RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: In a certain year, the population of a certain town was 9000. If in the next year the population of males increases by 4% and that of the females by 8% and the total population increases to 9600, then what was the ratio of population of males and females in that given year?
A.1 : 2
B.5 : 4
C.2 : 3
D.Data inadequate
Answer: A.1 : 2
Explanation: Let the population of males = x; then the population of females = 9000 – x
Now, 4% of x + 8% of (9000 – x)
= (9600 – 9000 ) = 600
or 0.04x + 720 – 0.08x = 600
or 720 – 600 = 0.08x – 0.04x
or, 120 = 0.04x
x = 3000
Reqd ratio of population of males and females
3000/9000−3000=3000/6000=1:2
Answer A
Question: Average of 7 results is 121. If the average of first three results is 115 and average of last three results is 120 Then find the fourth result?
A.142
B.150
C.126
D.185
Answer: A.142
Explanation: Option 'A'
Question: In an election between two candidates, 70% of the voters cast their votes, out of which 4% of the votes were declared invalid. A candidate got 6552 votes which were 75% of the total valid votes. Find the total number of votes enrolled in that election.
A.13000
B.12500
C.14000
D.12000
Answer: A.13000
Explanation: Explanation :
Solution: let the total number of votes enrolled be x. then, number of votes cast = 70% of x. valid votes = 96% of(70% of x). .'. 75% of(96% of (70% of of x)) = 6552.
(75/100 * 96/100 * 70/100 * x) = 6552.
=> x = (6552*100*100*100)/(75*96*70) = 13000
Answer : A
Question: 100 oranges are bought at the rate of Rs. 350 and sold at the rate of 48 per dozen. The percentage of profit is
A.12 2/7%
B.13 2/7%
C.14 2/7%
D.15 2/7%
Answer: C.14 2/7%
Explanation: Explanation:
So before solving this question we will get the C.P. and S.P. of 1 article to get the gain percent.
C.P. of 1 orange = 350/100 = Rs 3.50
S.P. of one orange = 48/12 = Rs 4 [note: divided by 12 as 1 dozen contains 12 items]
Gain = 4 - 3.50 = Rs 0.50
Gain%=0.50/ 3.50∗100=100 /7%=14 2/7%
Option C
Question: The Kiljaro Highway is marked with Milestones denoting the distance to the town of Kiljaro. Tommy left kiljaro and drove the highway, passing the 30 km milestone at 8:30. Some time afterwards, Tommy got a phone call asking him to return home, and he made a U-turn at the 160 km milestone. At 09:A0 Tommy passed the milestone marking 70 km to Kiljaro. The variable A represents the tens digit of the minutes in 09:A0. Assuming Tommy maintained the same constant speed during the entire drive, how many kilometers did Tommy travel in one minute?
A.220/(30+10A)
B.220/(30+60A)
C.220/36A
D.220/(30+10A)
Answer: A.220/(30+10A)
Explanation: Since we are dealing with the variables in the answer choices,the best possible method according to me would besubstitution.
Substitute A with 3.meaning tommy would have travelled a distance of ((160-30) + (160-70)) in 60 minutes.
220 Kms in 60 minutes ==> 3.6km/hr.
Substitute A with 3 in the answer options.
Option A
Question: The compound ratio of 5:1, 3:1 and 2:5?
A.6:1
B.1:3
C.1:5
D.1:1
Answer: A.6:1
Explanation: 5/1 * 3/1 * 2/5 = 30/56:1Answer: A
Question: Mahesh can do a piece of work in 45days. He works at it for 20days and then Rajesh finished it in 30days. How long will Y take to complete the work?
A.54
B.25
C.37
D.41
Answer: A.54
Explanation: Work done by Mahesh in 45days = 20*1/45 = 4/9
Remaining work = 1 - 4/9 = 5/9
5/9 work is done by Rajesh in 30days
Whole work will be done by Rajesh is 30*9/5 = 54days
Answer is A
Question: A lemonade stand sold only small and large cups of lemonade on Tuesday. 5/9 of the cups sold were small and the rest were large. If the large cups were sold for 12/11 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups?
A.(a) 7/16
B.(b) 7/15
C.(c) 48/103
D.(d) 17/35
Answer: C.(c) 48/103
Explanation: A simpler way i guess would be to think that in total 9 cups were sold. Out of which 5 are small and 4 are large. Now let the small ones cost $11. so the large ones would cost $12.
So,
5*11=55 and 4*12=48.
Total revenue was 55+48=103
and Large cup sales as found above is 48
Therefore answer is 48/103
C
Question: A square, with perimeter 80, is inscribed in a circle. What is the area of the circle?
A.400π
B.200π
C.250π
D.300π
Answer: B.200π
Explanation: Area of circuscribed circle = pi/2*area of square
Area of square = (80/4)^2 = 20^2= 400
Area of circle = pi/2*400=200pi
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?
A.73
B.44
C.72
D.62
Answer: B.44
Explanation: 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: Option B
Question: A car takes 6 hours to cover a distance of 630 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
A.60
B.50
C.40
D.70
Answer: D.70
Explanation: Time = 6
Distance = 630
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 630/9 = 70 Kmph
Answer D.
Question: In a forest 150 deer were caught, tagged with electronic markers, then released. A week later, 50 deer were captured in the same forest. Of these 50 deer, it was found that 5 had been tagged with the electronic markers. If the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest, and if no deer had either left or entered the forest over the preceding week, what is the approximate number of deer in the forest?
A.150
B.750
C.1,250
D.1,500
Answer: D.1,500
Explanation: Given 150 deers were caught and they are tagged in the first slot.
In the second slot , 50 were caught and 5 we tagged then 10% of them are tagged.
Given this 10% approximates the percentage of tagged deer in the forest..here number is 150..
then 100% is 1500.. is the number of deers population in the forest..
Answer: D is correct answer..
Question: At 9 am a car (A) began a journey from a point, traveling at 40 mph. At 10 am another car (B) started traveling from the same point at 60 mph in the same direction as car (A).
At what time will car B pass car A?
A.12 pm
B.1 pm
C.2 pm
D.3 pm
Answer: A.12 pm
Explanation: After t hours the distances D1 traveled by car A is given by
D1 = 40 t
Car B starts at 10 am and will therefore have spent one hour less than car A when it passes it. After (t - 1) hours, distance D2 traveled by car B is given by
D2 = 60 (t-1)
When car B passes car A, they are at the same distance from the starting point and therefore D1 = D2 which gives
40 t = 60 (t-1)
Solve the above equation for t to find
t = 3 hours
Car B passes car A at
9 + 3 = 12 pm
Answer A
Question: The balance of a trader weighs 8% less than it should. Still the trader marks up his goods to get an overall profit of 20%. What is the mark up on the cost price?
A.40%
B.8%
C.10.4%
D.16.66%
Answer: C.10.4%
Explanation: The most natural way to deal with 'weights' questions is by assuming values.
Say the trader's balance shows 100 gms. It is actually 92 gms because it weighs 8% less. Say, the cost price is $92 ($1/gm). Since he gets a profit of 20%, the selling price must be 92+(20/100)*92 = $110.4
Since the cost price is actually supposed to be $100 (for 100 gms) and the selling price is $110.4, the mark up is simply 10.4%.
Ans : C
Question: What are the unit's digits of 369, 6864, 4725 respectively ?
A.2
B.8
C.3
D.5
Answer: C.3
Explanation: Cyclicity of 3 is 4. 369 = (34)k.31(34)k.31 = (1)k.31(1)k.31 = 3
Power of 6 always gives units digit 6 only.
If power of 4 is odd, then we will get 4 as units digit, if power of 4 is even, then we get 6 as units digit.
Hence, Option 3 is correct.
Answer:C
Question: A bag contains 3 red, 4 black and 2 white balls. What is the probability of drawing a red and a white ball in two successive draws,each ball being put back after it is drawn?
A.2/27
B.1/9
C.1/3
D.4/27
Answer: D.4/27
Explanation: P=2∗39∗29=427P=2∗39∗29=427
We are multiplying by 2 as there are two possible wining scenarios RW and WR.
Answer: D.
Question: In Kaya's teacher's desk there are 10 pink highlighters, 15 yellow highlighters, and 8 blue highlighters. How many highlighters are there in all?
A.11
B.22
C.77
D.33
Answer: D.33
Explanation: Add the numbers of highlighters.
10 + 15 + 8 =33.
Answer is D.
Question: If m is an integer such that (-2)^2m=2^(21-m) then m=?
A.5
B.6
C.7
D.8
Answer: C.7
Explanation: 2m = 21-m
3m = 21
m = 7
The answer is C.
Question: In 1995, the Jossy spent $800 on the family’s water bills. Anticipating that water rates would increase in 1996 by 50%, the Jossy cut back their water usage. By how much must the Jossy have reduce their 1996 water usage to pay exactly the same amount in 1996 as they paid in 1995?
A.a)	33 1/3 %
B.b)	40 %
C.c) 50 %
D.d)	66 2/3 %
Answer: A.a)	33 1/3 %
Explanation: Let x be the water usage and c be the cost waterof Jossy
We have
xc =800, c=800/x
Y(1.5c)=800 where Y is the water usage in 1996
Y= 800/ (1.5*800/x)= 1/1.5x=2/3x
Thus reduction will be x-2/3x=1/3x=A
Question: If 6 years are subtracted from the present age of Arun and the remainder is divided by 18, then the present age of his grandson Gokul is obtained.If Gokul is 2 years younger to Madan whose age is 5 years, then what is the age of Arun?
A.48
B.60
C.84
D.96
Answer: B.60
Explanation: arun age x.
(x-6)/18=y
y is gokul age which is 3
x=60
ANSWER:B
Question: Rita bought 105 items from the market, and each item is either glass, cup, or spoon. If she ownsbought 5 more cups than glasses, and twice as many cups as glasses, how many glasses Rita did buy ?
A.20
B.25
C.30
D.40
Answer: B.25
Explanation: x = the number of glasses
y = the number of cups
z = the number of spoons
From the first sentence we have
Equation #1: x + y + z = 105
...she bought 5 more spoons than glasses...
Equation #2: z = 5 + x
...twice as many cups as glasses...
Equation #3: y = 2x
Now, we can replace y with x in Equation #1
x + 2x + z = 105
Equetion 4 : 3x + z = 105
by adding Equetion #2 and Equetion #4
4x = 100
x = 100/4
x = 25
There are 25 glasses. That's the answer. Just for check, this is 5 less than the number of spoons, so z = 30, y = 50, and 25 + 50 + 30 = 105.
Answer = 25,(B)
Question: If f(x) = -2x2 + 8x - 4, which of the follwoing is true?
A.The maximum value of f(x) is -4.
B.The graph of f opens upward.
C.The graph of f has no x-intercept
D.f is not a one to one function.
Answer: D.f is not a one to one function.
Explanation: f(x) is a quadratic function and its graph is a parabola that may be intercepted by horizontal lines at two points and therefore is not a one to one function. The answer is D
correct answer D
Question: In an xy-coordinate plane, a line is defined by y = kx + 1. If (3, b), (a, 4), and (a, b+1) are three points on the line, where a and b are unknown, then k = ?
A. 1/2
B. 1
C. 3/2
D. 2/3
Answer: D. 2/3
Explanation: b=3k+1...(1)
b+1=ak+1...(2)
4=ak+1...(3)
Taking (2) and (3)
4=b+1
b=3
Taking (1)
3=3k+1
k=2/3
Answer : D
Question: There are 1400 jelly beans divided between two jars, Jar X and Jar Y. If there are 300 fewer jelly beans in jar X than three times the number of beans in jar Y, how many beans are in jar X?
A.925
B.950
C.975
D.1000
Answer: C.975
Explanation: X+Y=1400 so Y=1400-X
X=3Y-300
X=3(1400-X)-300
4X=3900
X=975
The answer is C.
Question: A, B, C are three consecutive positive integers (A>B>C). What is the value of the expression 2A +B + C?
A.6A+7.
B.5A+1.
C.4A-3.
D.6A-5.
Answer: C.4A-3.
Explanation: B = A-1
C= A-2
Putting these values in 2A +B + C we get 4A-3
C is the answer
Question: Last year, for every 100 million vehicles that travelled on a certain highway, 90 vehicles were involved in accidents. If 3 billion vehicles travelled on the highway last year, how many of those vehicles were involved in accidents? (1 billion = 1,000,000,000)
A.288
B.320
C.2,700
D.3,200
Answer: C.2,700
Explanation: To solve we will set up a proportion. We know that “100 million vehicles is to 90 accidents as 3 billion vehicles is to x accidents”. To express everything in terms of “millions”, we can use 3,000 million rather than 3 billion. Creating a proportion we have:
100/90 = 3,000/x
Cross multiplying gives us:
100x = 3,000 * 90
x = 30 * 90 = 2,700
Correct answer is C.
Question: A hiker walked for 3 days. She walked 18 miles on the first day, walking 3 miles per hour. On the second day she walked for one less hour but she walked two mile per hour, faster than on the first day. On the third day she walked the same number of hours as on the first day, but at the same speed as on the second day. How many miles in total did she walk?
A.24
B.44
C.73
D.60
Answer: C.73
Explanation: She walked 18 miles on the first day, walking 3 miles per hour i.e. total time of walk on Day-1 = 18/3 = 6 Hours
Second day time of walk = 6-1 = 5 hours and Speed = 3+2=5 miles per hour i.e. Distance walked on second day = 5*5 = 25 miles
Third day time of walk = 6 hours and Speed = 5 miles per hour i.e. Distance walked on second day = 6*5 = 30 miles
Total Distance travelled on three days = 18+25+30 = 73
Answer: Option C
Question: What should come in place of the question mark (X) in the following equation ?
60% of X + 2/3 of 39 = 44
A.30
B.37
C.28
D.26
Answer: A.30
Explanation: Explanation:
60% of X + 2/3 of 39 = 44
i.e. 3/5 of X + 2/3 of 39 = 44 (60% = 3/5)
3/5 * X + 2/3 * 39 = 44
3/5 * X + 26 = 44
3/5 * X = 18
X = 18 * 5/3
X = 30
ANSWER: A
Question: The ratio of ducks and frogs in a pond is 35 : 39 respectively. The average number of ducks and frogs in the pond is 152. What is the number of frogs in the pond ?
A.160
B.152
C.156
D.144
Answer: A.160
Explanation: Solution:
Ratio of Ducks and Frogs in Pond,
= 35 : 39.
Average of Ducks and Frogs in Pond,
= 152.
So, total number of Ducks and Frogs in the Pond,
= 2* 152 = 304.
Therefore,
Number of Frogs, = (304 *39)/74 = 160.
Answer: Option A
Question: If x/(12p) is an even prime number, where x is a positive integer and p is a prime number, what is the least value of x?
A. 22
B. 33
C. 44
D. 48
Answer: D. 48
Explanation: x/(12p) = even prime number
x = even prime number * 11p
Least value of x = Lowest even prime number * 12 * Lowest value of p
= 2 * 12* 2 = 48
Answer D
Question: What number has a 5:1 ratio to the number 10?
A.88
B.50
C.66
D.2881
Answer: B.50
Explanation: 5:1 = x: 10
x = 50
Answer: B
Question: A clock shows the time as 3:30 P.m. If the minute hand gains 2 minutes every hour, how many minutes will the clock gain by 1 a.m.?
A.23 Minutes
B.19 Minutes
C.25 Minutes
D.26 Minutes
Answer: B.19 Minutes
Explanation: if the minute hand gains 2 minutes in 1 hour the from 3:30 p.m-4:00 p.m it gains 1 min
then from 4:00p.m-4:00 a.m =9*2=18 total=19
ANSWER:B
Question: A can do a job in 15days and B in 20days. If they work on it together for 4 days, then the fraction of the work that is left is?
A.2/15
B.8/15
C.3/11
D.1/12
Answer: B.8/15
Explanation: A's 1 day work = 1/15
B's 1day work = 1/20
A+B 1day work = 1/15 + 1/20 = 7/60
A+B 4days work = 7/60*4 = 7/15
Remaining work = 1 - 7/15 = 8/15
Answer is B
Question: Two trains are moving at 80 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?
A.4 sec
B.5 sec
C.6 sec
D.7 sec
Answer: C.6 sec
Explanation: 70 + 80 = 150 * 5/18 = 125/3 mps
D = 150 + 100 = 250 m
T = 250 * 3/125 = 6 sec
Answer:C
Question: The radius of a cylindrical vessel is 5cm and height is 3cm. Find the whole surface of the cylinder?
A.251.4 sq cm
B.220 sq cm
C.440 sq cm
D.132 sq cm
Answer: A.251.4 sq cm
Explanation: r = 5 h = 3
2πr(h + r) = 2 * 22/7 * 5(8) = 251.4
ANSWER:A
Question: In a apartment, 30% of the people speak English, 20% speak Hindi and 13% speak both. If a people is selected at random, what is the probability that he has speak English or Hindi?
A.1/30
B.2/30
C.10/27
D.2/90
Answer: C.10/27
Explanation: P (E) = 30 / 100 , P (H) = 20 / 100 and P (E âˆ© H) = 13 / 100 =
P (E or H) = P (E U H)
= P (E) + P (H) - P (E âˆ© H)
= (30 / 100) + (20/100 - (13 / 100) = 37/100 = 10/27
C
Question: If 36 men can do a piece of work in 25 hours, in how mwny hours will15 men do it?
A.22
B.38
C.60
D.88
Answer: C.60
Explanation: Explanation:
Let the required no of hours be x. Then
Less men , More hours (Indirct Proportion)
\inline \fn_jvn \therefore 15:36 ::25:x \inline \fn_jvn \Leftrightarrow (15 x X)=(36 x 25) \inline \fn_jvn \Leftrightarrow \inline \fn_jvn x=\frac{36\times 25}{15}=60
Hence, 15 men can do it in 60 hours.
Answer: C) 60
Question: In the xy-plane, a line has slope 3 and x-intercept 4. What is the y-intercept of the line?
A.-12
B.-3
C.0
D.3
Answer: A.-12
Explanation: Let the line be represented by a general equation y=mx+b, where m = slope (3) and b=y intercept. We are also given the value of x-intercept 4.
Theory : y intercept represents the point on the line where the x=0, and x intercept represents the point on the line where the y=0.
Putting these values in the equation : 0 = 3*4 + b => b = -12. Hence A.
Question: 5 men and 5 women participated in a interview. If two people get the job, how many chances there will be at least a man is
selected?
A.30
B.32
C.35
D.31
Answer: C.35
Explanation: 5 women and 5 men. Two people is slelected
It is always better to subtract the total from none in case of at least one problems.
Total ways = 10C2 = 45
Total ways without any man = 5C2 = 10
Hence ways in which at least one man will be present = 45 - 10 = 35
Correct option: C
Question: A right triangle PQR has sides such that the longest side PR is twice the length of side PQ and thrice the length of side QR. If PR = 6, what is the area of the triangle?
A.6
B.36
C.3
D.2
Answer: C.3
Explanation: Since PR is twice of PQ, so PQ=3 and QR=2 since PR is thrice of QR. Area of right triangle equals PQ*QR/2. So the correct answer is C.
Question: An isosceles triangle has a perimetre of 37 centimetres and its base has a length of 9 centimetres. The other two sides will each have a length of
?
A.14 cm
B.15 cm
C.16 cm
D.17 cm
Answer: A.14 cm
Explanation: Solution:
The isosceles triangle has two equal sides. The sum of the equal sides will be 37 - 9 = 28 cm . Thus, one of them will be 28 ÷ 2 = 14 cm
Answer A
Question: Of the employees in a company, 30 % are female who have a master degree. If 20 % of the female employees do not have a master degree, what percent of the employees in the company are female?
A.25 %
B.30 %
C.32.5 %
D.37.5 %
Answer: D.37.5 %
Explanation: No. of female employees with Masters = 0.3 x E (From the question)
No. of female employees without masters = 0.2 x F (From the question)
Therefore No. of female employees with masters = F - 0.2 F = 0.8 F
The 2 expressions equal each other therefore 0.8F = 0.3E; F/E = 0.3/0.8 = 37.5%
Ans: D
Question: If a coin has an equal probability of landing heads up or tails up each time it is flipped , what is the probability that the coin will land Tails up exectly twice in 3 consecutive flips ?
A.0.375
B.0.25
C.0.325
D.0.5
Answer: A.0.375
Explanation: Total number of ways in which H or T can appear in 3 tosses of coin is
= 2 * 2 * 2 = 8 ways
For 2 T and 1 TH
Thus probability is
= P(HTT) + P(TTH) + P(THT)
= 1/8 + 1/8 + 1/8
= 3/8
= .375
Answer :A
Question: Find the no.of ways of arranging the boy and 4 guests at a circular table so that the boy always sits in a particular seat?
A.7!
B.4!
C.9!
D.10!
Answer: B.4!
Explanation: Ans.(B)
Sol. Total number of persons = 5 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 4 places in 4P4 = 4! Ways ... The number of required arrangements = 4! x 1= 4! = 4! ways
Question: The difference of 2 digit number & the number obtained by interchanging the digits is 36. What is the difference the sum and the number if the ratio between the digits of the number is 1:2 ?
A.4
B.8
C.9
D.10
Answer: B.8
Explanation: Let the number be xy.
Given xy – yx = 36.
This means the number is greater is than the number got on reversing the digits.
This shows that the ten’s digit x > unit digit y.
Also given ratio between digits is 1 : 2 => x = 2y
(10x + y) – (10y +x) = 36 => x – y = 4 => 2y – y =4.
Hence, (x + y) – (x – y) = 3y – y = 2y = 8
B
Question: The length of the rectangular field is double its width. Inside the field there is square shaped pond 5m long. If the area of the pond is 1/8 of the area of the field. What is the length of the field?
A.54
B.32
C.75
D.20
Answer: D.20
Explanation: A/8 = 5 * 5 => A = 5 * 5 * 8
x * 2x = 5 * 5 * 8
x = 10 => 2x = 20
Answer:D
Question: Given 2 numbers; 8 and q, the LCM and HCF of both numbers is 72 and 1 respectively. Find q?
A.3
B.5
C.6
D.9
Answer: D.9
Explanation: HCF x LCM = Product of Numbers
1 x 72 = 8 x q
q = (1 x 72) / 8
other number = 9
ANSWER : D
Question: Right triangle PQR is to be constructed in the xy-plane so that the right angle is at P and PR is parallel to the x-axis. The x and Y coordinates of P,Q and R are to be integers that satisfy the inequalitites -4≤ X≤ 5 and 6≤ y≤ 16. How many different triangles with these properties could be constructed?
A.110
B.1100
C.9900
D.10000
Answer: C.9900
Explanation: total values for x=10;y=11
x1,y1=10*11.......................coordinates of 1st pnt
x2,y2=9*1(y2=y1)............... coordinates of 2nd pnt y coordinates will be same as that of 1st pnt bcoz it is parallel to x axis
x3,y3=1*10(x2=x3)..........coordinates of 3rd pt. x coordinates will be same as that of 2nd point bcoz to make a right angle it has to be parallel to y axis
tot ways=10*11*9*1*1*10=9900
ANS:C
Question: What is the dividend. divisor 16, the quotient is 6 and the remainder is 2
A.86
B.87
C.88
D.89
Answer: C.88
Explanation: C = d * Q + R
C = 16 * 6 + 2
C = 86 + 2
C = 88
Question: If a trader sold two cars each at Rs. 325475 and gains 12% on the first and loses 12% on the second, then his profit or loss percent on the whole is?
A.1.44%
B.1.74%
C.1.84%
D.1.47%
Answer: A.1.44%
Explanation: SP of each car is Rs. 325475, he gains 12% on first car and losses 12% on second car.
In this case, there will be loss and percentage of loss is given by
= [(profit%)(loss%)]/100
= (12)(12)/100 % = 1.44%
Answer:A
Question: Three hundred students at College Q study a foreign language. Of these, 120 of those students study French, and 170 study Spanish. If at least 90 students who study a foreign language at College Q study neither French nor Spanish, then the number of students who study Spanish but not French could be any number from
A.10 to 40
B.50 to 90
C.60 to 100
D.60 to 110
Answer: B.50 to 90
Explanation: 120 students study French
180 students do not study French
170 students study Spanish
130 students do not study Spanish
90 students study neither French nor Spanish
180-130=50
180-90=90
B. 50 to 90
Question: If a - b = 5 and a2 + b2 = 34, find the value of ab.
A.A)4.5
B.B)12
C.C)15
D.D)18
Answer: A.A)4.5
Explanation: Explanation:
2ab = (a2 + b2) - (a - b)2
= 34 - 25 = 9
ab = 4.5.
Answer: A
Question: Dawson got a weekly raise of $160. If he gets paid every other week, write an integer describing how the raise will affect his paycheck.
A.150
B.160
C.170
D.180
Answer: B.160
Explanation: Let the 1st paycheck be x (integer).
Dawson got a weekly raise of $ 160.
So after completing the 1st week she will get $ (x+160).
Similarly after completing the 2nd week she will get $ (x + 160) + $ 160.
= $ (x + 160 + 160)
= $ (x + 320)
So in this way end of every week her salary will increase by (B)$ 160.
Question: $500 will become $1000 in 6 years find the rate of interest?
A.A)16.67%
B.B)20%
C.C)25%
D.D)30%
Answer: A.A)16.67%
Explanation: SI = simple interest = A-P = 1000-500 = $500
R = 100SI/PT = 100*500/500*6 =16.67%
Answer is A
Question: Which one of the following numbers can be removed from the set S = {0, 2, 4, 5, 9} without changing the average of set S?
A.0
B.2
C.4
D.5
Answer: C.4
Explanation: Solution:
The average of the elements in the original set S is: (0+2+4+5+9) /5 =20 /5 =4.
If we remove an element that equals the average, then the average of the new set will remain unchanged. The new set after removing 4 is {0, 2, 5, 9}.
The average of the elements is,
(0+2+5+9) /4=16 /4 =4.
Answer: Option C