divelab/Sys2Bench huggingface dataset:
Question: If the value of a piece of house decreases by 10% while the new tax rate on the house represent 110% of the original tax rate, what is the effect on the taxes?
Options:
A)a - taxes increase by 10%
B)b- taxes increase by 1%
C)c- there is no change in taxes
D)d- taxes decrease by 1%
E)c- taxes decrease by 10%
Rationale: Cansider the value of house = 100, Original tax rate 10%, hence tax value = 100*10% = 10.
Decreased value of house = 90, New tax rate = 110% of 10 = 11%, hence tax value = 90*11% = 9.9
10-9.9 = decrease by 1%.
Answer D.
Answer: D
Question: In a stockpile of products produced by three machines M1, M2 and M3, 40% and 30% were manufactured by M1 and M2 respectively. 3% of the products of M1 are defective, 1% of products of M2 defective, while 92% of the products of M3 III are not defective. What is the percentage of defective in the stockpile?
Options:
A)3%
B)5%
C)3.9%
D)4.9%
E)6.5%
Rationale: Explanation :
Let there be 100 products in the stockpile. 40% and 30% were manufactured by M1 and M2 respectively. So, 30% are manufactured by M3.
Products from M1 = 40, from M2 = 30 and from M3 = 30.
Number of defective products from M1 = 0.03 x 40 = 1.2, from M2 = 0.01 x 30 = 0.3 and from M3 = 0.08 x 30 = 2.4
Therefore, total number of defective products = 3.9
Answer : C
Answer: C
Question: Angles AMB and CMD are right angles, ∠AMD is acute, and ∠BMC=y° is acute. What is ∠AMD ?
Options:
A)90°−y
B)180°−y
C)90°+y
D)2y
E)y
Rationale: LAMB = 90
LCMB = y
so, LAMC = 90-y
and since LDMC = 90
LDMA = 90 - (90-y) = y
Answer: E
Answer: E
Question: A larger cube has 216 cubic inch as a volume and in the cube there are 216 smaller cubes such that their volume is 1 cubic inch. What is the difference between the surface areas’ sum of the 216 smaller cubes and the surface area of the larger cube, in square inch?
Options:
A)54
B)64
C)81
D)1080
E)120
Rationale: Volume of larger cube = 216 = 6^3
Side of larger cube = 6
Volume of smaller cube = 1 --> Side of smaller cube = 1
Surface area of larger cube = 6 * 6^2 = 216
Surface area of 27 smaller cubes = 216 * 6 * 1 = 1296
Difference = 1296 - 216 = 1080
Answer: D
Answer: D
Question: At a certain resort, each of the 39 food service employees is trained to work in a minimum of 1 restaurant and a maximum of 3 restaurants. The 3 restaurants are the family buffet, the dining room, and the snack bar. Exactly 15 employees are trained to work in the family buffet, 18 are trained to work in the dining room, and 12 are trained to work in the snack bar. If 4 employees are trained to work in exactly 2 restaurants, how many employees are trained to work in all 3 restaurants?
Options:
A)2
B)3
C)4
D)5
E)1
Rationale: 39 = 15+ 18 + 12 - 4 - 2x
2x = 15 + 18 + 12 - 4 - 39
= 41 - 39
= 2
x =1
E
Answer: E
Question: 587 * 999 = ?
Options:
A)586411
B)586413
C)486411
D)486413
E)None of these
Rationale: Explanation:
Trick: 587 * (1000 - 1) = 587000 - 587 = 586413
Option B
Answer: B
Question: A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 81 km/hr. What is the length of the platform?
Options:
A)240
B)288
C)277
D)360
E)422
Rationale: Speed = 81 * 5/18 = 22.5 m/sec.
Length of the train = 22.5 * 20 = 450 m.
Let the length of the platform be x m . Then,
(x + 450)/36 = 22.5 => x = 360 m.
Answer: D
Answer: D
Question: Find compound interest on $ 8000 at 15% per annum for 2 years 4 months, compounded annually.
Options:
A)3109
B)3209
C)3108
D)3107
E)3100
Rationale: Time = 2 years 4 months = 2(4/12) years = 2(1/3) years.
Amount = $ [8000 X (1+­(15/100))2 X (1+((1/3)*15)/100)]
=$ [8000 * (23/20) * (23/20) * (21/20)]
= $ 11109.	.
:. C.I. = Rs. (11109 - 8000) = $ 3109.
Answer A.
Answer: A
Question: In a rare coin collection, all coins are either pure gold or pure silver, and there is initially one gold coin for every three silver coins. With the addition of 11 more gold coins to the collection, the ratio of gold coins to silver coins is 1 to 2. Based on this information, how many total coins are there now in this collection (after the acquisition)?
Options:
A)64
B)72
C)80
D)90
E)99
Rationale: Initially the number of gold coins and silver coins is 2k and 6k.
After adding gold coins, the number of coins is 3k and 6k.
Thus k = 11 and the total number of coins is 9k = 99.
The answer is E.
Answer: E
Question: Find the area of a rhombus one side of which measures 20 cm and one diagonal is 27 cm.
Options:
A)600cm2
B)500cm2
C)400cm2
D)432cm2
E)100cm2
Rationale: Explanation: Let other diagonal = 2x cm.
Since diagonals of a rhombus bisect each other at right angles, we have:
(20)2 = (12)2 + (x)2 =>x =√(20)2 – (12)2= √256= 16 cm. _I
So, other diagonal = 32 cm.
Area of rhombus = (1/2) x (Product of diagonals) =(1/2× 27 x 32) cm2 = 432 cm2
Answer: Option D
Answer: D
Question: A, Band C can do a piece of work in 11 days, 20 days and 20 days respectively, working alone. How soon can the work be done if A is assisted by Band C on alternate days?
Options:
A)7 days
B)8 days
C)9 days
D)10 days
E)11 days
Rationale: (A+B)'s 1 day's work = 1/11+1/20 = 31/220
(A+C)'s 1 day's work = 1/11+1/20 = 31/220
work done in 2 day's = 31/220+31/220= 31/110
31/110th work done in 2 days
work done= 110/31*2 = 7 days (approx)
ANSWER:A
Answer: A
Question: Meg and Bob are among the 4 participants in a cycling race. If each participant finishes the race and no two participants finish at the same time, in how many different possible orders can the participants finish the race so that Meg finishes ahead of Bob?
Options:
A)24
B)30
C)12
D)90
E)120
Rationale: Total # of ways the race can be finished is 4!. In half of the cases Meg finishes ahead of Bob and in other half Bob finishes ahead of Meg. So, ways Meg to finish ahead of Bob is 4!/2=12.
Answer: C.
Answer: C
Question: The length of a rectangle hall is 5 m more than its breadth. The area of the hall is 750 m2. The length of the hall is :
Options:
A)15 m
B)22.5 m
C)25 m
D)30 m
E)None of these
Rationale: Solution
Let breadth = x metres. Then, length = (x + 5) metres.
Then x(x+5) = 750 ⇔ x2 + 5x −750 = 0 ⇔ (x + 30) (x + 25) = 0 ⇔ x = 25.
∴ Length = (x + 5) = 30 m. Answer D
Answer: D
Question: Find the L.C.M of 2^2 * 3^3 * 5 *7^2*11, 2^3 * 3^2* 5^2* 7^4*11, 2 * 3* 5^3* 7^4*11
Options:
A)2^3 * 3^3 * 5^3 * 7^4 * 11
B)2^2*3^3*5^3 * 7^4 * 11
C)2^2*3^3*5^2 * 7^4 * 11
D)2^3*3^3*5^2* 7^4 * 11
E)2^3*3^3*5^2* 7^3 * 11
Rationale: L.C.M= product of the highest powers of 2,3,5,7 and 11=2^3 * 3^3 * 5^3 * 7^4 * 11
Answer (A)
Answer: A
Question: Michele invests 500 of her money in a mutual fund that quickly goes sour, losing 25% of its value each day for a week. Which of the following COULD be the value of Michele’s investment at the close-of-business any day that week?
Options:
A)$0.00
B)$133.00
C)$250.05
D)$66.74
E)$10000.00
Rationale: Suppose she invests n$ in the starting then in the subesequent days the money left after the day will be
n/4, n/8, n/16, n/32
So, answer will be D
Answer: D
Question: A boat can move upstream at 25 kmph and downstream at 35 kmph, then the speed of the current is?
Options:
A)5
B)9
C)4
D)1
E)3
Rationale: US = 25
DS = 35
M = (35 - 25)/2
= 5
Answer: A
Answer: A
Question: Kishore has 4 pairs of shoes; each pair is a different color. If Kim randomly selects 2 shoes without replacement from the 8 shoes, what is the probability that she will select 2 shoes of the same color?
Options:
A)2/5
B)1/5
C)1/9
D)1/7
E)1/25
Rationale: Can be tackled in this way as well: Probability of selecting any 1 out of 8 shoes = 8/8 = 1
Probability of selecting the next shoe (out of 8 available) having the same color = 1/7 (as after selecting the 1st one, there is only 1 another shoe left with the same color).
Thus the total probability = 1*1/7=1/7.
D is the correct answer.
Answer: D
Question: A boat speed with the diesel is 15 km/hr and the speed of the diesel is 2.5 km/hr. The boat 's speed against the diesel is
Options:
A)9 km/hr
B)10 km/hr
C)12 km/hr
D)13 km/hr
E)14 km/hr
Rationale: Boat's rate in still water = (15 - 2.5) km/hr = 12.5 km/hr.
Boat's rate against the diesel= (12.5 - 2.5) km/hr = 10 km/hr
B
Answer: B
Question: 50% of x is greater than 1/3rd of x by 110.what is x?
Options:
A)100
B)200
C)300
D)350
E)660
Rationale: 5x/10-x/3=110
1x/6=110
x=660
ANSWER:E
Answer: E
Question: The population of a city is 5265538. If there are 4169577 adults in the city, how many children are there in the city?
Options:
A)1095961
B)1065961
C)1085961
D)1097961
E)1056961
Rationale: population of a city = 5265538
Number of Adults = 4169577
Number of Children = 5265538-4169577
= 1095961
answer :A
Answer: A
Question: In the sixth grade at Parkway elementary school there are 450 students. 300 students are boys and 250 students are playing soccer. 86% of the students that play soccer are boys. How many girl student are in Parkway that is not playing soccer?
Options:
A)69.
B)115
C)81.
D)91.
E)108.
Rationale: Total students = 450
Boys = 300, Girls = 150
Total playing soccer = 250
86%of 250 = 215 are boys who play soccer.
Girls who play soccer = 35.
Total girls who do not play soccer = 150 - 35 = 115.
Correct option: B
Answer: B
Question: How many seconds does Sandy take to cover a distance of 500 meters, if Sandy runs at a speed of 18 km/hr?
Options:
A)80
B)100
C)120
D)140
E)160
Rationale: 18 km/hr = 18000 m / 3600 s = 5 m/s
time = 500 / 5 = 100 seconds
The answer is B.
Answer: B
Question: Speed of a boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph. A man rows to a place at a distance of 105 km and comes back to the starting point. The total time taken by him is:
Options:
A)24 hours
B)22 hours
C)23 hours
D)21 hours
E)41 hours
Rationale: Speed upstream = 7.5 kmph.
Speed downstream = 10.5 kmph.
Total time taken =105/7.5+105/10.5=24 hours
Answer: A
Answer: A
Question: If a man lost 8% by selling oranges at the rate of 18 a rupee at how many a rupee must he sell them to gain 45%?
Options:
A)33.56
B)23.68
C)11.42
D)9.56
E)23.55
Rationale: 92% ---- 18
145% ---- ?
92/145 * 18 = 11.42
Answer: C
Answer: C
Question: What is the unit’s digit of 7^4
Options:
A)3
B)1
C)5
D)7
E)9
Rationale: 7^1=7
7^2=49
7^3=343
7^4=1(last digit)
Therefore, last digit of 7^4=1
Answer B
Answer: B
Question: A boat has an upstream speed of at 50 kmph and downstream at 80 kmph, and then find the speed of the boat in still water?
Options:
A)65
B)60
C)75
D)70
E)90
Rationale: US = 25
DS = 35
M = (50 +80)/2
= 65
Answer:A
Answer: A
Question: How many seconds does a train 110 meters long, traveling at 54 km/h, take to completely cross a bridge of 160 meters in length?
Options:
A)18
B)20
C)22
D)24
E)26
Rationale: 54 km/h = 54000/3600 = 15 m/s
Time = 270 / 15 = 18 seconds
The answer is A.
Answer: A
Question: An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m?
Options:
A)Rs.4082.43
B)Rs.4082.20
C)Rs.4882.40
D)Rs.4082.40
E)Rs.4082.21
Rationale: Length of the first carpet = (1.44)(6) = 8.64 cm
Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100)
= 51.84(1.4)(5/4) sq m = (12.96)(7) sq m
Cost of the second carpet = (45)(12.96 * 7) = 315 (13 - 0.04)
= 4095 - 12.6 = Rs.4082.40
Answer:D
Answer: D
Question: Anitha had 80 currency notes in all, some of which are of Rs 95 denomination and the remaining of Rs 45 denomination. The total amount of all these currency notes was Rs. 4000. How much amount (in Rs) did she have in the denomination of Rs 45?
Options:
A)3500
B)72
C)2000
D)3000
E)4000
Rationale: Let the number of 45-rupee notes = x
Then, the number of 95-rupee notes = (80 – x)
45x + 95(80 – x) = 4000 or x + 2(80 – x) = 95 or x = 72.
ANSWER:B
Answer: B
Question: One-tenth of the students at a nursery school are 4 years old or older. If 20 students have not yet reached their third birthday, and a total of 50 students are not between 3 years old and 4 years old, how many children are in the nursery school?
Options:
A)150
B)300
C)450
D)490
E)620
Rationale: x/10 students are > 4 yrs
20 students are < 3 yrs
x/10+ 20 = 50
x/10 = 30
x = 300
Answer: B
Answer: B
Question: A train is moving at a speed of 75km/hr and its length is 500m. Find the time taken by it to pass a man standing near the railway line?
Options:
A)30sec
B)45sec
C)36sec
D)24sec
E)52sec
Rationale: Speed of the train = 75*5/18 = 125/6 m/sec
Distance moved in passing the standing man = 500m
Required time taken = 500/(125/6) = 24sec
Answer is D
Answer: D
Question: A man is 20 years older than his son. In two years, his age will be twice the age of his son. What is the present age of his son?
Options:
A)23 years
B)22 years
C)21 years
D)20 years
E)18 years
Rationale: Let present age of the son =x years
Then, present age the man =(x+20) years
Given that, in 2 years, man's age will be twice the age of his son
â‡’(x+20)+2=2(x+2)
â‡’x=18
ANSWER:E
Answer: E
Question: At a certain college there are twice as many English majors as history majors and three times as many English majors as mathematics majors. What is the ratio of the number of mathematics majors to the number of history majors?
Options:
A)2 o 3
B)3 to 2
C)2 to 4
D)1 to 5
E)1 to 6
Rationale: This is how I translated the question:
At a certain college there are twice as many english majors as history majors
E = 2H
and three times as many english majors as mathematics majors.
E = 3M
What is the ratio of the number of history majors to the number of mathematics majors?
What is H:M?
Just set E equal to each other to get the ratio in terms of H and M.
2H = 3M
H/M = 2/3
The answer is 2:3
Answer : A
Answer: A
Question: The price of sugar is increased by 2%. By how much percent should a home maker reduce her consumption of sugar to have no extra expenditure?
Options:
A)(700/107) %
B)(107/100) %
C)(100/107)%
D)(7/100)%
E)(200/102)%
Rationale: Old price = $100 (assume);
Old consumption = 1 kg (assume).
New price = $102.
We want the spendings to remain at $100.
(New consumption)*102 = 100 --> (New consumption) = 100/102 kg.
Percent decrease = Change/Original *100 = (1 - 100/102)/1*100 = 200/102%.
Answer: E.
Answer: E
Question: Look at this series: 97, 92, 85, 78, 71, 64, 57, 50, ... What number should come next?
Options:
A)45
B)33
C)43
D)38
E)36
Rationale: Explanation:
In this series, each number 7 is subtracted from previous number to arrive at the next number.
Answer: Option C
Answer: C
Question: A bank pays interest to its customers on the last day of the year. The interest paid to a customer
is calculated as 10% of the average monthly balance maintained by the customer. John is a
customer at the bank. On the last day, when the interest was accumulated into his account, his
bank balance doubled to $5660. What is the average monthly balance maintained by John in his
account during the year?
Options:
A) 28300
B) 5680
C) 6840
D) 7540
E) 28400
Rationale: bank balance is doubled with accumulation of interest tp 5660..
this means INTEREST is 5660/2=2830 for entire year..
although since interest is 10% of avg MONthly balance, it becomes 28300..
A
Answer: A
Question: A certain sum of money at simple interest amounted Rs.940 in 5 years at 2% per annum, find the sum?
Options:
A)450
B)867
C)899
D)854
E)261
Rationale: 940 = P [1 + (5*2)/100]
P = 854
Answer: D
Answer: D
Question: The length of a side of a hexagon is 5 inches. What is the perimeter?
Options:
A)116
B)25
C)30
D)24
E)15
Rationale: Hexagon. It means 6 equal sides.
p = 5 + 5 + 5 + 5 + 5 + 5 = 10+ 10 + 10 = 30 inches
Answer C
Answer: C
Question: A prison of 10,000 inmates has enough food to feed them all for 50 days. After 10 days some of the inmates leave and the food is now enough for the same period of 50 days as before. How many of them left?
Options:
A)3,000
B)2,200
C)2,000
D)1,000
E)200
Rationale: 10,000 --- 50
10,000 --- 40
x --- 50
x*50 = 10,000*40
x = 8,000
10,000
--------
2,000
Answer = C
Answer: C
Question: 7, 26, 63, 124, (....)
Options:
A)342
B)125
C)289
D)564
E)36
Rationale: Explanation:
Numbers are
2^3-1=7
3^3-1=26
4^3-1=63
5^3-1=124
6^3-1=342
ANSWER:A
Answer: A
Question: The present ages of three persons in proportions 4 : 5 : 9. Eight years ago, the sum of their ages was 30. Find their present ages (in years).
Options:
A)19, 20, 28
B)12, 15, 27
C)20, 35, 45
D)33,42,43
E)13, 23,34
Rationale: Let their present ages be 4x, 5x and 9x years respectively.
Then, (4x - 8) + (5x - 8) + (9x - 8) = 30
18x = 54
x = 3.
Their present ages are 4x = 12 years, 5x = 15 years and 9x = 27 years respectively.
ANSWER:B
Answer: B
Question: Water consists of hydrogen and oxygen, and the approximate ratio, by mass, of hydrogen to oxygen is 2:16. Approximately how many grams of oxygen are there in 144 grams of water?
Options:
A)16
B)72
C)112
D)128
E)142
Rationale: See H/O = 2 / 16
Add 1 to both sides:
H/O + 1 = 2/16 + 1
Take LCM
(H+O)/O = (2+16)/16
Water/O = 18/16
Now that we have the Water to Oxygen ratio, put in the amount of water i.e. 144 gm
=>O= 144*16/18 = 128
ANSWER:D
Answer: D
Question: At what rate of interest is an amount doubled in two years, when compounded annually?
Options:
A)41.7%
B)41.4%
C)49.4%
D)81.4%
E)31.4%
Rationale: Let the rate of interest be r. The amount gets doubled in two years => P(1 + r/100)2 = 2p => 1 + r/100 = √2 => r/100 = √2 - 1 = 0.414 => r = 100(0.414) = 41.4%.Answer: B
Answer: B
Question: one out of ten employees are capable of doing a certain task. 40 percent of the five employees, including the one who are capable, are assigned to a project involving this task. what percentage of employees assigned to the project are not capable?
Options:
A)43.33%
B)75%
C)13.33%
D)38.33%
E)23.33%
Rationale: Given 40% of 10 employees including 1 who are capable of doing task.
40% of 10 employeees
= 40/100 * 10
= 4 employees
===> 1 employees who are capable of doing the task and three employee who is not capable.
percentage of employees assigned who are not capable
= 3/4 * 100
=75%
ANSWER:B
Answer: B
Question: The radius of a cone is 10 m, height 21 m. The volume of the cone is:
Options:
A)2200
B)1100
C)5500
D)3300
E)1050
Rationale: 1/3 πrh = 1/3 × 22/7 × 100 × 21
= 2200 m(power3)
Answer is A.
Answer: A
Question: The average salary of a person for the months of January, February, March and April is Rs.8000 and that for the months February, March, April and May is Rs.8200. If his salary for the month of May is Rs.6500, find his salary for the month of January?
Options:
A)2177
B)2876
C)4500
D)5700
E)6711
Rationale: Sum of the salaries of the person for the months of January, February, March and April = 4 * 8000 = 32000 ----(1)
Sum of the salaries of the person for the months of February, March, April and May = 4 * 8200 = 32800 ----(2)
(2)-(1) i.e. May - Jan = 800
Salary of May is Rs.6500
Salary of January = Rs.5700.Answer: D
Answer: D
Question: [(3/2 ÷ 1/2 × 3/2)]/[(3/2 × 1/2 ÷ 3/2)] = ?
Options:
A)6
B)8
C)10
D)9
E)3
Rationale: Explanation:
[(3/2 ÷ 1/2 × 3/2)]/[(3/2 × 1/2 ÷ 3/2)]
= [3/2 × 2/1 × 3/2]/[3/2 × 1/2 × 2/3]
= (9/2)/(1/2) = (9/2) × (2/1) = 9
Answer: Option D
Answer: D
Question: Find the slope of the line perpendicular to the line y = (1/5)x - 7
Options:
A)1
B)2
C)-5
D)4
E)5
Rationale: Two lines are perpendicular if the product of their slopes is equal to -1. The slope of the given line is equal to 1 / 5. If m is the slope of the line perpendicular to the given line, then
m × (1/5) = -1
Solve for m
m = - 5
correct answer C) -5
Answer: C
Question: Six points lie on the circumference of a circle. What is the positive difference between the number of triangles and the number of quadrilaterals that can be created by connecting these points?
Options:
A)4
B)5
C)6
D)15
E)20
Rationale: Let's start with the triangle: You have 6 points to choose from but only 3 points you will connect and 3 points you will not connect.
Hence number of possibilities for triangle: 6! / 3! * 3! = 20
Same goes for the quadrilateral: 6 points to choose from, 4 points which you will connect and 2 points which you won't connect.
Number of possibilities for quadrilateral: 6! / 4! * 2! = 15
Difference = 5
Answer B
Answer: B
Question: A train ride from Town P to Town Q costs $6.85 more than does a bus ride from Town P to Town Q. Together, the cost of one train ride and one bus ride is $9.45. What is the cost of a bus ride from Town P to Town Q?
Options:
A)$1.30
B)$2.50
C)$4.10
D)$4.70
E)$8.20
Rationale: Let x be the cost of a bus ride.
x + (x+685) = 945
2x = 260
x = $1.30
The answer is A.
Answer: A
Question: The sum of three consecutive integers is 102. Find the lowest of the three?
Options:
A)15
B)33
C)56
D)96
E)88
Rationale: Explanation:
Three consecutive numbers can be taken as (P - 1), P, (P + 1).
So, (P - 1) + P + (P + 1) = 102
3P = 102 => P = 34.
The lowest of the three = (P - 1) = 34 - 1 = 33.
Answer B
Answer: B
Question: A company plans to award prizes to its top 3 salespeople, with the largest prize going to the top salesperson, the next-largest prize to the next salesperson, and a smaller prize to the third-ranking salesperson. If the company has 12 salespeople on staff, how many different arrangements of winners are possible?
Options:
A)1,728
B)1,440
C)1,320
D)220
E)6
Rationale: Choose 3 people out of 12 and arrange these 3 people between themselves.
12!/(3!x9!)x3!=12x11x10x9!/(3!x9!)x3!=12x11x10=1320
ANSWER:C
Answer: C
Question: The average of seven numbers is 21. The average of first three numbers is 19 and the average of last three numbers is 23. What is the middle number?
Options:
A)20
B)22
C)18
D)19
E)21
Rationale: The total of seven numbers = 7X21 = 147
The total of first 3 and last 3 numbers is = 3 X 19+3 X 23 = 126
So, the middle number is (147 - 126 ) = 21
E
Answer: E
Question: Which of the listed below number is the odd one out?
Options:
A)17642
B)36119
C)84129
D)67626
E)65612
Rationale: E
65612
All the others are three digit numbers followed by their square root, eg 361 followed by its square root, 19.
Answer E
Answer: E
Question: If the probability of rain on any given day in Chicago during the summer is 50%, independent of what happens on any other day, what is the probability of having exactly 3 rainy days from July 4 through July 7, inclusive?
Options:
A)1/4
B)1/8
C)3/8
D)3/16
E)5/16
Rationale: One case is rainy-rainy-rainy-not rainy.
The probability of this case is (1/2)^4 = 1/16
The number of possible cases is 4C3 = 4.
P(exactly 3 rainy days) = 4*1/16 = 1/4
The answer is A.
Answer: A
Question: 1: 3 = 1 2/3: x. The value of x is?
Options:
A)1
B)6
C)7
D)5
E)8
Rationale: x * 1 = 3 * 5/3
x = 5
Answer: D
Answer: D
Question: The number of bacteria in a petri dish increased by 50 percent every 2 hours. If there were 108 million bacteria in the dish at 2: 30 p.m., at what time were there 32 million bacteria in the dish?
Options:
A)6: 00 p.m.
B)8: 00 p.m.
C)6: 00 a.m.
D)8: 30 a.m.
E)10: 00 a.m.
Rationale: Given:
The number of bacteria in a petri dish increased by 50 percent every 2 hours
There were 108 million bacteria in the dish at 2: 00 p.m
Since the bacteria is increasing by 50% every 2 hours, this means that the number is multiplied by 1.5 every 2 hours.
Required: At what time were there 32 million bacteria in the dish?
Assume that there were n intervals of 2 hours between 32 million and 108 million.
32 * (1.5)^n = 108
(3/2)^n = 108/32 = 27/8 = (3/2)^3
Hence n = 3 intervals.
Each interval was of 2 hours. Therefore, the number of hours = 6
Subtracting 6 hours from 2H30 PM, we get 8H30 AM as the answer.
Option D
Answer: D
Question: If A:B:C = 2:3:4, then find AB:BC:CA
Options:
A)5:9:24
B)6:9:24
C)7:9:24
D)8:9:24
E)None of these
Rationale: Explanation:
Let A = 2x, B = 3x, C = 4x, then,
AB=2x3x=23BC=3x4x=34CA=4x2x=21=>AB:BC:CA=23:34:21=8:9:24
Answer: D
Answer: D
Question: If n is a positive integer and the product of all the integers from 1 to n, inclusive, is a multiple of 170, what is the least possible value of n?
Options:
A)14
B)13
C)15
D)17
E)16
Rationale: 17, since n needs to be the largest of the prime factors. Therefore, the answer is D.
Answer: D