divelab/Sys2Bench huggingface dataset:
Question: If a^5 ≤ a, which of the following must be true?
I. –1 ≤ a ≤ 0
II. a=0
III. 0 ≤ a ≤ 1
Options:
A)None of the above
B)I only
C)II only
D)III only
E)I and III only
Rationale: The trick here is more on the answer choices.
Look at I II and III. all are right (pick out some numbers).
Therefore I was totally confused because non of the answers had the right answer (I II and III)
I finally chose D, but hesitate between A and D quite a long time...
This is a tricky tricky question, since it takes into consideration that the answers are correct but they do not cover all the POSSIBLE answers.
Therefore it is A.
Answer: A
Question: How many seconds will a train 100 meters long take to cross a bridge 120 meters long if the speed of the train is 36 kmph?
Options:
A)54 sec
B)65 sec
C)25 sec
D)22 sec
E)24 sec
Rationale: D = 100 + 120 = 220
S = 36 * 5/18 = 10 mps
T = 220/10 = 22 sec
Answer:D
Answer: D
Question: A 300 m long train crosses a platform in 42 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
Options:
A)288
B)350
C)400
D)276
E)234
Rationale: Speed = 300/18 = 50/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/42 = 50/3
3x + 900 = 2100 => x = 400 m.
Answer:C
Answer: C
Question: How many times digit 6 is used while writing numbers from 150 to 1000?
Options:
A)648
B)300
C)252
D)225
E)26
Rationale: There are 100 numbers which begin with 600
Next, In every 10 numbers such as 100 to 110, 110 to 120, 120 to 130 6 comes at least once. Number of such intervals = End limit - First no. / interval. Our range of numbers is 100 - 1000
1000 - 100 = 900/10 = 90
Number of 10s interval in this is 90. So 90 '6s'
So far we have calculated 190.
The total now comes to 280. The nearest to which is 252. Hence C.
Answer: C
Question: Tough and Tricky questions: Combinations.
The product of the digits of the four-digit number h is 42. No two digits of h are identical. How many different numbers are possible values of h?
Options:
A)12
B)36
C)24
D)42
E)54
Rationale: Answer = C = 24
Let number =abcd
Given that a*b*c*d = 42
a,b,c,d can be 1,2,3,7
Number of ways = 4*3*2 = 24
Answer: C
Question: What is the cost of leveling the field in the form of parallelogram at the rate of Rs.50/10 sq.metre, whose base & perpendicular distance from the other side being 94m & 54m respectively?
Options:
A)s. 6420
B)s. 3563
C)s. 2400
D)s. 5480
E)s. 5076
Rationale: Area of the parallelogram = Length of the base * Perpendicular height
= 94 * 54 = 5076m.
Total cost of levelling = Rs.5076
E
Answer: E
Question: If 'a' and 'b' are non-zero numbers such that their sum is eight times the product, what is the value of 1/a + 1/b?
Options:
A)2
B)4
C)8
D)12
E)16
Rationale: a+b = 8ab
1/a + 1/b = (b + a)/(ab) = 8.
The answer is C.
Answer: C
Question: If [x] is the greatest integer less than or equal to x, what is the value of [1.6]+[-3.4]+[10.7]?
Options:
A) 3
B) 4
C) 5
D) 6
E) 7
Rationale: You are asked what the closest lesser integer value to [x] is.
[1.6] = 1.0
[-3.4] = -4.0
[10.7] = 10.0
Therefore , answer is: 1.0 -4.0 + 10.0 = 7.0
Option E.
Answer: E
Question: Of the three numbers, second is twice the first and is also thrice the third.If the average of the three numbers is 44.Find the largest number.
Options:
A)70
B)72
C)66
D)74
E)71
Rationale: Let the third number be x.
Then second number = 3x.
First number=3x/2.
Therefore x+3x+(3x/2)=(44*3) or x=24
So largest number= 2nd number=3x=72.
Answer is B.
Answer: B
Question: Tim and Élan are 30 miles away from one another. They are starting to move towards each other simultaneously, Tim at a speed of 10 Mph and Élan at a speed of 5 Mph. If every hour they double their speeds, what is the distance that Tim will pass until he meets Élan?
Options:
A)20 miles.
B)35 miles.
C)45 miles.
D)60 miles.
E)65 miles.
Rationale: Tim and Elan will meet at the same time while their ratio of speed is 2:1 respectively.So their individual distance traveled ratio will be same.
Plugging in the answer choice Only Answer Choice A meet the 2:1(Tim:Elan=20:10) ratio of maintaining total distance traveled 30 miles
So Correct answer A
Answer: A
Question: A used-book dealer sells paperback books at 3 times dealer's cost and hardback books at 4 times the dealer's cost. Last week, the dealer sold a total of 160 books, each of which had cost the dealer $1. If the gross profit (sales revenue minus the dealer's cost) on the sale of all of these books was $400, how many of the books sold were paperbacks?
Options:
A)60
B)80
C)100
D)120
E)140
Rationale: The dealer earns a profit of $2 per paperback and $3 per hardback.
If all 160 books were paperbacks, the dealer would earn a profit of $320.
Since the actual profit was $400, the dealer must have sold 80 hardbacks.
Then the number of paperbacks sold was 160-80 = 80.
The answer is B.
Answer: B
Question: Cost of 1 chair is Rs. 214 and cost of one table is Rs. 937, then what is the approximate cost of 6 dozen chairs and 4 dozen table ?
Options:
A)Rs. 60000
B)Rs. 58000
C)Rs. 55000
D)Rs. 62000
E)None
Rationale: Answer
∵ Cost of 6 dozen chairs = 6 x 12 x214 = Rs. 15408
And cost of 4 dozen tables = 4 x 12 x 937 = Rs. 44976
∴ Total cost =15408 + 44976
= Rs. 60384
= Rs. 60000 (Approximately)
Option: A
Answer: A
Question: Three hundred multiples of seven are chosen at random, and 200 multiples of eight are chosen at random. Approximately what percentage of the 500 selected numbers are odd?
Options:
A)20%
B)25%
C)30%
D)35%
E)40%
Rationale: About half the multiples of seven will be odd while all the multiples of eight are even.
The percentage of odd numbers is about (1/2)(300) / 500 = 30%
The answer is C.
Answer: C
Question: A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
Options:
A)300
B)320
C)350
D)345
E)568
Rationale: Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 39 = 50/3
3(x + 300) = 1950 è x = 350
Answer: Option C
Answer: C
Question: Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
Options:
A)477
B)444
C)279
D)276
E)291
Rationale: 1h ----- 5
? ------ 60
12 h
RS = 16 + 21 = 37
T = 12
D = 37 * 12 = 444.Answer: B
Answer: B
Question: A hotel has 10 storeys.Which floor is above the floor below the floor, below the floor above the floor, below the floor above the fifth.
Options:
A)5 th Floor
B)4 th Floor
C)6 th Floor
D)1 st Floor
E)None of these
Rationale: Explanation :
Just start from last
below the floor above the 5th is again -- 5th only [since above d 5th is 6th nd below the 6th is 5th]
below the floor above the floor means -- 5th only [above the 5th is 6th nd below the 6th is 5th]
above the floor below the floor means -- again 5th only [below the 5th is 4th nd above the 4th is 5th]
Hence (A) is correct answer.
Answer : A
Answer: A
Question: In an election between 2 candidates, 75% of the voters cast their votes, out of which 2% of the votes were declared invalid. A candidate got 9261 votes which were 75% of the total valid votes. Find the total number of votes enrolled in that election?
Options:
A)16800
B)15268
C)14800
D)15620
E)16850
Rationale: Let the total number of votes enrolled be x.
Then, number of votes cast = 75% of x.
Valid votes = 98% of (75% of x)
75% of (98% of (75% of x)) = 9261
(75/100)*(98/100)*(75/100)x = 9261
x = 16800
Answer is A
Answer: A
Question: If 48 men can do a piece of work in 25 hours, in how many hours will 15 men
do it ?
Options:
A)80 hours
B)75 hours
C)70 hours
D)65 hours
E)60 hours
Rationale: Let the required number of hours be x. Then,
Less men, More hours	(Indirect Proportion)
15 : 48 : : 25 : x<=>(15 x x) =(48 x 25)<=>(48 x 25)/15 = 80
Hence, 15 men can do it in 60 hours
Answer is A.
Answer: A
Question: Two boats are heading towards each other at constant speeds of 3 miles/hr and 21 miles/hr respectively. They begin at a distance 20 miles from each other. How far are they (in miles) one minute before they collide ?
Options:
A)1/12
B)5/12
C)1/6
D)1/3
E)3/15
Rationale: The question asks: how far apart will they be 1 minute=1/60 hours before they collide?
Since the combined rate of the boats is 3+21=24 mph then 1/60 hours before they collide they'll be rate*time=distance --> 24*1/60=3/15 miles apart.
Answer: E.
Answer: E
Question: There are 250men and 150 women in a committee, if all will work they will complete 12 units per day, if all men work they will complete 15 units per day, how many units will women complete per day?
Options:
A)2
B)3
C)4
D)5
E)7
Rationale: I think there is a mistake in this question. If all men and women together complete 12 units, how only men can do 15 Units of work a day?
Forgetting about the reality, Women can do -3 units a day.
Answer:	B
Answer: B
Question: If A is thrice as fast as B and together can do a work in 18 days. In how many days A alone can do the work?
Options:
A)36
B)42
C)24
D)54
E)45
Rationale: A’s one day’s work= 1/X
B’s one day’s work= 1/3x
A + B’s one day’s work= 1/x + 1/3x = 1/18
= 3+1/3x = 4/3x = 1/18
x = 18*4/3 = 24
ANSWER:C
Answer: C
Question: In a division sum, the divisor is 10 times the quotient and 5 times the remainder. If the remainder is 46, what is the dividend ?
Options:
A)4236
B)4306
C)4336
D)5336
E)None of these
Rationale: Divisor = (5 x 46) = 230
10 x Quotient = 230 =	230/10= 23
Dividend = (Divisor x Quotient) + Remainder
= (230 x 23) + 46
= 5290 + 46
= 5336.
Answer :D
Answer: D
Question: Two men A and B start from place X walking at 4 ½ kmph and 5 ¾ kmph respectively. How many km apart they are at the end of 2 ½ hours if they are walking in the same direction?
Options:
A)7 km
B)6 km
C)3 1/8 km
D)9 km
E)5 km
Rationale: RS = 5 ¾ - 4 ½ = 1 ¼
T = 2 ½ h.
D = 5/4 * 5/2 = 25/8
= 3 1/8 km
Answer:C
Answer: C
Question: Kelly and Jody packed boxes with books. If Jody packed 40% of the total number of boxes, what was the ratio of the number of boxes Kelly packed to the number that Jody packed?
Options:
A)1 to 6
B)1 to 4
C)2 to 5
D)3 to 5
E)3 to 2
Rationale: Explanation:
If Jody packed 40% of the boxes then Kelly packed 60%. The ratio of the number of boxes Kelly packed to the number Jody packed is thus 60%/40%=3/2
Answer: Option E
Answer: E
Question: How many 1/8's are there in 371/2 ?
Options:
A)1384
B)1484
C)1584
D)1684
E)1784
Rationale: no of 1/8 's in 371/2 = (371/2)/(1/8)= 8*371/2= 371*4= 1484
ANSWER:B
Answer: B
Question: Three candidates contested an election and received 1136, 7636 and 14628 votes respectively. What percentage of the total votes did the winning candidate got?
Options:
A)55%
B)56%
C)62.5%
D)58%
E)59%
Rationale: Total number of votes polled = (1136 + 7636 + 14628) = 23400
So, Required percentage = 14628/23400 * 100 = 62.5%
ANSWER : C
Answer: C
Question: what is the least number by which 2,100 must be divided to get a number perfect square
Options:
A)21
B)42
C)24
D)40
E)45
Rationale: 2,100/21=100
100=(10)^2
Ans-21
ANSWER:A
Answer: A
Question: Rick deposited $750 to his bank account using $5 and $15 dollar bills only. If Rick came to the bank with 70 bills and left with 10 bills only, how many $15 dollar billsმ did he deposit?
Options:
A)5.
B)45.
C)50.
D)55.
E)65.
Rationale: 5x+15y=750 --1
x+y=60 ---2
multiply eq 2 with 5 and subtract from eq 1
5x+15y=750
5x+5y=300
10y= 450
y=45 and x = 15
therefore $15 bills = 45
Answer B
Answer: B
Question: Find large number from below question The difference of two numbers is 1390. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
Options:
A)1245
B)1345
C)1455
D)1577
E)1665
Rationale: Let the smaller number be x. Then larger number = (x + 1390).
x + 1390 = 6x + 15
5x = 1375
x = 275
Large number = 275+1390 = 1665
E
Answer: E
Question: 10 litres of water are poured into an aquarium of dimensions 50cm length, 20cm breadth, and 40cm height. How high (in cm) will the water rise?
(1 litre = 1000cm³)
Options:
A)6
B)8
C)10
D)20
E)40
Rationale: lXbXh= 10000
h= 10000/50*20= 10 cm
'C' is the answer.
Answer: C
Question: The average marks obtained by 120 cndidates in a certainexaminationis 35.if the average marks of passed candidate is 39 and that of the failedcandidates is 15,what is the number of candidates who passed the examination
Options:
A)12 years 8 month
B)13 years
C)14 years 8 month
D)15 years 7 month
E)16 years 9 month
Rationale: (d) Let No. of passed candidates are x
So, x * 39 + (120 – x) 15= 120 * 35
x = 100
2.(a) Total increase = 8 * 2 = 16 years
So, total age of two women = 35 + 45 +16= 96
Average age of two women=96/2=48 years
3(d) Total decrease = 20 * 2 = 40 month
= 3 years 4 month
So, age of new boy = 18 years – 3 years 4 month
= 14 years 8 month
C
Answer: C
Question: What is the approx. value of W, if W=(1.5)11, Given log2 = 0.301, log3 = 0.477
Options:
A)85
B)84
C)86
D)87
E)99
Rationale: Explanation :
W = (1.5)11
Take log both sides:
=> logW = 11 x log(1.5) =11 x log(3/2)
=> logW = 11 x (log3 - log2) = 11 x 0.176 = 1.936
=> W = 101.936
=> W = 86 (approx)
Answer : C
Answer: C
Question: Jane had an average of 87 on his first 7 tests. She had an average score of 90 on her first 6 tests. What did he score on the 7th test?
Options:
A)69
B)75
C)90
D)86
E)50
Rationale: The sum of Jane's first 7 scores is 7 Â· 87 and the sum of her first 6 scores is 6 Â· 90, so she received
7 Â· 87 âˆ’ 6 Â· 90 on her 7th quiz. You can do the arithmetic or notice that the answer ends in a 9. The correct answer is A.
Answer: A
Question: Find the remainder when 6^23 is divided by 5 ?
Options:
A)3
B)2
C)1
D)0
E)4
Rationale: 6^23 = 6^(4*5+3) = 6^(20) * 6^3 last 3 digits = 216
216/5 remainder = 1
ANSWER:C
Answer: C
Question: 60 percent of movie theatres in Town X have 3 screens or less. 20% of those theatres sell an average of more than $300 worth of popcorn per showing. 50 percent of all the movie theatres in Town X sell $300 or less of popcorn per showing. What percent of all the stores on the street have 4 or more screens and sell an average of more than $300 worth of popcorn per day?
Options:
A)12
B)18
C)32
D)40
E)44
Rationale: Lets take numbers here.
Assume that the total number of movie theaters in the town = 100
Then number of movie theaters with 3 screens or less = 60
=> Number of movie theaters with 4 screens or more = 40
Movie theaters with 3 screens or less selling popcorn at more than $300 = 20% of 60 = 12
Number of movie theaters selling popcorn at $300 or less = 56
=> Number of movie theaters selling popcorn at more than $300 = 100-56 = 44
Of these 44 theaters, 12 are those with 3 screens or less
Therefore 44 (44-12) must be those with four screens or more
E is the answer
Answer: E
Question: Which is the least number that must be subtracted from 1856 so that the remainder when divided by 7, 12, 16 is 6?
Options:
A)168
B)172
C)170
D)174
E)176
Rationale: First we need to figure out what numbers are exactly divisible by 7,12,16. This will be the set {LCM,LCMx2,LCMx3,...}
LCM(7,12,16) = 48*7 = 336
The numbers which will leave remainder 6 will be {336+6, 336x2 +6, 336x3 +6,...}
The largest such number less than or equal to 1856 is 336x5+6 or 1686
To obtain this you need to subtract 170.
C
Answer: C
Question: There are 40 people in a party. If everyone is to shake hands with one another, how many hand shakes are possible?
Options:
A)780
B)667
C)661
D)297
E)261
Rationale: Explanation:
Total number of persons = n = 40
Shake hands involve only 2 persons = r = 2
Number of shake hands = nCr = 40C2
40C2 = (40 * 39) /(2 * 1) = 780
ANSWER:A
Answer: A
Question: A and B invests Rs.10000 each, A investing for 9 months and B investing for all the 12 months in the year. If the total profit at the end of the year is Rs.21000, find their shares?
Options:
A)1300,1500
B)9000,12000
C)7290,8000
D)15000,12000
E)72821,75000
Rationale: The ratio of their profits A:B = 9:12 = 3:4
Share of A in the total profit = 3/7 * 21000 = Rs.9000
Share of B in the total profit = 4/7 * 21000 = Rs.12000
Answer:B
Answer: B
Question: A can do a piece of work in 3days of 8 hours each and B alone can do it in 4 days of 9 hours each.how long will they take it to do working together
7 1/5 hours a day?
Options:
A)3 days
B)2 days
C)5 days
D)7 days
E)4 days
Rationale: A's work per hour=1/24
B's work per hour=1/36
A & B's work per hour together=(1/24)+(1/36)=5/72
so A & B together complete the work in 72/5 hours...
if they work 7 1/5=36/5 hours a day,
it will take (72/5)/(36/5) days=2 days...
ANSWER:B
ANSWER:B
Answer: B
Question: If n > 0 , which of the following must be true?
I n^2 > 1
II	n - n^2 < 0
III	2n - 1 < 0
Options:
A)I only
B)II only
C)III only
D)I and II only
E)none
Rationale: I. True for all values of n except 1
When n = 1 ; n^2 = 1
II. True for all values of n except 1
When n = 1 ; n - n^2 = 1 - 1 =>0
III	false for all values of n
Hence the correct answer will be (D)
Answer: D
Question: What value of K gives the equation,3k-2=2k-1?
Options:
A)ONE
B)TWO
C)THREE
D)FOUR
E)NONE
Rationale: 3k-2=2k-1
If k=1
3(1)-2=2(1)-1
3-2=2-1
1=1
Option A is answer
Answer: A
Question: How many paying stones, each measuring 2 1/2 m * 2 m are required to pave a rectangular court yard 30 m long and 16 1/2 m board?
Options:
A)99
B)88
C)77
D)55
E)22
Rationale: Answer: Option A
Explanation:
30 * 33/2 = 5/2 * 2 * x => x = 99
Answer: A
Answer: A
Question: The average temperature for Tuesday, Wednesday and Thursday was 42°C. The average temperature for Wednesday, Thursday and Friday was 44°C. If the temperature on Friday be 43°C, what was the Temperature on Tuesday?
Options:
A)39°C
B)44°C
C)37°C
D)42°C
E)None of these
Rationale: Explanation:
T + W + T = 42 × 3 = 126°C
W+ T+ F = 44 × 3 = 132°C
Also, temperature on Friday = 43°C
Temperature on Tuesday = 126 +43 - 132 = 37°C
Answer: Option C
Answer: C
Question: A trader has 40 kg of rice, a part of which he sells at 14% profit and rest at 6% loss. On the whole his loss is 4% . What is the quantity sold at 14% profit and that at 6% loss?
Options:
A)4 and 36 kg
B)10 and 40 kg
C)15 and 35 kg
D)20 and 30 kg
E)40 and 30 kg
Rationale: Alligation Method
I PART II PART
14 (x1) -6 (x2)
\ /
x
/ \
(x2-x) (x-x1)
2 18
1 9
Ratio of quantities sold at 14% profit and 6% loss = 1: 9
Quantity sold at 14% profit = 40/1+9 *1 = 4 kg
Quantity sold at 6% loss = 40/1+9 *9 = 36kg
ANSWER:A
Answer: A
Question: The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 9 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?
Options:
A)s.4538
B)s.8154
C)s.4518
D)s.4530
E)s.4517
Rationale: Area of the four walls = 2h(l + b)
Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.
Total cost = 906 * 9 = Rs.8154
Answer: B
Answer: B
Question: The no. of girls in a class are seven times the no. of boys, which value cannever be the of total students?
Options:
A)10
B)15
C)30
D)34
E)36
Rationale: Let the boys are X, then girls are 7X, total = X+7X = 8X
So it should be multiple of 8, 30 is not a multiple of 8.
C
Answer: C
Question: Divide $672 among A,B in the ratio 5:3. How many $ that A get?
Options:
A)$120
B)$500
C)$420
D)$610
E)$315
Rationale: Sum of ratio terms = 5+3 = 8
A = 672*5/8 = $420
Answer is C
Answer: C
Question: P alone can complete a job in 5 days. The work done by Q alone in one day is equal to one-fourth of the work done by P alone in one day. In how many days can the work be completed if P and Q work together?
Options:
A)2.5
B)3.0
C)3.5
D)4.0
E)4.5
Rationale: P's rate is 1/5
Q's rate is 1/20
The combined rate is 1/5 + 1/20 = 1/4
If they work together, the job will take 4 days.
The answer is D.
Answer: D
Question: Find the compound ratio of (2:3), (5:11) and (11:2) is
Options:
A)3:2
B)2:1
C)1:2
D)4:5
E)5:3
Rationale: Required ratio = 2/3 * 5/11 * 11/2 = 2/1 = 5:3
Answer is E
Answer: E
Question: A and B start a business, with A investing the total capital of Rs.50000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.1500 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year?
Options:
A)28999
B)27888
C)27838
D)59000
E)28992
Rationale: Interest received by A from B = 10% of half of Rs.50000 = 10% * 25000 = 2500.
Amount received by A per annum for being a working partner = 1500 * 12 = Rs.18000.
Let 'P' be the part of the remaining profit that A receives as his share. Total income of A = (2500 + 18000 + P)
Total income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally.
Income of A = Twice the income of B
(2500 + 18000 + P) = 2(P)
P = 20500
Total profit = 2P + 18000
= 2*20500 + 18000 = 59000
Answer: D
Answer: D
Question: How many seven-digit numbers that do not contain the digits 2 or 9 are there?
Options:
A)178546
B)44786544
C)435786
D)1599678
E)1835008
Rationale: We can have 7 digits ( 1,3,4,5,6,7,8) for the first place ( million's place).
and similarly 8 digits for hundred thousands, ten thousands, thousands, hundred's, tenth's and unit digit. ( 0,1,3,4,5,6,7,8)
So in total 7*8*8*8*8*8*8= 1835008
Hence E
Answer: E
Question: A salesman's income consists of a commission and a base salary of $370 per week. Over the past 5 weeks, his weekly income totals have been $406, $413, $420, $436 and $395. What must his average (arithmetic mean) commission be per week over the next two weeks so that his average weekly income is $500 over the 7-week period?
Options:
A)$150
B)$345
C)$365
D)$715
E)$730
Rationale: Total weekly income over 5 weeks=$406+$413+$420+$436+$395=$2070
For avg weekly income to be $500 over 7 weeks, we need total weekly income over 7 weeks=$3500
Now, $3500-$2070=$1430
From this, we subtract base salary for 2 weeks i.e $370*2=$740
Therefore, commission=$1430-$740=$690 for 2 weeks
Avg weekly commission=$345
Answer B
Answer: B
Question: A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 60 percent of the distribution lies within one standard deviation d of the mean, what percent of the distribution is less than m + d ?
Options:
A) 80%
B) 32%
C) 48%
D) 84%
E) 92%
Rationale: This is easiest to solve with a bell-curve histogram. m here is equal to µ in the Gaussian normal distribution and thus m = 50% of the total population.
So, if 60% is one st.Dev, then on either side of m we have 60/2 = 30%. So, 30% are to the right and left of m (= 50%). In other words, our value m + d = 50 + 30 = 80% goingfrom the mean m, to the right of the distributionin the bell shaped histogram.. This means that 80% of the values are below m + d.
Like I said, doing it on a bell-curve histogram is much easier to fullygethow this works, or you could apply GMAT percentile jargon/theory to it
A
Answer: A
Question: If the average ages of three groups of 30, 40, 50 people respectively is 30,40,50 what is the average ages of all the people?
Options:
A)23.78
B)41.66
C)34.67
D)23.9
E)43.98
Rationale: Average ages of group 1 =30
people in group 1 = 30
Total ages of group 1 = 30*30
Average ages of group 2 = 40
people in group 2 = 40
Total ages of group 2 = 40*40
Average ages of group 3 = 50
people in group 3 = 50
Total ages of group 3 = 50*50
Total people = 40 + 30 + 50 = 120
Average ages of all the people
=((40*40)+(50×50)+(30×30))/120
=125/3
=41.66
Answer is B.
Answer: B
Question: The probability that a number selected at random from the first 50 natural numbers is a composite number is?
Options:
A)17/22
B)17/25
C)17/21
D)17/91
E)17/12
Rationale: 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.
Answer:B
Answer: B