RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: The surface area of a sphere is 4πR2, where R is the radius of the sphere. If the area of the base of a hemisphere is 3, what is the surface area Q of that hemisphere?
A. 6/π
B. 9/π
C. 6
D. 9
Answer: D. 9
Explanation: Given Area of the base of a hemisphere is 3 = PI * R^2
Thus R = Sqrt ( 3 / PI ) .
Surface area of whole sphere = 4*PI*R^2 .
= 4 * PI * 3 / PI
= 12 .
Since the hemisphere is half of a sphere the Surface area of the hemisphere = 12 / 2
= 6 ( curved part , not including the flat rounded base ) .
But the total surface area = 6 + Area of the base of a hemisphere .
= 6 + 3
= 9.
Answer is D !!
Question: On dividing 15 by a number, the quotient is 4 and the remainder is 3. Find the divisor?
A.3
B.6
C.9
D.12
Answer: A.3
Explanation: d = (D-R)/Q
= (15 - 3)/4
= 12/4 = 3
A)
Question: The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8339 for a computer table, then what was the cost price of the computer table?
A.7297
B.2977
C.2871
D.6725
Answer: D.6725
Explanation: Explanation:
CP = SP * (100/(100 + profit%))
= 8339(100/124) = Rs. 6725.
Answer: D
Question: As a bicycle salesperson, Norman earns a fixed salary of $20 per week plus $6 per bicycle for the first six bicycles he sells, $12 per bicycle for the next six bicycles he sells, and $18 per bicycle for every bicycle sold after the first 12. This week, Norman earned more than twice as much as he did last week. If he sold n bicycles last week and y bicycles this week, which of the following statements must be true?
I. y > 2n
II. y > n
III. y > 3
A.I only
B.II only
C.I and II
D.II and III
Answer: D.II and III
Explanation: This is kind of like doing your taxes, lets summarize the data in terms of bike sales and salary -
0 Bikes - $20
6 Bikes - $56
12 Bikes - $128
More than 12 bikes - 128 + 18*(n-12) where n is the total number of bikes sold (when n>12).
XN = cycles sold last week
NS = Salary last week.
Y = cycles sole this week
YS = Salary this week.
given YS>2NS
lets test all statements with N=0;
NS = 20
YS >40
True when Y = 4
satisfies all the statements but we can only be sure of iii as Y will only increase from here. So iii must be true. Eliminate A,B,C
lets test all statements with N=1;
NS = 26
YS>52
True when Y=6
Still satisfies all the statements - Nothing achieved
lets test all statements with N=6;
NS = 56
YS>112
True when Y = 11
This proves statement i wrong, hence eliminate E so we are left with
Answer D
Question: To mail a package, the rate is 30 cents for the first pound and 5 cents for each additional pound. Two packages weighing 4 pounds and 6 pounds, respectively can be mailed seperately or combined as one package. Which method is cheaper and how much money is saved?
A.Combined, with a saving of 20 cents
B.Separately, with a saving of 5 cents
C.Combined, with a saving of 25 cents
D.Separately, with a saving of 15 cents
Answer: C.Combined, with a saving of 25 cents
Explanation: 4 pounds cost = 30+3*5 = 45
6 pounds cost = 30+5*5 = 55
Total = 100
10 pounds cost = 30+ 9*5 =75 dif. 25
Answer : C
Question: A certain football coach allows his quarterback to call three plays in a row. If the quarterback can choose from 3 passing plays, 4 running plays, and 2 trick plays, how many different W arrangements of plays can be run, if the same play can’t be run more than once?
A.24
B.125
C.243
D.504
Answer: D.504
Explanation: Number of W ways to choose the first play: 9
Second play: 8
Third:7
9*8*7= 504.D
Question: On a game show, a contestant is given three keys, each of which opens exactly one of the three identical boxes.The contestant assigns each key to one of the boxes and wins the amount of money contained in any box that is opened by the key assigned to it. The first box contains $4, the second $400, and the third $4000. What is the probability that a contestant will win more than $4000?
A.2/6
B.1/6
C.1/8
D.1/3
Answer: B.1/6
Explanation: Let's call the boxes that contain $4, $400, and $4000, respectively, Box A, Box B, Box C. These are opened, respectively, by Key A, Key B, and Key C.
We want to know the probability of winning more than $4000. Notice that if the distribution of keys is:
Box A = Key B
Box B = Key A
Box C = Key C
then the contestant wins exactly $4000, not more than $4000. The only configuration that leads to winning more than $1000 is:
Box A = Key A
Box B = Key B
Box C = Key C
i.e., getting all three keys correct. That's the only way to be more than $4000. So, really, the question can be rephrased: what is the probability of guessing the order of keys so that each key matches the correct box?
Well, for a set of three items, the number of possible permutations is 3! = 3*2*1 = 6.
Of those 6 possible permutations, only one of them leads to all three keys being paired with the right box. So, the answer is
Probability = 1/6
Answer: B
Question: How many bricks, each measuring 5 cm x 11 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 2 cm?
A.5600
B.6000
C.2909
D.7200
Answer: C.2909
Explanation: Number of bricks =Volume of the wall/Volume of 1 brick =	(800 x 600 x 2)/(5 x 11 x 6) = 2909.
Answer: Option C
Question: If x =- |x| , then which one of the following statements could be true?
I. x = 1
II. x < 0
III. x > 0
A. None
B. I only
C. II only
D. I and II
Answer: C. II only
Explanation: Answer copied from NOVA guide
Statement I could be true because + 1 = −(+1) = −(1) = -1 .
Statement II could be true because the right side of the equation is always negative [ ± x = –(a positive number) = a negative number].
Now, if one side of an equation is always negative, then the other side must always be negative,
otherwise the opposite sides of the equation would not be equal.
Since Statement III is the opposite of Statement II, it must be false. But let’s show this explicitly:
Suppose x were positive. Then x = x, and the equation x = ± x becomes x = –x. Dividing both sides of this equation by x yields 1 = –1. This is contradiction.
Hence, x cannot be positive. The answer is (C).
Question: The length and breadth of a rectangle is increased by 10% and 25% respectively. What is the increase in the area?
A.37.5
B.25.7
C.30.5
D.22.5
Answer: A.37.5
Explanation: 100 * 100 = 10000
110 * 125 = 13750
-----------
3750
10000 ------ 3750
100 ------- ? => 37.5%
ANSWER A
Question: The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?
A.16
B.17
C.18
D.19
Answer: D.19
Explanation: Explanation:
Average of 20 numbers = 0.
Sum of 20 numbers (0 x 20) = 0.
It is quite possible that 19 of these numbers may be positive and if their sum is a then 20th number is (-a).
Answer D
Question: In the sequence 1, 2, 4, 8, 16, 32, …, each term after the first is twice the previous term. What is the sum of the 16th, 17th terms in the sequence?
A.2^18
B.3(2^17)
C.7(2^16)
D.3(2^15)
Answer: D.3(2^15)
Explanation: the sequence comes out to be 2^0,2^1,2^2,2^3 and so on...
so 16th term will be 2^15
17th term 2^16
adding all three
we get
2^15+(2^15)*2
so answer is 2^15(1+2)=>3(2^15)
answer D
Question: A train 110 m long is running with a speed of 84 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
A.7 sec
B.6 sec
C.8 sec
D.4.4 sec
Answer: D.4.4 sec
Explanation: Speed of train relative to man = 84 + 6
= 90 km/hr.
= 90 * 5/18 = 25 m/sec.
Time taken to pass the men = 110/25
= 4.4 sec.
Answer:D
Question: In Anthony's toy bin there are 17 red blocks. There are 8 more yellow blocks than red blocks. There are also 4 more blue blocks than red blocks. How many blocks are there in all?
A.22
B.11
C.29
D.63
Answer: D.63
Explanation: Step 1: Find the number of yellow blocks.
17 + 8 = 25
Step 2: Find the number of blue blocks.
17 + 4 = 21
Step 3: Find the total number of red, yellow, and blue blocks.
17 + 25 + 21 = 63
There are 63 blocks in Anthony's toy bin.
Answer is D.
Question: A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
A.150m
B.288m
C.278m
D.229m
Answer: A.150m
Explanation: Length of the train be ‘X’
X + 150/15 = X + 250/20
4X + 600 = 3X + 750
X = 150m
Answer: A
Question: Four-ninths of a drink mix is dye and the rest is sugar. When the mix is added to water a gallon of drink is made that is 7.5% sugar. What percentage of the gallon is dye?
A.6
B.6.5
C.7.5
D.8
Answer: A.6
Explanation: The proportion of Dye and sugar will remain constant.
Dye/Sugar = (4/9)/(5/9) = x/7.5
=> 4/5 = x/7.5 => x = 4*7.5/5 = 6.
Answer is A.
Question: The three digits of a number add up to 14. The number is divisible by 5. The leftmost digit is double the middle digit. What is the product of the three digits?
A.40
B.72
C.78
D.90
Answer: D.90
Explanation: Say the three-digit number is abc.
The leftmost digit is double the middle digit --> a=2b;
The number is divisible by 5 --> c is either 0 or 5;
The three digits of a number add up to 13 --> a+b+c=14
So, either a+b+c=2b+b+0=14 or a+b+c=2b+b+5=14. The first equation does not give an integer value of b, so it's not the case. From the second we get that b=3 --> a=6 and c=5 --> a*b*c=90.
Answer: D.
Question: David deposited $5,000 to open a new savings account that earned six percent annual interest, compounded semi-annually. If there were no other transactions in the account, what the amount of money in David account one year after the account was opened?
A. $5,306
B. $6,120
C. $5,136
D. $5,405
Answer: A. $5,306
Explanation: Approach #1:
6 percent annual interest compounded semi-annually --> 3% in 6 moths.
For the first 6 moths interest was 3% of $5,000, so $150;
For the next 6 moths interest was 3% of $5,000,plus3% earned on previous interest of $150, so $150+$6=$156;
Total interest for one year was $150+$156=$306, hence balance after one year was $5,000+ $306=$5,306.
Answer: A.
Question: If the average (arithmetic mean) of 102 consecutive odd integers is 414, then the least of these integers is
A.a) 160
B.b) 289
C.c) 250
D.d) 313
Answer: D.d) 313
Explanation: A very helpful rule to know in arithmetic is the rule that in evenly spaced sets, average = median. Because the average will equal the median in these sets, then we quickly know that the median of this set of consecutive odd integer numbers is 414.
There are 102 numbers in the set, and in a set with an even number of terms the median is just the average of the two most median terms (here the 51st and 52nd numbers in the set). This means that numbers 51 and 52 in this set are 413 and 415. Because we know that number 51 is 413, we know that the smallest number is 50 odd numbers below this, which means that it is 50*2 = 100 below this (every odd number is every other number). Therefore 413-100 = 313, answer choice D
Question: Which of the following equations passes through the points (2,4) and (-3,-6)?
A.y = (1/2)x - 2
B.y = 2x
C.y = (-1/2)x + 2
D.y = 2x + 4
Answer: B.y = 2x
Explanation: Find slope first = (y1-y2)/(x1-x2) = (-6-4)/(-3-2) = 2
Using the point (2,4) in options
we get,
y = 2x as right answer.
Ans- B
Question: Ratio between 2 numbers is 5 : 7 and their product is 560.what is the difference between 2 numbers?
A.6
B.7
C.8
D.9
Answer: C.8
Explanation: Explanation:
x/y = 5/7
x × y = 560 ⇒ x = 560/y
Substituting this value in first equation, we get 560/yy=57560/yy=57 ⇒560y2=57560y2=57 ⇒ y = 28
x = 20
So difference between the numbers could be
x – y = –8
y – x = 8
Answer: C
Question: Three 8 faced dice are thrown together. The probability that all the three show the same number on them is ?
A.1/38
B.1/48
C.1/56
D.1/64
Answer: D.1/64
Explanation: It all 3 numbers have to be same basically we want triplets. 111, 222, 333, 444, 555, 666, 777 and 888. Those are eight in number. Further the three dice can fall in 8 * 8 * 8 = 512 ways.
Hence the probability is 8/512 = 1/64
Answer:D
Question: The difference of two numbers is 1375. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?
A.240
B.272
C.295
D.360
Answer: B.272
Explanation: Let the smaller number be x. Then larger number = (x + 1375).
x + 1375 = 6x + 15
5x = 1360
x = 272
Smaller number = 270.
ANSWER B
Question: Two alloys A and B are composed of two basic elements. The ratios of the compositions of the two basic elements in the two alloys are 7 : 5 and 1 : 2, respectively. A new alloy X is formed by mixing the two alloys A and B in the ratio 4 : 3. What is the ratio of the composition of the two basic elements in alloy X ?
A.1 : 1
B.2 : 3
C.5 : 2
D.10 : 11
Answer: D.10 : 11
Explanation: Mixture A has a total of 7 + 5= 12 parts. If in the final mixture this represents 6 parts, then the total number of parts in mixture B should be (12/6)*3 = 6.
So, we should take of mixture B a quantity with 3 and 6 parts, respectively.
This will give us in the final mixture (7 + 3) : (5 + 6), which means 10:11
Answer D.
Question: What is the sum of all the prime numbers greater than 10 but less than 40?
A.190
B.189
C.180
D.199
Answer: C.180
Explanation: Required sum = (11 +13 + 17 + 19 + 23+ 29 + 31 + 37) = 180
Note: 1 is not a prime number
Answer C
Question: The fourth proportional to 5, 8, 15 is:
A.9
B.24
C.18
D.19
Answer: B.24
Explanation: Let the fourth proportional to 5, 8, 15 be x.
Then, 5 : 8 : 15 : x
5x = (8*15)
x = (8*15)/5 = 24
ANSWER B
Question: The volumes of two cones are in the ratio 1 : 10 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire?
A.2 : 5
B.1 : 5
C.3 : 5
D.4 : 5
Answer: A.2 : 5
Explanation: The volume of the cone = (1/3)πr2h
Only radius (r) and height (h) are varying.
Hence, (1/3)π may be ignored.
V1/V2 = r12h1/r22h2 => 1/10 = (1)2h1/(2)2h2
=> h1/h2 = 2/5
i.e. h1 : h2 = 2 : 5
ANSWER:A
Question: Ages of two persons differ by 16 years. If 6 year ago, the elder one be 3 times as old the younger one, find their present age
A.77
B.30
C.66
D.55
Answer: B.30
Explanation: Let the age of younger person is x,
Then elder person age is (x+16)
=> 3(x-6) = (x+16-6) [6 years before]
=> 3x-18 = x+10
=> x = 14.
So other person age is x + 16 = 30
Answer:B
Question: Richard will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row. The heights of the people within each row must increase from left to right, and each person in the second row must be taller than the person standing in front of him or her. How many such arrangements of the 6 people are possible?
A.5
B.6
C.9
D.24
Answer: A.5
Explanation: Richard will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row.person with max height is in the second row, person with min height is in the first row. We need to select 1 person in the middle of each row... In the middle of the first row we can put only 2, 3 or 4. In the middle of the second row we can put only 3, 4, 5. If we select {3 in the sec. row, 2 in the first}, {4,2}, {5,2}, {4,3}, {5,3}, {5,4}. So, there are 0*1 + 1*1 + 2*1 + 1*1 + 1*1 + 0*1 = 5 cases...A
Question: The length and breadth of a rectangle is increased by 10% and 25% respectively. What is the increase in the area?
A. 27.5%
A.1 1/2
B.1 1/6
C.1 1/8
D.1 1/1
Answer: B.1 1/6
Explanation: 3/20 * 2 + (2 + x)/5 = 1
x = 1 1/2 days
Answer:B
Question: Solve the equation for x : 19(x + y) + 17 = 19(-x + y) - 21?
A.-1
B.77
C.8
D.3
Answer: A.-1
Explanation: 19x + 19y + 17 = -19x + 19y - 21
38x = -38 => x = -1
Answer: A
Question: A chemist mixes one liter of pure water with x liters of a 45% salt solution, and the resulting mixture is a 15% salt solution. What is the value of x?
A.1/4
B.1/3
C.1/2
D.1
Answer: C.1/2
Explanation: Concentration of salt in pure solution = 0
Concentration of salt in salt solution = 45%
Concentration of salt in the mixed solution = 15%
The pure solution and the salt solution is mixed in the ratio of --> (45 - 15)/(15 - 0) = 2/1
1/x = 2/1
x = 1/2
Answer: C
Question: At Joes Steakhouse the hourly wage for a chef is 22% greater than that of a dishwasher, and the hourly wage of a dishwasher is half as much as the hourly wage of a manager. If a managers wage is $8.50 per hour, how much less than a manager does a chef earn each hour?
A.$1.40
B.$2.40
C.$3.315
D.$4.40
Answer: C.$3.315
Explanation: Manager wages per hour = $8.50
Dishwasher wages per hour = half of manager's wages. = 1/2($8.50) ==> $4.25
Chef wages per hour = 22% greater than Dishwasher wages
--> 22% of $4.25 = (22*($4.25)) /100
--> ($93.5)/100
--> $0.935
Therefore,
Chef wages per hour = $4.25 + $0.935 ==> $5.185
Difference of wages between manager and chef = $8.50 - $5.185 ==> $3.315
ANSWER:C
Question: An art gallery has only paintings and sculptures. Currently, 1/3 of the pieces of art are displayed, and 1/6 of the pieces on display are sculptures. If 1/3 of the pieces not on display are paintings, and 1400 sculptures are not on display, how many pieces of art does the gallery have?
A.360
B.3150
C.540
D.640
Answer: B.3150
Explanation: Too many words and redundant info there.
(i) 1/3 of the pieces of art are displayed, hence2/3 of the pieces of art are NOT displayed.
(ii) 1/6 of the pieces on display are sculptures, hence 5/6 of the pieces on display are paintings.
(iii) 1/3 of the pieces NOT on display are paintings, hence2/3 of the pieces NOT on display are sculptures.
1400 sculptures are not on display, so according to (iii) 2/3*{not on display} = 1400 --> {not on display} = 2100.
According to (i) 2/3*{total} = 2100 --> {total} = 3150.
Answer: B.
Question: Among a group of 2500 people, 35 percent invest in municipal bonds, 18 percent invest in oil stocks, and 7 percent invest in both municipal bonds and oil stocks. If 1 person is to be randomly selected from 2500 people, what is the probability that the person selected will be one who invests in municipal bonds but not in oil stocks
A.7/29
B.7/25
C.7/23
D.7/22
Answer: B.7/25
Explanation: Ans: Here 2500 does not require.
From the diagram we know that only ones who invested in municipal bonds are 28%, the probability is 28 / 100
= 7/25
Answer:B
Question: The overall age of X and Y is 15 year greater than the overall age of Y and Z. Z is how many decades younger that X?
A.11
B.15
C.12
D.17
Answer: B.15
Explanation: B
15
(X + Y) â€“ (Y + Z) = 15
X â€“ Z = 15
Question: The 280 students in a group are to be seated in rows so that there is an equal number of students in each row. Each of the following could be the number of rows EXCEPT
A. 4
B. 20
C. 30
D. 40
Answer: C. 30
Explanation: Obviously the number of rows must be a factor of 280. The only option which is not a factor of 280 is C (30).
Answer: C.
Question: How long does a train 165 meters long running at the rate of 54 kmph take to cross a bridge 660 meters in length?
A.62
B.72
C.55
D.82
Answer: C.55
Explanation: Explanation:
T = (660 + 165)/54 * 18/5
T = 55
Answer: Option C
Question: A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
A.177 m
B.189 m
C.120 m
D.178 m
Answer: C.120 m
Explanation: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec
= 20 m/sec.
Length of the train = 20 * 6
= 120 m.
Answer: C
Question: A lawn has equally distributed grass. It takes 24 days to 70 cows and 60 days to 30 cows to eat the whole of grass. How many cows will be needed to eat the grass in 96 days.
A.20
B.30
C.40
D.50
Answer: A.20
Explanation: g - grass at the beginning
r - rate at which grass grows, per day
y - rate at which one cow eats grass, per day
n - no of cows to eat the grass in 96 days
g + 24*r = 70 * 24 * y
g + 60*r = 30 * 60 * y
g + 96*r = n * 96 * y
Solving, n = 20.
ANSWER:A
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 12 sec, then the speed of each train is?
A.25
B.22
C.36
D.12
Answer: C.36
Explanation: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (120 + 120)/12 => x = 10
Speed of each train = 10 m/sec.
= 10 * 18/5 =- 36 km/hr.
Answer:C
Question: The volumes of two cones are in the ratio 1 : 10 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire?
A.2:5
B.2:8
C.2:1
D.2:4
Answer: A.2:5
Explanation: The volume of the cone = (1/3)πr2h
Only radius (r) and height (h) are varying.
Hence, (1/3)π may be ignored.
V1/V2 = r12h1/r22h2 => 1/10 = (1)2h1/(2)2h2
=> h1/h2 = 2/5
i.e. h1 : h2 = 2:5
Answer:A
Question: A completes a work in 12 days and B complete the same work in 24 days. If both of them work together, then the number of days required to complete the work will be ?
A.8 days
B.10 days
C.18 days
D.28 days
Answer: A.8 days
Explanation: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days
Therefore, here, the required number of days = 12 × 24/ 36 = 8 days.
A)
Question: The citizens of planet nigiet are 5 fingered and have thus developed their decimal system in base 8. A certain street in nigiet contains 1000 (in base 5) buildings numbered 1 to 1000. How many 3s are used in numbering these buildings? Express result in terms of base 10.
A.54
B.64
C.75
D.85
Answer: C.75
Explanation: no of 3s b/w 1-99 is 20,100-199 is 20 and so on. so leavn d range b/w 300-399 total no of 3s is(9*20=)180. no of 3s b/w 300-399 is(20+100=)120.
total no of 3s b/w 1-1000=120+180=300
in base 10 300=3*5^2=75.
ANSWER:C
Question: If s, t, and p are positive numbers such that (s/(s+t))(10) + (t/(s+t))(20)=p and if s<t which of the following could be the value of p?
A.10
B.12
C.15
D.18
Answer: D.18
Explanation: The answer is D. For any positive s and t, p is a number between 10 and 20. Since s < t, weight of 10 is inferior of weight of 20 -> p is > 15 -> 18 is the answer.
Question: From a well shuffled deck of cards, what would be the probability that you would draw a two or a spade?
A.4 in 12
B.4 in 10
C.4 in 13
D.4 in 8
Answer: C.4 in 13
Explanation: P(C)+P(2)-P(Cn2)
P(Cu2)=13/52 + 4/52 - 1/52 = 4/13
Question: What is the minimum percentage increase in the mean of set S {-4, -1, 0, 6, 9} if its two smallest elements are replaced with two different primes?
A. 25%
B. 50%
C. 75%
D. 100%
Answer: D. 100%
Explanation: Mean of S is (-4-1+0+6+9)/5=2;
In order the increase to be minimal we should replace two smallest elements of S, which are -4 and -1, with two smallest primes, which are 2 and 3. Hence our new set will be {2, 3, 0, 6, 9} --> new mean is (2+3+0+6+9)/5=4.
Percent increase=(4-2)/2*100=100%.
Answer: D.
Question: Of the goose eggs laid at a certain pond, 1/2 hatched and 3/4 of the geese that hatched from those eggs survived the first month. Of the geese that survived the first month, 3/5 did not survive the first year. If 120 geese survived the first year and if no more than one goose hatched from each egg, how many goose eggs were laid at the pond?
A.800
B.840
C.880
D.920
Answer: A.800
Explanation: Let x be the number of eggs that were laid.
(2/5)(3/4)(1/2)x = 120
(6/40)x = 120
x = 800
The answer is A.
Question: If x + (1/x) = 5, what is the value Q of x^2 + (1/x)^2?
A.Q=21
B.Q=22
C.Q=23
D.24
Answer: C.Q=23
Explanation: Squaring on both sides,
x^2 + (1 /x)^2 + 2(x)(1/x) = 5^2
x^2 + (1 /x)^2 = 23
Answer: C
Question: For how many unique pairs of nonnegative integers {a, b} is the equation a^2 - b^2 = 25 true?
A.1
B.3
C.5
D.2
Answer: D.2
Explanation: Answer D
(a+b)(a-b)=25
5cases For (a+b), (a-b)
25, 1
5, 5
Answer D
Question: Find a 8 digit number that if multiplied by the number 9 or any of its multiplications products (18, 27, 36, 45,..) will result in the multiplication factor repeated (n) number of times.
A.12435687
B.12345679
C.10000000
D.99999999
Answer: B.12345679
Explanation: B
The number is: 12345679
12345679 * 9 = 111111111
12345679 * 18 = 222222222
12345679 * 27 = 333333333