RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: If x^2 − 2x − 15 = (x + r)( x + s) for all values of x, and if r and s are constants, then which of the following is a possible value of( r − s)/2?
A.8
B.2
C.− 2
D.− 4
Answer: D.− 4
Explanation: We know that given ax^2 + bx + c = 0, Sum of the roots = -b/a and product of the roots = c/a.
The roots here are -r and -s.
-r - s = -(-2)/1 = r + s = -2
(-r)*(-s) = -15/1 = rs
So one of r and s is -5 and the other is 3. So (r - s)/2 could be 4 or -4.
Answer (D)
Question: A student is ranked 12th from right and 6th from left. How many students are there in totality ?
A.17
B.19
C.20
D.21
Answer: B.19
Explanation: From right 12 , From left 6
Total = 12+6-1 = 17
ANSWER:B
Question: If all the fractions 3/10, 1/16, 4/11, 2/9, 1/7, 5/14 and 5/24 arranged in descending order of their values, then which one will be the third?
A.3/17
B.3/15
C.3/10
D.3/14
Answer: C.3/10
Explanation: Explanation:
3/10 = 0.3, 1/16 = 0.0625, 4/11 = 0.36, 2/9 = 0.22, 1/7 = 0.14, 5/14 = 0.36 and 5/24 = 0.21
4/11 > 5/14 > 3/10 > 2/9 > 5/24 > 1/7 > 1/16
3/10 will be the third.
Answer: C
Question: A train speeds past a pole in 10seconds and a platform 50 m long in 20 seconds. Its length is:
A.30 m.
B.40 m.
C.60 m.
D.50 m.
Answer: D.50 m.
Explanation: Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 10 => y = x/10
x + 50 / 20 = x / 10
x = 50 m.
Answer: Option D
Question: If A^2 + B^2 = 25 and AB = 10, what is the value of the expression (A - B)^2 + (A + B)^2?
A.10
B.20
C.30
D.50
Answer: D.50
Explanation: (a-b)^2 = a^2 + b^2 - 2ab = 25-20= 5
(a+b)^2 = a^2 + b^2 + 2ab = 25+20=45
so (a+b)^2 + (a-b)^2 = 45 + 5 = 50
D
Question: The price of a car is marked at $12,000. If the car has successive discounts of 20%, 15% and 5%, then at what price does a customer buy the car?
A.$7524
B.$7752
C.$7880
D.$8196
Answer: B.$7752
Explanation: 0.95*0.85*0.8*12000 = $7752
The answer is B.
Question: If a^2=b^2 and b^2=1 ,then what will be the value of a^2+b^2?
A.0
B.1
C.2
D.3
Answer: C.2
Explanation: The answer is 2.
a^2+b^2=b^2+b^2(a^2=b^2)
=1+1(b^2=1)
So the option is C
Question: a,b,c,d,e,f,g,h sitting in a row what is the probability that a,b,d are sitting together?
A.1/5
B.3/28
C.1/7
D.1/14
Answer: B.3/28
Explanation: total number of arrangement is= 8!= 40320
Favorable event i.e a,b and d can be arranged in 3! and the remaining can be arranged in 6! since abd can be in any of the six positions.
so 3!*6!/8! = 3/28
ANSWER:B
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?
A.766m
B.587m
C.350m
D.686m
Answer: C.350m
Explanation: 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 = 350m.
Answer:C
Question: If the wheel is 14 cm then the number of revolutions to cover a distance of 2288 cm is?
A.26
B.28
C.17
D.12
Answer: A.26
Explanation: 2 * 22/7 * 14 * x = 2288 => x = 26
Answer: A
Question: In the storage room of a certain bakery, the ratio of sugar to flour is 3 to 8, and the ratio of flour to baking soda is 10 to 1. If there were 60 more pounds of baking soda in the room, the ratio of flour to baking soda would be 8 to 1. How many pounds of sugar are stored in the room?
A.600
B.900
C.1500
D.1600
Answer: B.900
Explanation: Sugar:Flour = 3:8 = 15:40;
Flour:Soda = 10:1 = 40:4;
Thus we have that Sugar:Flour:Soda = 15x:40x:4x.
Also given that 40x/(4x+60) = 8/1 --> x=60 --> Sugar = 15x = 900.
Answer: B.
Question: How much more would Rs.10000 fetch, after two years, if it is put at 20% p.a. compound interest payable half yearly than if is put at 20% p.a. compound interest payable yearly?
A.241
B.725
C.992
D.837
Answer: A.241
Explanation: 10000(11/10)4 - 10000(6/5)2 = 241
Answer:A
Question: A four-sided shape has angles with ratio 1:2:3:4. What is the measurement of one of its angles?
A.32Â°
B.70Â°
C.112Â°
D.144Â°
Answer: D.144Â°
Explanation: The angles of a four-sided shape should add up to 360Â°. Using the 1:2:3:4 ratio, we use the equation
x + 2x + 3x + 4x = 360Â°
10x = 360Â°
x = 36Â°
x = 36Â°
2x = 72Â°
3x = 108Â°
4x = 144Â°, which is D, so this is the correct answer.
Question: Find the odd man out. 18, 16, 12, 24, 12, 34, 15
A.16
B.46
C.15
D.11
Answer: C.15
Explanation: Explanation :
15 is the only odd number in the given series
Answer : Option C
Question: The size of a television screen is given as the length of the screen's diagonal. If the screens were flat, then the area of a square 22-inch screen would be how many square inches greater than the area of a square 20-inch screen?
A.2
B.4
C.16
D.42
Answer: D.42
Explanation: Pythogoras will help here!
let the sides be x and diagonal be d
Then d ^2 = 2x^2
and
Area = x^2
Now plug in the given diagonal values to find x values
and then subtract the areas
Ans will be 22^2/2 - 20^2 /2 = 84 /2 = 42
Ans D.
Question: Which of the following is not the square of an integer?
A.640828
B.478864
C.227529
D.690561
Answer: A.640828
Explanation: The square of an integer (n^2) can have only the following units digit:
0, if the units digit of n is 0;
1, if the units digit of n is 1 or 9;
4, if the units digit of n is 2 or 8.
5, if the units digit of n is 5;
6, if the units digit of n is 6 or 4;
9, if the units digit of n is 3 or 7.
The square of an integer cannot have the units digit of 2, 3, 7, or 8.
The answer is A.
Question: Six people are on an elevator that stops at exactly 6 floors. What is the probability that exactly one person will push the button for each floor?
A.6!/6^6
B.6^6/6!
C.6/6!
D.6/6^6
Answer: A.6!/6^6
Explanation: Each person out of 6 has 6 options, hence total # of outcomes is 6^6;
Favorable outcomes will be 6!, which is # of ways to assign 6 different buttons to 6 people:
1-2-3-4-5-6 (floors)
A-B-C-D-E-F (persons)
B-A-C-D-E-F (persons)
B-C-A-D-E-F (persons)
...
So basically # of arrangements of 6 distinct objects: 6!.
P=favorable/total=6!/6^6
Answer: A.
Question: What are the last two digits of 63*35*37*82*71?
A. 10
B. 30
C. 40
D. 70
Answer: C. 40
Explanation: We know that to find the last two digits, we need to find the remainder we get when we divide the product by 100.
Remainder of (63*35*37*82*71*41)/ 100
Note that we can simplify this expression by canceling out the 5 and 2 in the numerator and denominator. But before we do that, here is an important note:
Note: We cannot just cancel off the common terms in the numerator and denominator to get the remainder. But, if we want to cancel off to simplify the question, we can do it, provided we remember to multiply it back again.
So say, we want to find the remainder when 14 is divided by 10 i.e. 14/10 (remainder 4). But we cancel off the common 2 to get 7/5. The remainder here will be 2 which is not the same as the remainder obtained by dividing 14 by 10. But if we multiply 2 back by 2 (the number we canceled off), the remainder will become 2*2 = 4 which is correct.
Take another example to reinforce this – what is the remainder when 85 is divided by 20? It is 5.
We might rephrase it as – what is the remainder when 17 is divided by 4 (cancel off 5 from the numerator and the denominator). The remainder in this case is 1. We multiply the 5 back to 1 to get the remainder as 5 which is correct.
So keeping this very important point in mind, let’s go ahead and cancel the common 5 and 2.
We need the
Remainder of (63*7*37*41*71*41*5*2)/10*5*2
Remainder of (63*7*37*41*71*41)/10
Now using concept 2, let’s write the numbers in form of multiples of 10
Remainder of (60+3)*7*(30+7)*(40+1)*(70+1)*(40+1)/10
Remainder of 3*7*7*1*1*1/10
Remainder of 147/10 = 7
Now remember, we had canceled off 10 so to get the actual remainder so we need to multiply by 10: 7*10 = 70.
When 63*35*37*82*71*41 is divided by 100, the remainder is 70. So the last two digits of 63*35*37*82*71*41 must be 40.
Answer (C)
Question: A train moves fast a telegraph post and a bridge 264 m long in 2 sec and 20 sec respectively. What is the speed of the train?
A.89
B.23
C.52.8
D.79.2
Answer: C.52.8
Explanation: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 2=> x = 2y
(x + 264)/20 = y
y = 14.67
Speed = 14.67 m/sec = 14.67 * 18/5 = 52.8 km/hr.
Answer: Option C
Question: An electric pump can fill a tank in 6 hours. Because of a leak in the tank, it took 12hours to fill the tank. If the tank is full, how much time will the leak take to empty it?
A.10hours
B.12hours
C.8hours
D.5hours
Answer: B.12hours
Explanation: Work done by the leak in 1 hour = 1/6 - 1/12 = 1/12
The leak will empty the tank in 12hours
Answer is B
Question: During the months May through October, Teddy the bear quadruples his weight, and during the months November through April, Teddy loses 100 pounds. If at the beginning of November 1973, Teddy's weight was m pounds, what was Teddy's weight in pounds by the end of April 1976?
A.16m - 1300
B.16m - 1200
C.4m - 1300
D.4m - 1200
Answer: A.16m - 1300
Explanation: Nov ' 73 = m
April ' 74 = m - 100
Oct ' 74 = 4m - 300
April' 75 = 4m - 400
Oct' 75 = 16m - 1200
April'76 = 16m - 1300
Hence answer will be (A) 16m - 1300
Question: What least number should be subtracted from 13604 such that the remainder is divisible by 87 ?
A.32
B.29
C.28
D.30
Answer: A.32
Explanation: 13604 ÷ 87 = 156, remainder = 32
Hence 32 is the least number which can be subtracted from 13604 such that the remainder
is divisible by 87
Answer is A
Question: A can do a particular work in 6 days . B can do the same work in 8 days. A and B signed to do it for Rs. 3360. They completed the work in 3 days with the help of C. How much is to be paid to C?
A.s. 380
B.s. 600
C.s. 420
D.s. 400
Answer: C.s. 420
Explanation: Explanation :
Amount of work A can do in 1 day = 1/6
Amount of work B can do in 1 day = 1/8
Amount of work A + B can do in 1 day = 1/6 + 1/8 = 7/24
Amount of work A + B + C can do = 1/3
Amount of work C can do in 1 day = 1/3 - 7/24 = 1/24
work A can do in 1 day: work B can do in 1 day: work C can do in 1 day
= 1/6 : 1/8 : 1/24 = 4 : 3 : 1
Amount to be paid to C = 3360 × (1/8) = 420
Answer : Option C
Question: Rs. 5200 is divided into three parts A, B and C. How much A is more than C if their ratio is 1/2:1/3:1/4?
A.1600
B.1500
C.1200
D.600
Answer: C.1200
Explanation: 1/2:1/3:1/4
= 6:4:3
3/13*5200
= 1200
Answer: C
Question: A boat goes 100 km downstream in 10 hours, and 75 m upstream in 15 hours. The speed of the stream is?
A.2 (1/9) km/h
B.2 (1/5) km/h
C.2 (3/2) km/h
D.2 (1/2) km/h
Answer: D.2 (1/2) km/h
Explanation: :100 --- 10 DS = 10
? ---- 1
75 ---- 15 US = 5
? ----- 1 S = (10 - 5)/2
= 2 2 ½ kmph
Answer: D
Question: On Monday morning, Chris receives tickets to a baseball game that will be played at 7pm on the next evening that it does not rain. However, Chris is only in town until Wednesday morning, at which point he must fly to another city. If there is a 60% chance of rain each of the next two evenings, what is the probability that Chris will be able to attend the game?
A. 36%
B. 60%
C. 64%
D. 80%
Answer: C. 64%
Explanation: Chris won't be able to attend the game if it be raining on Monday eveningandTuesday evening. The probability of that is 0.6*0.6 = 0.36. So, the probability that he will be able to attend is 1 - 0.36 = 0.64.
Answer: C.
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
A.187 m
B.278 m
C.876 m
D.150 m
Answer: D.150 m
Explanation: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train
= (Speed x Time)
= (50/3 * 9) m
= 150 m.
Answer: D
Question: In an election between two candidates first candidate got 60% of votes polled and second Candidate got 290 votes. The total number of votes polled was?
A.votes
B.votes
C.votes
D.votes
Answer: A.votes
Explanation: Total = 100 %,
First person got 60%
second person got remaining 40 % of votes.
than 40 % = 290
40% = 40×7 = 290
100% =100×7 =700 votes
A)
Question: if a@b = a * b^(1/2) then 4@9 = ?
self made
A.2
B.12
C.3
D.8
Answer: B.12
Explanation: 4* (9)^1/2= 4*3= 12
B is the answer
Question: What is the next number of the following sequence
2,2,12,12,30,30,_?
A.54
B.55
C.56
D.57
Answer: C.56
Explanation: 1^2+1=2
2^2-2=2
3^2+3=12
4^2-4=12
5^2+5=30
6^2-6=30
next is (7^2+7)=56
ANSWER:C
Question: The smallest number which when diminished by 12, is divisible 12, 24, 36, 48 and 56 is:
A.1008
B.1015
C.1020
D.1032
Answer: C.1020
Explanation: Required number = (L.C.M. of 12, 24, 36, 48,56 ) + 12
= 1008 + 12
= 1020
Answer: Option C
Question: A k-almost prime number is defined as a positive integer with exactly k prime factors that are not necessarily distinct. The third smallest 4-almost prime number, less the fourth smallest 3-almost prime number is
A.6
B.8
C.16
D.24
Answer: C.16
Explanation: Solution: 3-almost prime numbers : 8(as 8 = 2*2*2) , 12 (2*2*3) , 18 (2*3*3) , 20 (2*2*5)....
4-almost prime numbers : 16(as 8 = 2*2*2*2) , 24 (2*2*2*3) , 36 (2*2*3*3)...
The third smallest 4-almost prime number, less the fourth smallest 3-almost prime number = 36-20 = 16.
Option C.
Question: If the line L passes through the point (3,n) and (n,3), where n is not equal to 3, which of the following must be true?
1. Line L must passes through the first quadrant
2. Line L does pass the origin
3..The slope of L is negative
A.I only
B.II only
C.III only
D.I and II
Answer: C.III only
Explanation: Slope of the given line= 3-n/n-3
Given information is that n is not equal to 3, that means n <3 or n>3. In both these conditions the slope will be negative.
1) n<3 (n=2)
3-2/2-3= -1
2) n<3 (n= 0)
3-0/0-3= -1
3) n<3 (n=-3)
3+3/ -3-3= -2/3
4) n>3
3-4/4-3= -1
NAswer C
Question: 2: 5 = 4/3: x. The value of x is?
A.10/3
B.2
C.3
D.4
Answer: A.10/3
Explanation: x * 2 = 5 * 4/3
x *2= 20/3
x=10/3
ANSWER:A
Question: A fruit seller had some oranges. He sells 40% oranges and still has 420 oranges. How many oranges he had originally?
A.420
B.700
C.220
D.400
Answer: B.700
Explanation: Explanation :
He sells 40% of oranges and still there are 420 oranges remaining
=> 60% of oranges = 420
⇒ (60 × Total Oranges)/100 = 420
⇒ Total Oranges/100 = 7
⇒ Total Oranges = 7 × 100 = 700
Answer : Option B
Question: A man purchased 3 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.140. Find the unknown rate of two blankets?
A.350
B.550
C.490
D.450
Answer: A.350
Explanation: 10 * 140 = 15=1400
3 * 100 + 5 * 150 = 1050
1400 – 1050 = 350
Answer:A
Question: 10 years ago, the average age of a family of 4 members was 24 years. Two children having been born (with age diference of 2 years), the present average age of the family is the same. The present age of the youngest child is ?
A.1
B.7
C.3 years
D.9
Answer: C.3 years
Explanation: Total age of 4 members, 10 years ago = (24 x 4) years = 96 years.
Total age of 4 members now = [96 + (10 x 4)] years = 136 years.
Total age of 6 members now = (24 x 6) years = 144 years.
Sum of the ages of 2 children = (144 - 136) years = 8 years.
Let the age of the younger child be years.
Then, age of the elder child = years.
So,
Age of younger child = 3 years.
Answer: C
Question: The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:
A.15360
B.153600
C.30720
D.307200
Answer: B.153600
Explanation: Perimeter = Distance covered in 8 min. =(12000/60)x 8m = 1600 m.
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
Length = 480 m and Breadth = 320 m.
Area = (480 x 320) m2 = 153600 m2. Answer: Option B
Question: If the circus were to sell all of its 220 tickets for this month's performance at its usual price, the revenue from sales would be 10% greater than that collected last month. If the circus raised the ticket price by 8% and sold only 200 tickets as a result, what percent less would last month's revenue be compared to this month's revenue?
A.2
B.5
C.200/27
D.110/20
Answer: C.200/27
Explanation: Let price be 10/ticket
then 220 tickets for this month's performance at its usual price=2200
which is 10%greater than last month(let X)---->x(1+10/100)=2200----->x=2000
now new revenue this month=200*10.8=2160
as per question asked 2000=2160(1-A/100)----->A=200/27%
Ans C
Question: A train running at the speed of 60 km/hr crosses a pole in 9 sec. What is the length of the train?
A.227 m
B.150 m
C.187 m
D.167 m
Answer: B.150 m
Explanation: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 9
= 150 m
Answer: B
Question: How many integers between 1 and 10^18 are such that the sum of their digits is 2?
A.161
B.171
C.181
D.191
Answer: B.171
Explanation: The integers with a sum of 2 are:
2, 20, 200,...,2*10^17 and there are 18 integers in this list.
Also, these integers have a sum of 2:
11
101, 110
1001, 1010, 1100
etc...
The number of integers in this list is 1 + 2 + ... + 17
Thus, the total number of integers is 1 + 2 + ... + 17 + 18 = 18*19/2 = 171
The answer is B.
Question: A cylindrical water filter is filled with water at a rate of 11 cubic meters per hour, the level of water in the filter rises at a rate of 0.4 meters per hour. Which of the following best approximates the radius of the filter in meters?
A.√10/2
B.√10
C.4.183
D.5
Answer: C.4.183
Explanation: Here's my re-worked solution:
volume = 11 = pi (r^2)(0.4)
22 = 22/7 (4/10)(r^2)
70/4 = r^2
r = sqrt(70/4)
Ans: C
Question: A train 132 m long passes a telegraph pole in 6 seconds. Find the speed of the train
A.70 km/hr
B.72 km/hr
C.79.2 kilometre per hour
D.80 km/hr
Answer: C.79.2 kilometre per hour
Explanation: Solution
Speed	= (132 / 6) m/sec
= (22 x 18 /5) km/hr
= 79.2 km/hr
Answer C
Question: The units digit in the product 274 x 318 x 577 x 313 is
A.2
B.3
C.4
D.5
Answer: A.2
Explanation: Sol.
Required digit = Unit digit in (4 x 8 x 7 x 3) = 2.
Answer A
Question: For a journey the cost of a child ticket is 1/3rd of the cost of an adult ticket. If the cost of the ticket for 4 adults and 5 children is Rs. 85, what is the cost of a child ticket?
A.3
B.4
C.5
D.6
Answer: C.5
Explanation: cost of 1 child=C
cost of 1 adult=A
C=1/3 A =>A=3C
4A+5C=85
=> 12C+5C=85
=> 17C= 85
=>C=5
ANSWER:C
Question: This year, MBB Consulting fired 5% of its employees and left remaining employee salaries unchanged. Sally, a first-year post-MBA consultant, noticed that that the average (arithmetic mean) of employee salaries at MBB was 10% more after the employee headcount reduction than before. The total salary pool allocated to employees after headcount reduction is what percent of that before the headcount reduction?
A.98.5%
B.100.0%
C.102.8%
D.104.5%
Answer: C.102.8%
Explanation: 100 employees, each earning 1$.
After the cut, 95 are left, each earning 1.1$.
1.1*95 = 104.5
100*1 = 100
This gives you the answer.
ANSWER:C
Question: A farmer divided certain number of acres of land among 3 sons and 1 daughter in such a way that 1/3rd of the total land was given to elder son, 1/2 of the remaining was given to second son, 1/3rd of the remaining was given to his younger son, and the remaining to his daughter. As a result, the younger son and daughter received equal number of acres. Find the total number of acres divided, if daughter gets 12 acres land.
A.72
B.90
C.120
D.84
Answer: A.72
Explanation: Let total number of land Y acre
Elder son =
Y × 1/3 = 1/3 Y
Remaining = Y – 1/3 Y = 2/3 Y
Second son = 1/2 of 2/3 Y = 1/3 Y
Remaining = 1/3 Y = 24 acre [12 + 12 = 24, younger son + Daughter]
1/3 Y = 24, then Y = 24 × 3/1 = 72
Option A
Question: Margaret is 8 years more than twice the age of his son. The age of son is 12. Find the age of mother and find the difference between their ages
A.10yrs
B.20yrs
C.30yrs
D.40yrs
Answer: B.20yrs
Explanation: Let, age of son x=12
Margaret is 8 years more than twice the age of his son, y = 8+2(x)
=8+2(12)
=8+24
=32yrs
Difference = 32 - 12
=20yrs
ANSWER:B
Question: How many of the positive factors of 24 are not factors of 25
A.2
B.3
C.4
D.1
Answer: D.1
Explanation: factors of 24 - 1, 2, 3, 4, 6, 8, 12,24
factors of 25 -1,5, 25
Comparing both, we have 1 factor of 24 which are not factors of 25- 1
Answer: D
Question: If 2x + y + 3z = 10 ,-3x - 2y + 7z = 5 ,3x + 3y - 4z = 7 , what is the value of x ?
A.3
B.6
C.4
D.7
Answer: C.4
Explanation: Explanation:
2x + y + 3z = 10 â€“-------I
-3x - 2y + 7z = 5 â€“------ II
3x + 3y - 4z = 7 -------- III
add II and III
-3x - 2y + 7z =5
3x + 3y - 4z = 7
-------------------------------
0+y+3z = 12â€¦.......... IV
sub (IV)from 1, we get 2X= 8
x = 4
ANSWER: C
Question: If 0.4 of a number is equal to 0.06 of another number, the ratio of the numbers is :
A.2 :3
B.3 :4
C.3:20
D.20 : 3
Answer: C.3:20
Explanation: 0.4A = 0.06B
-> A/B = 0.06/0.40 = 6/40 = 3/20
:. A : B = 3 : 20
ANSWER:C
Question: A glucose solution contains 10 grams of glucose per 100 cubic centimeters of solution. If 45 cubic centimeters of the solution were poured into an empty container, how many grams of glucose would be in the container?
A. 3.00
B. 5.00
C. 4.50
D. 5.50
Answer: C. 4.50
Explanation: We are given that a glucose solution contains 10 grams of glucose per 100 cubic centimeters of solution. Since we are dealing with a solution, we know that the grams of glucose is proportional to the number of cubic centimeters of solution. Thus, to determine how many grams of glucose would be in the container when we have 45 cubic centimeters of solution, we can set up a proportion.
We can say: “10 grams of glucose is to 100 cubic centimeters of solution as x grams of glucose is to 45 cubic centimeters of solution.” Let’s now set up the proportion and solve for x.
10/100 = x/45
When we cross multiply we obtain:
(10)(45) = 100x
450 = 100x
4.50 = x
There are 4.5 grams of glucose in the solution in the container.
The answer is C.
Question: Tom has travelling to 7 cities. Gasoline prices varied from city to city. What is the median gasoline price?
A.$1
B.$1.84
C.$1.98
D.$2.34
Answer: B.$1.84
Explanation: Ordering the data from least to greatest, we get:
$1.61, $1.75, $1.79, $1.84, $1.96, $2.09, $2.11
The median gasoline price is $1.84. (There were 3 states with higher gasoline prices and 3 with lower prices.)
B
Question: r=3^(n+3), then in terms of r, 9^n=
A.r^2/81
B.r^3/729
C.r^2
D.r/3
Answer: B.r^3/729
Explanation: Questions in terms of variables can be easily solved by plugging in some values: Say n = 0
r = 3^2 = 27
and you need the value of 9^n which is 9^0 = 1
So when you put r = 27 in the options, you should get 1. Only option (A) satisfies.
Answer (B)
Question: In a certain game, each player scores either 2 points or 5 points. If n players score 2 points and m players score 5 points, and the total number of points scored is 50, what is the least possible positive T difference between n and m?
A.1
B.3
C.5
D.7
Answer: B.3
Explanation: We have equation 2n + 5m = 50
We have factor 2 in first number and we have factor 5 in second number.
LCM(2, 5) = 10
So we can try some numbers and we should start from 5 because it will be less list than for 2
2 * 5 = 10 and n should be equal 20
4 * 5 = 20 and n should be equal 15
6 * 5 = 30 and n should be equal 10
8 * 5 = 40 and n should be equal 5
10 * 5 = 50 and n should be equal 0
third variant give us the mininal difference
n - m = 10 - 6 = 4
And there is some mistake in my way of thinking because we don't have such answer )
If we change the task and will seek for difference between m and n
than minimal result T will be 8 - 5 = 3
And answer B
Question: Kamal started a business with Rs.25000 and after 4 months, Kiran joined him with Rs.60000. Kamal received Rs.58000 including 10% of profit as commission for managing the business. What amount did Kiran receive?
A.75000
B.70000
C.72000
D.78000
Answer: C.72000
Explanation: Explanation:
Ratio of the profits of Kamal and Kiran
=25000×12:60000×8
=25×12:60×8
=5×3:12×2
=5:4×2
=5:8
Let the total profit =x
Then Kamal received 10x/100=x/10 as commission for managing the business.
Remaining profit =x−x10=9x10 which is shared in the ratio =5:8
Total amount received by Kamal =x/10+9x/10×5/13
⇒x/10+9x/10×5/13=58000
⇒x+9x ×5/13=580000
⇒x(1+45/13)=580000
⇒x(58/13)=580000
⇒x x 1/13=10000
⇒x=130000
Kiran's share = 130000−58000=72000
Answer: Option C