RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: If (x+2) is the HCF of x2 + ax + b and x2 + cx + d , then which one of the following is correct ?
A.a + c = b + d
B.2a + b = 2c + d
C.b + 2c = 2a + d
D.b - 2c = 2a - d
Answer: C.b + 2c = 2a + d
Explanation: Answer
If (x+2) is the HCF of x2 + ax + b and x2 + cx + d.
Then, (-2)2 -2a +b = (-2)2 -2c + d
b + 2c = 2a + d
Correct Option: C
Question: Which of the following is equal to the value of 2^4 + 2^4 + 3^4 + 3^4 + 3^4 ?
A.2^5 + 3^10
B.2^5 + 3^9
C.2^5 + 3^8
D.2^5 + 3^5
Answer: D.2^5 + 3^5
Explanation: 2^4 + 2^4 + 3^4 + 3^4 + 3^4
= 2 (2^4) + 3 (3^4)
= 2^1 (2^4) + 3^1 (3^4)
= 2^(1+4) + 3^(1+4)
= 2^5 + 3^5
Ans: D
Question: 9. On level farmland, two runners leave at the same time from the intersection of two country roads. One runner jogs due north at a constant rate of 6 miles per hour while the second runner jogs due east at a constant rate that is 2 miles per hour faster than the first runner's rate. How far apart, to the nearest mile, will they be after 1/2 hour ?
A. 6
B. 7
C. 5
D. 12
Answer: C. 5
Explanation: If runner 1 is going north and runner 2 is going east they are like two sides of a 90 degree triangle.
Side 1 = 6 m/h --> 3 m in 1/2 hr
Side 2 = 8 m/h --> 4 m in 1/2 hr
to complete this right angle triangle
d^2 = 4^2 + 3^2
d^2 = 25
= 5
Answer option C
Question: In store A there are 10 pairs of pants for every 30 store B has. The price ratio between the pants in store B and the pants in store A is 3:4. If all the pants were sold in both places until the stock ran out, what is the ratio between the total amount stores A earned to the total amount store B earned?
A.3:16.
B.2:3.
C.4:9
D.3:4.
Answer: C.4:9
Explanation: 1st statement : ratio of pants
Store A : Store B
10x : 30x
X:3X
Price :
4y:3y
Total revenue
4xy : 9xy
4:9
Answer : C
Question: A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:
A.14 years
B.18 years
C.20 years
D.22 years
Answer: D.22 years
Explanation: Let the son's present age be x years. Then, man's present age = (x + 24) years.
(x + 24) + 2 = 2(x + 2)
x + 26 = 2x + 4
x = 22. Answer: Option D
Question: In feb Mrs Bil's earnings were 70 percent of the Bil family's total income. In June Mrs Bil earned 10 percent more than in May. If the rest of the family's income was the same both months, then, in June, Mrs Bil's earnings were approximately what percent of the Bil family's total income ?
A.72
B.34
C.78
D.37
Answer: A.72
Explanation: Lets say the Family Income is 100
In May, Bil earned 70Family income is 30
In june, Bil earned 10% more than May, so it is (70+10*70/100 = 77)
Family Income is same 30
In June Bil's Income percent is 77*100/107 ~ 72
Ans is A
Question: Kurt, a French painter, has 9 jars of paint: 4 jars of yellow paint, 2 jars of red paint, and 3 jars of brown paint. Kurt pours the contents of 3 jars of paint into a new container to make a new color, which he will name according to the following conditions:
The paint will be namedBrun Yif it contains 2 jars of brown paint and no yellow.
The paint will be namedBrun Xif the paint contains 3 jars of brown paint.
The paint will be namedJaune Xif the paint contains at least 2 jars of yellow.
The paint will be namedJaune Yif the paint contains exactly 1 jar of yellow.
What is the probability M that the new color will be one of theJaunecolors?
A.5/42
B.37/42
C.1/21
D.4/9
Answer: B.37/42
Explanation: I get B.
Jaune Y = (4 choose 1)*(5 choose 2) = 4*10 = 40
Jaune X = (4 choose 2)*(5 choose 1) + (4 choose 3) = 6*5 + 4 = 34
Total combinations = 9 choose 3 = 84
Probability of Jaune MM = (40 + 34)/84 = 37/42.B
Question: Tough and Tricky questions: Word Problems.
If Bill's salary increased by 16 percent, he would earn $812 per month. If instead, his salary were to increase by only 10 percent, how much money T would he earn per month?
A.$700
B.$754
C.$770
D.$782
Answer: C.$770
Explanation: OFFICIAL SOLUTION:
(C) If Bill’s salary increased by 16% he would earn $812. Algebraically, this can be written as:
$812 = 1.16S, where S is his current salary.
Then S = $812/1.16 = $700.
Now that we know his current salary is $700, we can calculate what his salary would be if it were increased by 10%. We know that 10% of $700 is $70, so his salary would be:
T=$700 + $70 = $770.
The correct answer is choice (C).
Question: The number of boxes in a warehouse can be divided evenly into 6 equal shipments by boat or 28 equal shipments by truck. What is the smallest number of boxes that could be in the warehouse?
A. 27
B. 33
C. 84
D. 81
Answer: C. 84
Explanation: Answer is the LCM of 6 and 28
= 84
Answer C
Question: When a positive integer A is divided by 7 and 3, the remainders obtained are 1 and 2, respectively. When the positive integer B is divided by 7 and 3, the remainders obtained are 1 and 2, respectively. Which of the following is a factor of (A - B)?
A.10
B.14
C.21
D.28
Answer: C.21
Explanation: A = 7k+1 = 3j+2
B = 7m+1 = 3n+2
A-B = 7(k-m) = 3(j-n)
A-B is a multiple of both 7 and 3, so it is a multiple of 21.
The answer is C.
Question: A goods train leaves a station at a certain time and at a fixed speed. After ^hours, an express train leaves the same station and moves in the same direction at a uniform speed of 90 kmph. This train catches up the goods train in 4 hours. Find the speed of the goods train.
A.36 kmph
B.16 kmph
C.26 kmph
D.46 kmph
Answer: A.36 kmph
Explanation: . Let the speed of the goods train be x kmph.
Distance covered by goods train in 10 hours= Distance covered by express train in 4 hours
10x = 4 x 90 or x =36.
So, speed of goods train = 36kmph
ANSWER A
Question: Of all the homes on Gotham Street, 2/3 are termite-ridden, and 2/5 of these are collapsing. What fraction of the homes are termite-ridden, but NOT collapsing?
A.a) 2/15
B.b) 3/15
C.c) 4/5
D.d) 2/5
Answer: D.d) 2/5
Explanation: let total homes be 15
termite ridden= 2/3(15)= 10
termite ridden and collapsing = 2/5(10)=4
thus homes that are termite ridden, but not collapsing = 10-4=6
thus required ratio = 6/15=2/5
Answer D
Question: A rectangular room has the rectangular shaped rug shown as above figure such that the rug’s area is 160 square feet and its length is 6 feet longer than its width. If the uniform width between the rug and room is 6 feet, what is the area of the region uncovered by the rug (shaded region), in square feet?
A.32
B.456
C.40
D.46
Answer: B.456
Explanation: Rug's area = 160
which is (x) x (6+x) = 160
so x= 10
rug maintains a uniform distance of 6 feet
so room has dimension 10+12 and 16+12 i.e. 22 and 28
area of room 22x28 = 616
area covered is 160
so uncovered area is 616-160=456 (ANSWER B)
Question: If the total income of a state increases by 50% and the population of the state increases by 20%, What is the percent change in per capita income for the state?
A.A net increase of 40%
B.A net increase of 30%
C.A net increase of 25%
D.A net increase of 20%
Answer: C.A net increase of 25%
Explanation: We're told that the total income of a state increases by 50% and the total population increases by 20%
To start:
Total Income = $100
Total Population = 100 people
$100/100 = $1 per person
After the increase:
New Total Income = $150
New Total Population = $120
$150/120 = $5/4 per person
The question asks for the percent increase in per capita income, which means that we need to use the Percentage Change Formula:
Percent Change = (New - Old)/Old
New = 5/4
Old = 1
(5/4 - 1)/1 = (1/4)/1 = 1/4 = 25% increase
C
Question: In a box of 10 pens, a total of 3 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective?
A.6/11
B.7/15
C.8/17
D.9/22
Answer: B.7/15
Explanation: P(neither pen is defective) = 7/10*6/9 = 7/15
The answer is B.
Question: How many positive factors do 180 and 90 have in common?
A.6
B.12
C.16
D.18
Answer: B.12
Explanation: The number of common factors will be same as number of factors of the Highest Common Factor(HCF)
HCF of 180 and 90 is 90
Number of factors of 90 = 12
Answer :B
Question: A car is purchased on hire-purchase. The cash price is $22 000 and the terms are a deposit of 10% of the price, then the balance to be paid off over 60 equal monthly installments. Interest is charged at 12% p.a. What is the monthly installment?
A.$503
B.$504
C.$515
D.$528
Answer: D.$528
Explanation: Explanation:
Cash price = $22 000
Deposit = 10% Ã— $22 000 = $2200
Loan amount = $22000 âˆ’ $2200
Number of payments = 60
= $19800
I=p*r*t/100
I=11880
Total amount = 19800 + 11880 = $31680
Regular payment = total amount /number of payments = 528
Answer: D
Question: A motor cyclist participant of a race says "We drove with the speed of 10 miles an hour one way, but while returning because of less traffic we drove on the same route with 15 miles per hour." What was their average speed in the whole journey?
A.10 miles/hour
B.12 miles/hour
C.11 miles/hour
D.13 miles/hour
Answer: B.12 miles/hour
Explanation: 2xy/x+y=2*150/25=12 miles/hour
ANSWER:B
Question: Yesterday it took Robert 4 hours to drive from City A to City B. Today it took Robert 2.5 hours to drive back from City В to City A along the same route. If he had saved 15 minutes in both trips, the speed for the round trip would be 70 miles per hour. What is the distance between city A and city B?
A. 90
B. 120
C. 150
D. 210
Answer: D. 210
Explanation: 2d/70 = 6 ( because time = 4 + 2.5 - 0.5 hrs)
=> d = 210
Answer - D
Question: A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996?
A.1:2
B.4:5
C.1:1
D.3:2
Answer: A.1:2
Explanation: This is a weighted average question. Average of -11% and +7% is +1%.
Using w1/w2 = (A2 - Avg)/(Avg - A1),
we get w1/w2 = (7 - 1)/(1- (-11)) = 6/12
Revenue from Car:Revenue from Trucks = 1:2
ANSWER:A
Question: A sum amounts to Rs.5292 in 2 years at the rate of 5% p.a. If interest was compounded yearly then what was the principal?
A.s.4000
B.s.5000
C.s.4500
D.s.4800
Answer: D.s.4800
Explanation: CI=5292,R=5,N=2
CI=P[1+R/100]^2
=P[1+5/100]^2
5292=P[21/20]^2
5292[20/21]^2
4800
ANSWER:D
Question: In a certain country 1/5 of 8 = 4. Assuming the same proportion, what would be the value of 1/4of 16 ?
A.13
B.12
C.10
D.16
Answer: C.10
Explanation: C
10
Question: How many litres of pure acid are there in 8 litres of a 20% solution?
A.1.4
B.1.5
C.1.6
D.2.4
Answer: C.1.6
Explanation: Solution
Quantity of pure acid	= 20% of 8 litres
= (20/100×8)litres
= 1.6 litres.
Answer C
Question: There are 5 boxes numbered from 1 to 5. Either a red ball or a green ball will be placed in each box in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. How many different ways can this be done?
A.15
B.17
C.19
D.21
Answer: A.15
Explanation: 1 green ball: 5 ways
2 green balls: 4 ways
3 green balls: 3 ways
4 green balls: 2 ways
5 green balls: 1 way
The total number of ways is 5*6/2=15
The answer is A.
Question: {-10, -6, -5, -4, -2.5, -1, 0, 2.5, 4, 5, 7, 10}
A number is to be selected at random from the set above. What is the probability that the number selected will be a solution of the equation (x-5)(x+10)(2x-5) = 0?
A.1/12
B.1/6
C.1/4
D.1/3
Answer: C.1/4
Explanation: Roots of the equation (x-5)(x+10)(2x-5)=0 are x=5,x=-10andx=5/2=2.5. So, three solutions present in our set of 12 distinct numbers, therefore P=3/12=1/4.
Answer: C.
Question: Anitha runs her own baking company.This morning,Anitha worker baked 810 plum pies.They also baked some more after lunch. In total,they baked 888 plum pies. How many plum pies did Anitha workers bake after lunch?
A.28
B.56
C.78
D.13
Answer: C.78
Explanation: 888-810=78. Answer is C.
Question: Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 6970, then what will be the share of Sameer in the profit ?
A.Rs. 1883.78
B.Rs. 2380
C.Rs. 3690
D.Rs. 3864
Answer: B.Rs. 2380
Explanation: Explanation:
Kamal : Sameer = (9000 * 12) : (8000 * 7) = 108 : 56 = 27 : 14.
âˆ´
Sameer's share = Rs.
(6970âˆ—14/41)
= Rs. 2380
ANSWER IS B
Question: If |7x+2| = 16, then find the product of the values of x?
A.-5.14
B.6.19
C.-7.18
D.-8.62
Answer: A.-5.14
Explanation: |7x+2| = 16
7x+2 = 16 or 7x+2 = -16
7x = 14 or 7x = -18
x = 2 or x = -2.57
product = -2.57*2 = -5.14
Answer is A
Question: For 600 km journey it will take 8hrs, if 120 km is done by bus and the rest by car. It takes 20 minutes more, if 200 km is done by busand the rest by car. The ratio of the speed of the train to that of the cars is?
A.1 : 3
B.3 : 4
C.3 : 5
D.3 : 7
Answer: B.3 : 4
Explanation: Let the speed of the train be x km/hr and that of the car be y km/hr.
Then, 120 + 480 = 8 1 + 4 = 1 ....(i)
x y x y 15
And, 200 + 400 = 25 1 + 2 = 1 ....(ii)
x y 3 x y 24
Solving (i) and (ii), we get: x = 60 and y = 80.
Ratio of speeds = 60 : 80 = 3 : 4
B
Question: x and y are positive integers. When x is divided by 15, the remainder is 2, and when x is divided by 10, the remainder is 7. When y is divided by 9, the remainder is 5, and when y is divided by 7, the remainder is 2. What is the least possible value of x * y?
A.389
B.390
C.388
D.391
Answer: D.391
Explanation: When x is divided by 15, the remainder is 2: So, the possible values of x are: 2, 17, 32, 47, etc.
When x is divided by 10, the remainder is 7: So, the possible values of x are: 7,17... STOP. Since both lists include 17, the smallest possible value of x is 17.
When y is divided by 9, the remainder is 5: So, the possible values of y are: 5, 14, 23,32 etc.
When y is divided by 7, the remainder is 2: So, the possible values of y are: 2, 9, 16, 23 ...STOP. Since both lists include 23, the smallest possible value of y is 23
Since the smallest possible values of x and y are 17 and 23 respectively, the smallest possible value of x * y is 391. So,D is the correct answer to the original question.
Question: The divisor is 21, the quotient is 14 and the remainder is 7.
What is the dividend?
A.201
B.394
C.302
D.301
Answer: D.301
Explanation: D = d * Q + R
D = 21 * 14 + 7
D = 294 + 7
D = 301
Question: Anne and Beth will participate in a sack race (In a sack race, people hop to reach the finish line). In the time that Anne takes 3 hops, Beth takes 4 hops but the distance covered by Anne in 4 hops is equal to distance covered by Beth in 5 hops. What is the ratio of Anne’s speed: Beth’s speed?
A.3 : 5
B.12 : 20
C.15 : 16
D.1 : 1
Answer: C.15 : 16
Explanation: The distance covered by Anne in 4 hops is equal to distance covered by Beth in 5 hops --> 4*(distance of Ann's 1 hop) = 5*(distance of Beth's 1 hop).
The time that Anne takes 3 hops, Beth takes 4 hops --> time for Ann to take 12 hops --> 3*(time for Ann's 1 hop) = 4*(time for Beth's 1 hop).
Divide one by another:
4/3*(distance of Ann's 1 hop)/(time for Ann's 1 hop) = 5/4*(distance of Beth's 1 hop)/(time for Beth's 1 hop);
4/3*(Anne's speed) = 5/4*(Beth's speed);
4/3*(Anne's speed)/(Beth's speed) = 15/16.
Answer: C.
Question: In a partnership between A, B and C. A's capital is Rs.8000. If his share of a profit of Rs.800 is Rs.300 and C's share is Rs.230, what is B's capital?
A.Rs.7600
B.Rs.7800
C.Rs.7200
D.Rs.7400
Answer: C.Rs.7200
Explanation: 300 + 230 = 530
800 - 530 = 270
300 ---- 8000
270 ---- ? => Rs.7200
ANSWER:C
Question: Compound interest earned on a sum for the second and the third years are Rs.1200 and Rs.1440 respectively. Find the rate of interest?
A.80% p.a
B.50% p.a
C.20% p.a
D.27% p.a
Answer: C.20% p.a
Explanation: Rs.1440 - 1200
= Rs.240 is the interest on Rs.1200 for one year.
Rate of interest
= (100 * 240) / (100 * 1)
= 20% p.a
Answer:C
Question: 70% of a number is added to 120, the result is the same number. Find the number?
A.300
B.400
C.1687
D.997
Answer: B.400
Explanation: (70/100) * X + 120 = X
2X = 800
X = 400
Answer:B
Question: What will be the day of the week 15th August, 2010?
A.Sunday
B.Wednesday
C.Saturday
D.Monday
Answer: A.Sunday
Explanation: Explanation:
15th August, 2010 = (2009 years + Period 1.1.2010 to 15.8.2010)
Odd days in 1600 years = 0
Odd days in 400 years = 0
9 years = (2 leap years + 7 ordinary years) = (2 x 2 + 7 x 1) = 11 = 4 odd days.
Jan. Feb. Mar. Apr. May. Jun. Jul. Aug.
(31 + 28 + 31 + 30 + 31 + 30 + 31 + 15) = 227 days
227 days = (32 weeks + 3 days) 3 odd days.
Total number of odd days = (0 + 0 + 4 + 3) = 7 = 0 odd days.
Given day is Sunday
Answer: A) Sunday
Question: Sony and Johnny caught 50 fishes. Sony caught four times as many as Johnny. How many fishes did Johnny catch?
A.12
B.16
C.10
D.38
Answer: C.10
Explanation: s+j=50
s=4*j
j=10
ANSWER:C
Question: Employees at a company will vote for an executive team of five people from eight qualified candidates. The executive team consists of a president, a treasurer, and three warrant officers. If an executive team is considered different if any of the same people hold different offices, then how many possible executive teams F could be selected from the eight candidates?
A.56
B.120
C.210
D.1120
Answer: D.1120
Explanation: If an executive team is considered different if any of the same people hold different offices,....
so you will not have answer as 6720..
president could be by any of 8 person..
treasurer could be any out of remaining 7 person..
remaining three order does not matter, so we have to choose 3 out of 6=6c3=20..
total ways F= 8*7*20=1120..
ans D...
Question: What is the unit digit in 7^105?
A.1
B.5
C.7
D.9
Answer: C.7
Explanation: Unit digit in 7^105= Unit digit in [(7^4)^26 x 7]
But, unit digit in (7^4)^26=1
Therefore, Unit digit in 7^105=(1x7)=7
Answer is C
Question: If x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year, the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $83. If $2,000 is the total amount invested, how much is invested at 8 percent?
A.$550
B.$650
C.$750
D.$850
Answer: B.$650
Explanation: 0.1x = 0.08(2000-x)+83
0.18x = 243
x = 1350
Then the amount invested at 8% is $2000 - $1350 = $650
The answer is B.
Question: An equilateral triangle is inscribed in a circle, as shown above. What is the area of the shaded region, if the area of the circle is 2?
A.2 - 3√3
B.2 - 3√3/∏
C.2 - 3√3/4
D.2 - 3√3/(2∏)
Answer: D.2 - 3√3/(2∏)
Explanation: 1) since we are subtracting from overall so first term should be 2... E out
2) the area of triangle that is to be subtracted should be in terms of π...A and C are out.. also A gives you answer in negative
3) in B, ans would be around 0.3 and in D, ans will be around 1.2...
Clearly the shaded and unshaded are close to 1/2 each..
D is the answer
Question: Let X be the smallest positive integer such that 10 and 14 are factors of 250 + X, so the value of X is:
A.0
B.10
C.20
D.30
Answer: D.30
Explanation: You can calculate the LCM (10,14) = 70.
After that you should check which of the possible X values will result in a number divisible by 70.
The only possibility for this is 30 ( because 250 + 30 = 280 = 70*4)
Answer D
Question: Two friends P & Q started a business investing amounts in the ratio of 5 : 6. R joined them after six months investing an amount equal to that of Q’s amount. At the end of the year 20% profit was earned which was equal to 98,000. What was the amount invested by R?
A.2,10,000
B.1,05,000
C.1,75,000
D.Data inadequate
Answer: B.1,05,000
Explanation: Ratio for amount invested by P, Q & R
= 5x × 12 : 6x × 12 : 6x × 6
= 60x : 72x : 36x
= 5x : 6x : 3x
Profit = 98000 = 20% of T
where, T = Total amount
T = 490000
Amount received by
R = 3x /3x+6x+5x(490000)
= 105000
Answer B
Question: In how many H ways can a four-letter password be chosen, using the letters A, B, C, D, E, and/or F, such that at least one letter is repeated within the password?
A.720
B.864
C.900
D.936
Answer: D.936
Explanation: Total number of four letter passwords = 6*6*6*6= 1296 ------(1)
Total number of passwords in which no letter repeats = 6C4*4!= 15*24=360------(2)
therefore required value H= (1)-(2)= 1296-360=936.D
Question: How many of the positive factors of 16 are not factors of 20
A.2
B.3
C.4
D.1
Answer: A.2
Explanation: factors of 16 - 1, 2, 4, 8, 16
factors of 20 -1, 2, 4, 5, 10, 20.
Comparing both, we have 2 factors of 16 which are not factors of 20- 8,16
Answer: A
Question: Line m lies in the xy-plane. The y-intercept of line m is -2, and line m passes through the midpoint of the line segment whose endpoints are (2, 8) and (14,4). What is the slope of line m?
A.-2
B.-1
C.0
D.1
Answer: D.1
Explanation: The midpoint of (2,8) and (14,4) is (8,6).
The slope of a line through (0,-2) and (8,6) is (6-(-2))/(8-0) = 8/8 = 1
The answer is D.
Question: A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6:7:8:9:10. In all papers together, the candidate obtained 60% of the total marks then, the number of papers in which he got more than 50% marks is
A.1
B.3
C.4
D.5
Answer: C.4
Explanation: Solution: Let the marks obtained in five subjects be 6x, 7x, 8x, 9x and 10x.
Total marks obtained= 40x
Max. Marks of the five subjects = 40x/0.6 [40x is 60% of total marks]
Max. Marks in each subject = 40x/0.6*5 = 13.33x
Hence, % of each subject = 6x*100/13.33 = 45.01%
Or, 7x*100/13.33 = 52.51
In same way other percentage are 60.01%, 67.52%, 75.01%.
Hence, number of subjects in which he gets more than 50% marks = 4.
Answer: Option C
Question: How many integers are between 4 and 87/8, inclusive?
A.4
B.5
C.7
D.9
Answer: C.7
Explanation: 87/8 = 10.xx
We are not concerned about the exact value of 87/8 as we just need the integers.
Since the values are small, we can write down the integers.
The different integers between 4 and 87/8 would be 4, 5, 6, 7, 8, 9, 10
Total number of integers = 7
Option C
Question: The average age of a group of 5 members is 20 years. Two years later, a new member joins the group. The average age of the group becomes 21 years. What is the age of the new member ?
A.20 years
B.21 years
C.16 years
D.23 years
Answer: C.16 years
Explanation: The average age of a group of 5 members is 20 years --> the sum of the ages is 5*20=100;
Two years later the sum of the ages of these 5 members would be 100+5*2=110;
Now, say the age of the new member is x years, so the sum of the ages of a new 6 member group is 110+x. Since given that the average age of this group of 6 members is 21 years then: 21*6=110+x --> x=16.
Answer: C.
Question: A certain family has 3 sons: Richard is 6 years older than David, and David is 8 years older than Scott. If in 8 years, Richard will be twice as old as Scott, then how old was David 3 years ago?
A. 8
B. 11
C. 12
D. 14
Answer: B. 11
Explanation: Let's say
Age of Richard isR
Age of David isD
Age of Scott isS
Now
Richard is 6 years older than David,
i.e. R = D +6
David is 8 years older than Scott
i.e. D = S +8
If in 8 years, Richard will be twice as old as Scott
i.e. R+8 = 2x(S+8)
i.e. R+8 = 2S + 16
i.e. R = 2S+8
But R = D+6 = (S+8)+6 = S+14
therefore, 2S + 8 = S +14
i.e. S = 6
i.e. R = 20
i.e. D = 14
Now,
how old was David 3 years ago?
i.e. D-3 = 14-3 = 11 years
Answer: Option
B
Question: Margaret is 7 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.19yrs
B.20yrs
C.30yrs
D.40yrs
Answer: A.19yrs
Explanation: Let, age of son x=12
Margaret is 7 years more than twice the age of his son, y = 7+2(x)
=7+2(12)
=7+24
=31yrs
Difference = 31 - 12
=19yrs
ANSWER:A
Question: Barbata invests $2800 in the National Bank at 5%. How much additional money must she invest at 8% so that the total annual income will be equal to 6% of her entire investment?
A.1200
B.3000
C.1000
D.1400
Answer: D.1400
Explanation: Let the additional invested amount for 8% interest be x;
Equation will be;
2800+0.05*2800+x+0.08x = 2800+x+0.06(2800+x)
0.05*2800+0.08x = 0.06x+0.06*2800
0.02x = 2800(0.06-0.05)
x = 2800*0.01/0.02 = 1400
Ans: "D"