divelab/Sys2Bench huggingface dataset:
Question: A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
Options:
A)33
B)38
C)37
D)90
E)28
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 480
⇒ 16x = 480
∴ x = 30.
Hence, total number of notes = 3x = 90
Answer:D
Answer: D
Question: The length of a room is 9 m and width is 4.75 m. What is the cost of paying the floor by slabs at the rate of Rs. 900 per sq. metre.
Options:
A)25650
B)25750
C)26550
D)30750
E)38475
Rationale: Area = 9 × 4.75 sq. metre.
Cost for 1 sq. metre. = Rs. 900
Hence total cost = 9 × 4.75 × 900
= 9 × 4275 = Rs. 38475
Answer is E.
Answer: E
Question: The average runs scored by a batsman in 22 matches is 28. In the next 13 matches the batsman scored an average of 15 runs. Find his average in all the 35 matches?
Options:
A)31.23
B)25.12
C)36.25
D)23.17
E)27.66
Rationale: Total score of the batsman in 22 matches = 616.Total score of the batsman in the next 13 matches = 195.Total score of the batsman in the 35 matches = 811.Average score of the batsman = 811/35 = 23.17.Answer: D
Answer: D
Question: Praveen starts business with Rs.3920 and after 5 months, Hari joins with Praveen as his partner. After a year, the profit is divided in the ratio 2 : 3. What is Hari’s contribution in the capital?
Options:
A)s.10080
B)s.8000
C)s.8500
D)s.9000
E)s.6000
Rationale: Let Hari’s capital be Rs. x. Then, 3920 * 12/7x = 2/3
=> 14x = 141120
=> x = 10080.
ANSWER:A
Answer: A
Question: A company organized a recruiting process for 3 vacant positions of assistant manager for its product launches. The company's efforts yielded 12 eligible candidates. How many sets of 3 candidates can the company choose to fill the 3 assistant manager positions?
Options:
A)2,060
B)1,320
C)545
D)315
E)220
Rationale: t will be 12C3: 12!9!3!12!9!3!
12∗11∗10/6 = 220
E is the answer.
Answer: E
Question: Which one of the following numbers is completely divisible by 45?
Options:
A)202860
B)331145
C)1254186
D)2534164
E)8756241
Rationale: 45 = 5 x 9, where 5 and 9 are co-primes.
Unit digit must be 0 or 5 and sum of digits must be divisible by 9.
Among given numbers, such number is 202860.
ANSWER A
Answer: A
Question: How many digits are required to number a book containing 300 pages?
Options:
A)792
B)684
C)492
D)372
E)340
Rationale: 9 pages from 1 to 9 will require 9 digits.
90 pages from 10 to 99 will require 90*2=180 digits.
300-(90+9)=201 pages will require 201*3=603 digits.
The total number of digits is 9+180+603=792.
The answer is A.
Answer: A
Question: A train 110 m long is running with a speed of 60 km/hr. In what time will it pass a trolley that is running with a speed of 12 km/hr in the direction opposite to that in which the train is going?
Options:
A)4.31
B)6.75
C)7.92
D)5.5
E)6.5
Rationale: Speed of train relative to trolley = 60 + 12 = 72 km/hr.
= 72 * 5/18 = 20 m/sec.
Time taken to pass the trolley = 110 * 1/20
= 5.5 sec.
Answer: D
Answer: D
Question: Two trains of length 100 m and 220 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?
Options:
A)18 sec
B)70 sec
C)21 sec
D)20 sec
E)16 sec
Rationale: Relative speed = (42 + 30) * 5/18 = 4 * 5
= 20 mps.
Distance covered in passing each other
= 100 + 220= 320 m.
The time required = d/s
= 320/20
= 16 sec.
Answer: E
Answer: E
Question: A football field is 9600 square yards. If 800 pounds of fertilizer are spread evenly across the entire field, how many pounds of fertilizer were spread over an area of the field totaling 3600 square yards?
Options:
A)450
B)600
C)750
D)2400
E)300
Rationale: Answer E) 9600 yards need 1200 lbs
1 Yard will need 800/9600 = 1/12 lbs
3600 Yards will need 1/12* 3600 Yards = 300lbs
Answer: E
Question: What is the least number which when divided by 12,21,35 will leave in each case the same reminder 6?
Options:
A)210
B)420
C)414
D)426
E)454
Rationale: Here least number means LCM
Hence LCM of 12,35,21 = 2^2 x 7 x 3 x 5
= 420
Therefore required number is 420 + 6 = 426
Ans - D
Answer: D
Question: (x + 3) is a factor in x^2 - mx - 15. What is the value of m?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: I solved the second degree equation and found it like this:
x^2 - mx - 15 = 0
(x-5)(x+3) = 0
x=5 or x= -3
Substituting both values for x in the equation we find:
x^2 - mx -15
=> (-3)^2 - m(-3) = 15
=> 9+ 3m= 15
=> 3m = 15-9=6
=> m = 2
And with 5, using a similar process we end up with:
(5)^2 - m(5) =15
-5m = 15-25= -10
m=2
Ao,ANS B
Answer: B
Question: If each digit in the set of A = (2,3,4,5) is exactly used once, in how many ways can the digits be arranged such that the 3 and 4 are not adjacent?
Options:
A)12
B)15
C)18
D)22
E)24
Rationale: The answer should be = total arrangements - arrangements when 2 and 5 are together.
= 4! - 3! * 2! = 24 -12 = 12
take 2,5,(3,4) here there are 3 entities whose number of arrangements are 3! and 2! is the arrangement between 3 and 4
Answer is A
Answer: A
Question: Mary’s annual income is $15,000 and John’s annual income is $18,000. By how much must Mary’s annual income increase so that it constitutes 60% of Mary and John’s combined income?
Options:
A) $3,000
B) $4,000
C) $7,000
D) $12,000
E) $25,000
Rationale: Let Mary's income increase by x, then the equation will be
15,000 + x= (60/100)* (15,000 + x + 18000 )
15,000 + x = (3/5) * (33,000 + x)
75,000 + 5x = 3x + 99,000
2x = 24,000
x = 12,000
So, Answer will be D
Answer: D
Question: The manager at a health foods store mixes a unique superfruit juice cocktail that costs $1399.45 per litre to make. The cocktail includes mixed fruit juice and açai berry juice, which cost $262.85 per litre and $3104.35 per litre, respectively. The manager has already opened 36 litres of the mixed fruit juice. How many litres of the açai berry juice does he need to add?
Options:
A)17 litres
B)24 litres
C)11 litres
D)07 litres
E)38 litres
Rationale: 262.85(36)+3,104.35x = 1,399.45(36 + x)
Solve the equation.
262.85(36)+3,104.35x = 1,399.45(36 + x)
9,462.6 + 3,104.35x = 50,380.2+ 1,399.45x
9,462.6 + 1,704.9x = 50,380.2
1,704.9x = 40,917.6
x = 24
Answer is B.
Answer: B
Question: The diagonals of two squares are in the ratio of 2 : 5. Find the ratio of their areas.
Options:
A)5:20
B)5:25
C)4:25
D)3:15
E)3:20
Rationale: Let the diagonals of the squares be 2x and 5x respectively.
Ratio of their areas = (1/2)*(2x) 2:(1/2)*(5x) 2= 4x2: 25x2= 4 : 25.
Option C
Answer: C
Question: A salt manufacturing company produced a total of 5000 tonnes of salt in January of a particular year. Starting from February its production increased by 200 tonnes every month over the previous months until the end of the year. Find its average monthly production for that year?
Options:
A)2989
B)2765
C)6110
D)2989
E)9772
Rationale: Total production of salt by the company in that year
= 5000 + 5200 + 5400 + .... + 7200 = 73400.
Average monthly production of salt for that year
= 73400/12
= 6116.
Answer:C
Answer: C
Question: The labeled price of a table is Rs. 7,500. The shopkeeper sold it by giving 5% discount on the labeled price and earned a profit of 15%. What approximately is the cost price of the table?
Options:
A)Rs. 5758
B)Rs. 6195
C)Rs. 6425
D)Rs. 7200
E)None of these
Rationale: Explanation:
Labeled price = Rs. 7,500
By giving 5% discount on labeled price, the selling price is
= 95 / 100 * 7500 = Rs. 7125
By earning 15% profit on the selling of price Rs. 7125 the cost price is
= 100 / 115 * 7125 = Rs. 6195.65
Therefore, approximate cost is 6195.65 (ANSWER ROUNDED OFF: Rs.6195)
ANSWER IS B
Answer: B
Question: A bag contains 6black pens and 8 white pens. One ball is drawn at random. What is the probability that the ball drawn is white?
Options:
A)4/7
B)2/3
C)5/8
D)1/4
E)4/9
Rationale: total number of pens = 14
number of white pens = 8
drawing a white pens= 8/14 = 4/7
Answer is A
Answer: A
Question: In covering a distance of 30 km, Arun takes 2 hours more than Anil. If Arun doubles his speed, then he would take 1 hour less than Anil. What is Arun's speed?
Options:
A)2
B)5
C)6
D)7
E)8
Rationale: Let the speed of Arun = x kmph
and the speed of Anil = y kmph
distance = 30 km
We know that distancespeed=timeHence30x−30y=2...........(Equation1)30y−302x=1...........(Equation2)Equation1 + Equation2⇒30x−302x=3⇒302x=3⇒15x=3⇒5x=1⇒x=5Hence Arun's speed = 5 kmph
Answer : B
Answer: B
Question: What is the sum of all 3 digit positive integers that can be formed using the digits 1, 5, and 8, if the digits are allowed to repeat within a number?
Options:
A)126
B)1386
C)3108
D)308
E)thirteen thousand nine hundred and eighty six (13986)
Rationale: This can also be solved by using a formula
Sum of N numbers
With repetition = N ^ ( N - 1 ) * Sum of the Numbers * 111..... N no. of times
With out repetition = ( N - 1 ) ! * Sum of the Numbers * 111.... N no. of times.
Here repetition is allowed, therefore N is 3 ( No. of digits given ) and sum of No is 14.
3^2 * 14 * 111 = 13986. ans:E
Answer: E
Question: A and B walk around a circular track. They start at 8 a.m. from the same point in the opposite directions. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other before 8.30 a.m. ?
Options:
A)7
B)2
C)9
D)2
E)8
Rationale: B
2
Relative speed = 2 + 3 = 5 rounds per hour.
So, they cross each other 5 times in an hour and 2 times in half an hour.
Hence, they cross each other 2 times before 8.30 a.m.
Answer: B
Question: x and y are positive integers. When x is divided by 6, the remainder is 3, and when x is divided by 16, the remainder is 5. When y is divided by 9, the remainder is 5, and when y is divided by 7, the remainder is 4. What is the least possible value of x / y?
Options:
A)2.5
B)3
C)2
D)1.3
E)1.5
Rationale: When x is divided by 6, the remainder is 3: So, the possible values of x are: 3, 9, 15, 21, etc.
When x is divided by 16, the remainder is 5: So, the possible values of x are: 5,21... STOP. Since both lists include 21, the smallest possible value of x is 21.
When y is divided by 9, the remainder is 5: So, the possible values of y are: 5, 14, 23,32 etc.
When y is divided by 7, the remainder is 4: So, the possible values of y are: 6, 14, ...STOP. Since both lists include 14, the smallest possible value of y is 14
Since the smallest possible values of x and y are 21 and 14 respectively, the smallest possible value of x / y is 1.5. So,E is the correct answer to the original question.
Answer: E
Question: Rahul can do a work in 3 days while Rajesh can do the same work in 2days. Both of them finish the work together and get $2250. What is the share of Rahul?
Options:
A)$50
B)$40
C)$60
D)$100
E)$900
Rationale: Rahul's wages: Rajesh's wages = 1/3 : 1/2 = 2:3
Rahul's share = 2250*2/5 = $900
Answer is E
Answer: E
Question: Working alone, pump A can empty a pool in 6 hours. Working alone, pump B can empty the same pool in 9 hours. Working together, how many minutes will it take pump A and pump B to empty the pool?
Options:
A)192
B)200
C)208
D)216
E)224
Rationale: Pump A can empty (1/6) of the pool per hour.
Pump B can empty (1/9) of the pool per hour.
Together the pumps can empty 1/6+1/9=5/18 of the pool per hour.
1 pool / (5/18) pool per hour = 18/5 hours = 216 minutes.
The answer is D.
Answer: D
Question: How many ways can the letters of the word, ‘MACHINE’ be arranged so that the vowels may occupy only the odd positions?
Options:
A)210
B)576
C)144
D)456
E)356
Rationale: In the word ‘MACHINE’ 3 vowels and 4 consonants.
v v v v
__ _ __ _ __ _ __
Now, 3 vowels can be placed at any of 3 places, out of which 4 marked 1,3,5,7.
Number of ways arranging the vowels= 4P3 = (4*3*2) =24
Also, 4 consonants at the remaining 4 positions may be arranged in = 4P4 = 4!= 24 ways.
Therefore, Required number of ways= (24*24) =576.
ANSWER:B
Answer: B
Question: A runs twice as fast as B and gives B a start of 83m.How long should the racecourse be so that A and B might reach in the same time?
Options:
A)75 m.
B)80 m.
C)150 m.
D)100 m.
E)None of the above
Rationale: ratio of speeds of a and b is 2:1
b is 83m away from a but we know that a covers 1 meter(2-1) more in every second than b
the time taken for a to cover 83m is 83/1=83m
so the total time taken by a and b to reach =2*83=166m
ANSWER:E
Answer: E
Question: What is the square root of 5,625?
Options:
A)A)18
B)B)75
C)C)45
D)D)62
E)E)81
Rationale: A square root of a number is a number times itself equals the original number.
Ex) The square root of 81 is 9 because 9 times itself(9) equals the original number(81).
75*75=5,625
5625 divided by x = 75
x=75
(B)75
Answer: B
Question: In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can?
Options:
A)40
B)44
C)48
D)47
E)50
Rationale: Let the capacity of the can be T litres.
Quantity of milk in the mixture before adding milk = 4/9 (T - 8)
After adding milk, quantity of milk in the mixture = 6/11 T.
6T/11 - 8 = 4/9(T - 8)
10T = 792 - 352 => T = 44.
ANSWER B
Answer: B
Question: From among the 38 students in a class, one leader and one class representative are to be appointed. In how many ways can this be done?
Options:
A)1360
B)1260
C)1060
D)1160
E)1406
Rationale: There are 38 students and every one has equal chance of being selected as a leader. Hence, the leader can be appointed in 38 ways. When one person is appointed as leader, we are left with 35 students. Out of these 37 teachers, we can select one class representative. So, a class representative can be selected in 37 ways. Hence, the number of ways in which a leader and class representative can be selected = 38 x 37 = 1406
ANSWER:E
Answer: E
Question: The H.C.F. of two numbers is 40 and the other two factors of their L.C.M. are 11 and 15. The larger of the two numbers is:
Options:
A)276
B)600
C)699
D)722
E)745
Rationale: the numbers are (40 x 11) and (40 x 15).
Larger number = (40 x 15) = 600.
ANSWER :B
Answer: B
Question: A bus trip of 450 miles would have taken 1 hour less if the average speed S for the trip had been greater by 5 miles per hour. What was the average speed S, in miles per hour, for the trip?
Options:
A)10
B)40
C)45
D)50
E)55
Rationale: (S+5)(T-1) = 450
S*T = 450
Solving both the equations, we get: S = 45 or -50
Since Speed should be positive, S = 45
Hence, option C
Answer: C
Question: If k is an integer and 0.00010101 x 10^k is greater than 1000, what is the least possible value of k?
Options:
A)6
B)7
C)8
D)9
E)10
Rationale: 0.00010101 * 10^k > 1000
We need to move the decimal point to the right 7 places to get 1010.1
This is equivalent to multiplying by 10^7.
The answer is B.
Answer: B
Question: If 7/w + 7/x = 7/y and wx = y, then the average (arithmetic mean) of w and x is
Options:
A)1/2
B)1
C)2
D)4
E)8
Rationale: Given: 7/w + 7/x = 7/ywx=y
Find: (w+x)/2 = ?
7(1/w + 1/x) = 7(1/y) - divide both sides by 7
(1/w + 1/x) = 1/y
(x+w)/wx = 1/wx - sub'd in y=wx
x+w - 1 = 0
x+w = 1
Therefore (w+x)/2 = 1/2
Ans: A
Answer: A
Question: #88
A necklace is made by stringing N individual beads together in the repeating pattern red bead, ORANGE bead, white bead, blue bead, and yellow bead. If the necklace design begins with a red bead and ends with a white bead, then N could equal
Options:
A)16
B)32
C)41
D)48
E)64
Rationale: You can just write out the pattern and count: RGWBYRGWBYRGWBY... But to save time a good test taker will just look for a pattern. Min # is 3, because W is the third one. Then every 5 beads another white comes, so it must be 3+5+5+5.. and so on...
3+5 = 8
3+5+5 = 13
3+5+5+5=18
3+5+5+5+5=23
So you see it ends in either 8 or 3. Pick an answer that ends in either 8 or 3. Only one answer does, D.
Answer: D
Question: There are between 120 and 130 cards in a collection of cards. If they are counted out 3 at a time, there are 2 left over, but if they are counted out 4 at a time, there is 1 left over. How many cards are in the collection?
Options:
A)121
B)123
C)125
D)127
E)129
Rationale: The numbers with the form 4n+1 are 121, 125, and 129.
Only 125 has the form 3k+2.
The answer is C.
Answer: C
Question: An automobile manufacturer offers a station wagon with either a 16-cylinder engine or a 14-cylinder engine and with either a manual transmission or an automatic transmission. A trailer hitch is also offered, but only on a station wagon with a 16-cylinder engine. How many combinations of the five options listed does the manufacturer offer for its station wagon?
Options:
A) 192
B) 128
C) 64
D) 56
E) 44
Rationale: 16-cylinder engine wagons = 2*2*2*2*2*2*2 = 128 (manual or automatic, with or without trailer);
14-cylinder engine wagons = 2*2*2*2*2*2 = 64 (manual or automatic).
Total = 128 + 64 = 192.
Answer: A.
Answer: A
Question: In an IT company, there are a total of 90 employees including 50 programmers. The number of male employees is 80, including 35 male programmers. How many employees must be selected to guaranty that we have 3 programmers of the same sex?
Options:
A)10
B)45
C)55
D)35
E)65
Rationale: You could pick 40 non-programmers, 2 male programmers, and 2 female programmers, and still not have 3 programmers of the same sex. But if you pick one more person, you must either pick a male or a female programmer, so the answer is 45.
B
Answer: B
Question: If x is an integer, and 144 < x^2 <= 361, which of the following is the sum of all possible values of x?
Options:
A) 135
B) 124
C) 116
D)None of the above
E) 105
Rationale: The range of x is from 13 .. to 19 and -13 to -19 so the sum is 0 hence ans D, I guess, unless I am missing something!
Answer: D
Question: The number of singles that a baseball player hit increased 15 percent from her first season to her second season, and the number of doubles that she hit in the same time period decreased by 5 percent. If the total number of singles and doubles that she hit increased 4 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)3:5
B)5:7
C)7:11
D)9:11
E)11:15
Rationale: Soln:-
1.15S + 0.95D = 1.04[S + d]
0.11S = 0.09D
S/D = 9/11
ANSWER:D
Answer: D
Question: How many ways are there to split a group of 4 boys into two groups of 2 boys each? (The order of the groups does not matter)
Options:
A)5
B)6
C)7
D)3
E)8
Rationale: the combination is 4C2 /2
= 4!/2!*2! *2 = 3
D
Answer: D
Question: Rs.1170 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?
Options:
A)Rs.547
B)Rs.519
C)Rs.520
D)Rs.540
E)Rs.529
Rationale: A+B+C = 1170
4A = 3B = 2C = x
A:B:C = 1/4:1/3:1/2 = 3:4:6
6/13 * 1170 = Rs.540
Answer:D
Answer: D
Question: In a 1400 m race Usha beats Shiny by 50 m. In the same race, by what time margin Shiny beat Mercy who runs at 4 m/s ?
Options:
A)100 sec.
B)70 sec
C)25 sec
D)Data not sufficient
E)None of these
Rationale: Speed of Shiny = 50/ 10 = 5m/s
Time taken by shiny to complete the race is B = 1400/5 = 280 sec.
Time taken by Baley to complete the race is D = 1400/4 = 350 sec.
Hence, D-B = 70 sec
ANSWER:B
Answer: B
Question: A room contains 140 people, 15 percent of whom are women. A group of people, 30 percent of whom are women, leaves the room. Of the people remaining in the room, 10 percent are women. How many people left the room?
Options:
A)10
B)35
C)40
D)60
E)80
Rationale: Say group of x people left the room.
# of women in the room was 0.15*140=21;
# of women in the group that left 0.3x;
# of women in the room after the group left it is 0.1(140-x);
So, 21-0.3x= 0.1(140-x) --> x=35.
Answer: B.
Answer: B
Question: Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 5 percent during the third year. What is the value of the account today?
Options:
A)$10,350
B)$10,972.50
C)$10,500
D)$11,500
E)$12,705
Rationale: Value after 1 year: 10,000 * 1.1 = 11,000
Value after 2 years: 11,000 * 1.05 = 11,550
Value today: 11,550 * 0.95 = 10,395
Answer B is correct.
Answer: B
Question: What is the greatest possible length which can be used to measure exactly the lengths 8 m, 4 m 20 cm and 12 m 20 cm?
Options:
A)10 cm
B)30 cm
C)25 cm
D)20 cm
E)35 cm
Rationale: Required length
= HCF of 800 cm, 420 cm, 1220 cm
= 20 cm
Answer: Option D
Answer: D
Question: Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is
Options:
A)17/25
B)17/24
C)17/23
D)17/20
E)17/21
Rationale: n(S) = 20
n(Even no) = 10 = n(E)
n(Prime no) = 8 = n(P)
P(EᴜP) = 10/20 + 8/20 - 1/20 = 17/20
Answer: D
Answer: D
Question: Aishwarya’s mom was 42 years of age at the time of her birth, while her mom was 32 years old when her 4 years younger sister was born. The variance between the parents ages is :
Options:
A)6 years
B)14 years
C)10years
D)9 years
E)4 years
Rationale: B
14 years
Mom’s age when Aishwarya’s sister was born = 32 years.
Dad’s age when Aishwarya’s sister was born = (42 + 4) years = 46 years.
Needed Variance = (46 – 32) years = 14 years.
Answer is B
Answer: B
Question: If x = a!, which of these following values of a is the least possible value (in this list) for which the last 7 digits of the integer x will all be zero?
Options:
A)28
B)32
C)36
D)40
E)44
Rationale: 2*5 will give one 0 at the end. We need 2^7*5^7 to get 7 zeroes at the end.
There are many 2's, so we need to find the first 7 appearances of 5.
These multiples of 5 are: 5, 10, 15, 20, 5*5, 30...which gives us 7.
To have at least 7 zeroes at the end, a => 30.
The answer is B.
Answer: B
Question: By selling 80 bananas, a fruit-seller gains the selling price of 10 bananas. Find the gain percent?
Options:
A)25.32%
B)17.46%
C)15.55%
D)14.28%
E)56.25%
Rationale: SP = CP + g
80 SP = 80 CP + 10 SP
70 SP = 80 CP
70 --- 10 CP
100 --- ? => 14.28%
Answer: D
Answer: D
Question: In a simultaneous throw of two dice , what is the probability of getting to total of 10 or 11?
Options:
A)5/4
B)9/8
C)4/11
D)5/36
E)7/52
Rationale: n(S)36
n(E)=5
P(E)=5/36
Ans: D
Answer: D
Question: On a certain date, Pat invested $9,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 10 years will be $36,000, in how many years total will the total value of the investment plus interest increase to $72,000?
Options:
A)15
B)16
C)18
D)20
E)24
Rationale: 36,000 = 9,000(1 + x)^10
4 = (1+x)^10 = 2^2
(1+x)^10 = ((1+x)^5)^2 = 2^2
Therefore, (1+x)^5 = 2
72,000 = 9,000(1 + x)^n
8 = (1+x)^n
2^3 = (1+x)^n
(1+x)^n = ((1+x)^5)^3 = (1+x)^15
Therefore, n = 15.
The answer is A.
Answer: A
Question: A box contains 100 balls, numbered from 1 to 100. If three balls are selected at random and with replacement from the box, what is the probability W that the sum of the three numbers on the balls selected from the box will be odd?
Options:
A)1/4
B)3/8
C)1/2
D)5/8
E)3/4
Rationale: The sum of the three numbers on the balls selected from the box to be odd one should select either three odd numbered balls (Odd+Odd+Odd=Odd) or two even numbered balls and one odd numbered ball (Even+Even+Odd=Odd);
P(OOO)=(1/2)^3;
P(EEO)=3*(1/2)^2*1/2=3/8 (you should multiply by 3 as the scenario of two even numbered balls and one odd numbered ball can occur in 3 different ways: EEO, EOE, or OEE);
So finally W=1/8+3/8=1/2.
Answer: C.
Answer: C
Question: Find the odd man out
2, 3, 12, 37, 86, 166, 288
Options:
A)2
B)3
C)86
D)116
E)126
Rationale: 2+(1)^2=3
3+(3)^2=12
12+(5)^2=37
37+(7)^2=86
86+(9)^2=167
167+(11)^2=288
ANSWER:D
Answer: D
Question: A worker earns $24 on the first day and spends $18 on the second day. The worker earns $24 on the third day and spends $18 on the fourth day. If this pattern continues, on which day will the worker first reach a net total of $48?
Options:
A)6
B)7
C)9
D)12
E)16
Rationale: Every two days, the net total is $6.
After 8 days, the worker will have $24.
On day 9, the worker will receive $24 for a net total of $48.
The answer is C.
Answer: C