Q/85 + x
24Q/85 = x
Q = (85/24)*x
The answer is C.
Answer: C
Question: If the population of a certain country increases at the rate of 10 person every 60 seconds, by how many persons does the population increase in 1 hour?
Options:
A)100
B)200
C)600
D)800
E)1000
Rationale: Answer = 10 * 60(1 hour = 60 minutes)= 600
Answer = C
Answer: C
Question: 252 can be expressed as a product of prime as
Options:
A)2 x 2 x 3 x 3 x 7
B)2 x 2 x 2 x 3 x 7
C)3 x 3 x 3 x 3 x 7
D)2 x 3 x 3 x 3 x 7
E)None
Rationale: Solution
Clearly, 252 =2 x 2 x 3 x 3 x 7
Answer A
Answer: A
Question: In a T.V. factory, an average of 62 TVs are produced per day for the fist 25 days of the months. A few workers fell ill for the next five days reducing the daily avg for the month to 58 sets/day . The average production per day for day last 5 days is ?
Options:
A)35
B)38
C)48
D)50
E)52
Rationale: Production during these 5 days = Total production in a month - production in first 25 days.
= 30 x 58 - 25 x 62
= 19
âˆ´ Average for last 5 days = 190 / 5
= 38
B
Answer: B
Question: There are three departments having students 70,58,24 .In an exam they have to be seated in rooms such that each room has equal number of students and each room has students of one type only (No mixing of departments). Find the minimum number of rooms required?
Options:
A)73
B)74
C)75
D)76
E)77
Rationale: WE NEED TO TAKE GCD WHICH IS 2
THUS ALL THE ROOMS WILL HAVE 2 STUDENTS OF THE SAME DEPT
1) 70/2 = 35
2) 58/2 = 29
3) 24/2 = 12
TOTAL NO. OF MIN ROOMS REQD = 35+12+29 = 76
ANSWER:D
Answer: D
Question: The cost of 16 apples and 8 mangos is $352 and the cost of 4 apples and 4 mangos is $96. Find the cost of each apple?
Options:
A)40
B)20
C)30
D)35
E)28
Rationale: B
20
Let the cost of each apple and mango be 'p' and 'q' respectively.
16p + 8q = 352 --- (1)
4p + 4q = 96
8p + 8q = 192 --- (2)
(1) - (2) => 8p = 160
=> p = 20
Answer: B
Question: If 0.4 of a number is equal to 0.06 of another number, the ratio of the numbers i
Options:
A)2 : 3
B)3 : 4
C)3 : 20
D)20 : 3
E)None
Rationale: Sol.
0.4A = 0.06 B ⇔ A / B = 0.06 / 0.40 = 6/40 = 3/20.
∴ A : B = 3 : 20.
Answer C
Answer: C
Question: Population of a city in 20004 was 1000000. If in 2005 there isan increment of 10% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city atthe end of the year 2007
Options:
A)976374
B)979923
C)980241
D)1036750
E)1083875
Rationale: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)
= P (1 + 10/100)(1 - 35/100)(1 + 45/100)
= 1036750
D
Answer: D
Question: List all the even integers between 1 and 11. Find the lowest positive interger that can be divided by each of those numbers.
Options:
A)120
B)234
C)231
D)183
E)123
Rationale: The even numbers between 1 and 11 are 2,4,6,8,10,
To get the least positive integer that can be divided by each of these numbers 1,2,3,4,5,6,7,8,9,10 you calculate the lowest common denominator of all the numbers. Express each number as a product of their prime factors and multiply the set of prime numbers from each set with the highest exponent value.
LCM=2^3*3*5
The answer is A)
Answer: A
Question: jerry and Michelle play a card game. In the beginning of the game they have an equal number of cards. Each player, at her turn, gives the other a third of her cards. Michelle plays first, giving jerry a third of her cards. jerry plays next, and Michelle follows. Then the game ends. jerry ended up with 14 more cards than Michelle. How many cards did each player have originally?
Options:
A)27
B)30
C)34
D)36
E)38
Rationale: Game Michelle Jerry michelle
Initially 2727 assume
After game 1 1836
After game 2 3024
After game 3 2034
Now jerry has 14 cards more than Michelle.
So the answer is A
Answer: A
Question: Using all the letters of the word "ANOTHER", how many words can be formed, which begin with A and end with R?
Options:
A)80
B)90
C)110
D)120
E)100
Rationale: There are seven letters in the given word.
Consider 7 blanks ....
The first blank and last blank must be filled with A and R all the remaining five blanks can be filled with the remaining 5 letters in 5! ways.
The number of words = 5! = 120.
ANSWER:D
Answer: D
Question: In a garden, there are 10 rows and 12 columns of mango trees. The distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden. What is the length of the garden?
Options:
A)22
B)24
C)26
D)28
E)30
Rationale: Between the 12 mango trees, there are 11 gaps and each gap has 2 meter length
Also, 1 meter is left from all sides of the boundary of the garden.
Hence, length of the garden = (11 × 2) + 1 + 1 = 24 meter
Answer is B.
Answer: B
Question: If (1+a)b=b, which of the following must be true?
Options:
A)a=-1 or b=0
B)a=0 or b=0
C)a=1 or b=1
D)a=-1 or b=-1
E)a=0 or b=1
Rationale: By only having ab=0, we cannot say answer is B as A and E options also satisfy the condition ab=0. ans B
Answer: B
Question: Each month a retailer sells 100 identical items. On each item he makes a profit of $30 that constitutes 16% of the item's price to the retailer. If the retailer contemplates giving a 5% discount on the items he sells, what is the least number of items he will have to sell each month to justify the policy of the discount?
Options:
A)157
B)213
C)221
D)223
E)226
Rationale: For this question, we'll need the following formula:
Sell Price = Cost + Profit
We're told that the profit on 1 item is $20 and that this represents 16% of the cost:
Sell Price = Cost + $20
Sell Price = $125 + $20
Thus, the Sell Price is $145 for each item. Selling all 100 items gives the retailer...
100($20) = $2,000 of profit
If the retailer offers a 5% discount on the sell price, then the equation changes...
5%(145) = $7.25 discount
$137.75 = $125 + $12.75
Now, the retailer makes a profit of just $12.75 per item sold.
To earn $2,000 in profit, the retailer must sell....
$12.75(X) = $2,000
X = 2,000/12.75
X = 156.8627 =157 items
A
Answer: A
Question: A bag has 1, 3, 5, 7, 9,11 and 13 cm sticks. Find the probability that they they will form a triangle if 3
sticks are drawn?
Options:
A)13 / 35
B)14 / 35
C)1 / 2
D)5 / 6
E)5 / 5
Rationale: Explanation :
Total Cases: =7C3=35
Favourable Cases: (3,5,7),(3,7,9),(3,9,11),(3,11,13),(5,7,9),(5,7,11),(5,9,11),(5,9,13),(5,11,13),
(7,9,11),(7,9,13),(7,11,13),(9,11,13)=total 13.
[Others are rejected because to form a triangle it is necessary that the sum of 2 small
sides must be greater than the third greatest side.]
Hence (A) is correct answer.
Answer : A
Answer: A
Question: Dacid obtained 76, 65, 82, 67 and 85 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
Options:
A)67
B)26
C)87
D)26
E)75
Rationale: Average
= (76 + 65 + 82 + 67 + 85)/5
= 375/5 = 75.
Answer: E
Answer: E
Question: If the probability that the NY Giants win the Super Bowl is 1/12 and the probability that the NY Mets win the World Series is 1/15, what is the probability that either the NY Giants win the Super Bowl or the NY Mets win the World Series (but not both)?
Options:
A)1/18
B)5/36
C)7/48
D)11/72
E)17/120
Rationale: 11/12*1/15 + 1/12*14/15 = 25/180 = 5/36
The answer is B.
Answer: B
Question: If n is a positive integer and n^3 is a multiple of 550, what is the least possible value of n?
Options:
A)8
B)27
C)81
D)110
E)125
Rationale: cube of a number entails having 3 copies of the original prime factors. Since 550 is a factor of n^3 the least possible value of n is 5(11)2 = 110
the answer is D.
Answer: D
Question: Two containers of milk contain mixtures of water and milk in ratio 5:4 and 7:9. In what ratio they should be mixed so that mixture is of 6:6 ratio?
Options:
A)6:5
B)7:5
C)9:8
D)8:9
E)8:7
Rationale: 6/6-5/4==>-1/4
7/9-6/6==>-2/9
now, -1/4=-2/9==>1/4=2/9==>9:8
ANSWER:C
Answer: C
Question: A team won 50 percent of its first 60 games in a particular season, and 80 percent of its remaining games. If the team won a total of 70 percent of its games that season, what was the total number of games that the team played?
Options:
A)75
B)90
C)120
D)150
E)180
Rationale: 70% is 20%-points above 50% and 10%-points below 80%.
Thus the ratio of "the first 60 games" to "remaining games" is 1:2.
So the team played a total of 60+120 = 180 games.
The answer is E.
Answer: E
Question: If a motorist had driven 1 hour longer on a certain day and at an average rate of 5 miles per hour faster, he would have covered 50 more miles than he actually did. How many more miles would he have covered than he actually did if he had driven 2 hours longer and at an average rate of 10 miles per hour faster on that day?
Options:
A) 100
B) 120
C) 140
D) 150
E) 160
Rationale: Case 1:
let rate = R, Time = T, and Distance =D
so D=RT
Case 2:
(D+50)=(R+5)(T+1)
Case 3:
(D+X)=(R+10)(T+2)
X=100
Ans A
Answer: A
Question: Angela’s grade was in the 90th percentile out of 80 grades in her class. In another class of 100 students there were 19 grades higher than Angela’s. If nobody had Angela’s grade, then Angela was what percentile of the two classes combined?
Options:
A)72
B)80
C)81
D)85
E)92
Rationale: If someone's grade is in xth percentile of the nn grades, this means that xx of people out of nn has the grades less than this person.
Being in 90th percentile out of 80 grades means Angela outscored 80∗0.9=7280∗0.9=72 classmates.
In another class she would outscored 100−19=8 students (note: Angela herself is not in this class).
So, in combined classes she outscored 72+81=153. As there are total of 80+100=180 students, so Angela is in 153/180=0.85=85, or in 85th percentile.
Answer: D.
Answer: D
Question: Find the number of square tiles to cover the floor of a room measuring 4.25 m * 9 m leaving 0.25 m space around the room. A side of square tile is given to be 25 cms?
Options:
A)478
B)476
C)472
D)471
E)510
Rationale: 3 3/4 * 8 1/2 = 1/4 * 1/4 * x => x
= 510
Answer:E
Answer: E
Question: Jeremy needs to choose three flowers for his mother from a group of 10 roses, six of which are red and four of which are white. What is the ratio of the number of ways in which he can select only red roses to the number of ways in which he can select only white roses?
Options:
A)30:1
B)10:1
C)5:1
D)3:2
E)1:5
Rationale: you are given 10 roses out of which 6 are red and 4 are white.
Ways of selecting 3 red roses only out of 6 available = 6C3 = 6!/(3!*3!)
Similarly, Ways of selecting 3 white roses only out of 4 available = 4C3 = 4!/(3!*1!)
Thus the ratio = 6C3/4C3 = 5:1
C is the correct answer.
Answer: C
Question: Yane and Thomas are among the 8 people from which a committee of 4 people is to be selected. How many different possible committees of 4 people can be selected from these 8 people if at least one of either Yane or Thomas is to be selected?
Options:
A)28
B)46
C)55
D)63
E)70
Rationale: Ans:C
Solution:
Y+T+6 = total 8 ,
we need to select at least one of the Y and T or both= total 4 out of 8 - 4 out of 6
8C4 - 6C4
=55
Answer: C
Question: The length of a rectangulat plot is 20 metres more than its breadth. If the cost of fencing the plot @ Rs. 26.50 per metre is Rs. 5300, what is the length of the plot in metres?
Options:
A)40
B)50
C)200
D)120
E)None
Rationale: Solution
Let breadth = x metres
Then, length = (x + 20)metres.
Perimeter	= (5300 / 26.50) m
= 200m
Answer C
Answer: C
Question: If two positive numbers are in the ratio 1/8 : 1/5, then by what percent is the second number more than the first?
Options:
A)67%
B)70%
C)60%
D)62%
E)65%
Rationale: Given ratio
= 1/8 : 1/5 = 5 : 8
Let first number be 5x and the second number be 8x.
The second number is more than first number by 3x.
Required percentage
= 3x/5x * 100 = 60%.
Answer:C
Answer: C
Question: A shopkeeper sold an article offering a discount of 5% and earned a profit of 20.65%. What would have been the percentage of profit earned if no discount was offered?
Options:
A)60%
B)27%
C)30%
D)56%
E)73%
Rationale: Let C.P. be Rs. 100.
Then, S.P. = Rs. 120.65
Let marked price be Rs. x. Then, 95/100 x = 120.65
x = 12065/95 = Rs. 127
Now, S.P. = Rs. 127, C.P. = Rs. 100
Profit % =27%.
Answer: B
Answer: B
Question: At a dinner party 4 people are to be seated around a circular table. Two sitting arrangements are considered different only when the positions of the people are different relative to each other.What is the total number of possible sitting arrangements or the group?
Options:
A)6
B)10
C)24
D)32
E)120
Rationale: Hi there,
You can treat this as an ordering question except thatfor a circular arrangement you need to divide by the number of spaces.So in this case:
4!/4=6
If you spin the circle to right, that doesn't count as a new arrangement. Dividing by the number of spaces takes that into consideration.
Happy Studies,
HG.
A
Answer: A
Question: Anna worked for h hours each day for d consecutive days. If she earns $3.50 per hour, what is the total amount she earned?
Options:
A)3.50/d + h
B)3.50 + d + h
C)3.50 + dh
D)3.50h + d
E)3.50dh
Rationale: H hours for d days.
Income each day = 3.5*h
Total income = 3.5*h*d
Correct option: E
Answer: E