RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Pat will walk from intersection A to intersection B along a route that is confined to the square grid of four streets and three avenues shown in the map above. How many routes from A to B can Pat take that have the minimum possible length?
A.6
B.8
C.10
D.14
Answer: C.10
Explanation: Consider this a as coordinate plane with A as origin and B as (2,3).
The shortest possible way is when you go take either right or up. (lefts and downs make repetitions and thus non shortest paths)
now, to get to (2,3) form (0,0) you need min 5 steps.
so you have to choose all the paths such that you have 2 steps out of 5 along x axis and getting to 3 of y axis.
The number of ways = 5C2 =10
(or alternately all paths that have 3 steps along y and takes you to 2 of x. .. 5C3 = 10)
Can you explicate your combinatorial method a bit more. For example, If I add another Avenue, eg, Avenue D, and another street, Street 5, I will have to go 3 steps right and 4 steps up to get to point C.
In order the length to be minimum Pat should only go UP and RIGHT: namely thrice UP and twice RIGHT.
So combination of UUURR: # of permutations of 5 letters out of which there are 3 identical U's and 2 identical R's is 5!/3!2!=10.
Answer: C.
Question: A person can row upstream 2 kmph and downstream 8 kmph. Find the rate of the stream and person rate in still water.
A.1,5
B.2,5
C.5,5
D.3,5
Answer: D.3,5
Explanation: Explanation:
Please remember,
If a is rate downstream and b is rate upstream
Rate of current = 1/2(a-b)
Rate in still water = 1/2(a+b)
=> Rate of current = 1/2(8-2) = 3 kmph
=> Rate in still water = 1/2(8+2) = 5 kmph
Option D
Question: In a certain game, each player scores either 2 or 5 points. If n players score 2 points and m players score 5 points and the total number of points scored is 55, what is the least possible difference between n and m.
A.a.1
B.b.3
C.c.4
D.d.7
Answer: C.c.4
Explanation: 2n+5m=55
try with n=5 and m=8 the equation will be satisfied
2(5)+5(9)=55
so difference between M and N is 4,
Answer C
Question: Hendrix works 20 days a month at d dollars per day for m months out of the year. Which of the following represents his 5 year pay?
A.m/(20d*5)
B.100md
C.50md/6
D.20d/5m
Answer: B.100md
Explanation: Total income of Amber in a year = d*20*m dollars. Now 5 year income = Total*5= d*20*m *5 = 100md Answer is B
Question: On January 1, 2010, Dave invests 70% of his retirement savings in Antarctic largecap stocks, 20% in Antarctic midcaps, and 10% in Antarctic smallcaps. In 2010, largecaps rise 5%, midcaps rise 10%, and smallcaps rise 15% in the Antarctic stock market; however, in 2011, largecaps fall 10% and midcaps fall 20%, while smallcaps rise x% in Antarctica. If, on January 1, 2012, Dave has the same total amount of retirement savings as he did two years before, then x is between
A.10 and 20
B.20 and 30
C.30 and 40
D.40 and 50
Answer: D.40 and 50
Explanation: Here are the starting values:
L = $7,000
M = $2,000
S = $1,000
Apply the first year’s changes, so that you have these numbers on 1/1/2011:
Newer L = $7,000 + 5% = $7,350
Newer M = $2,000 + 10% = $2,200
Newer S = $1,000 + 15% = $1,150
Now apply the second year’s changes to L and M:
Newest L = $7,350 – 10% = $7,350 – $735 = $6,615
Newest M = $2,200 – 20% = $2,200 – $440 = $1,760
Add these to get $8,375. So the newest S must be $10,000 (the target final total of Dave’s retirement savings) minus $8,375, or $1,625.
The dollar change in S from 1/1/11 to 1/1/12 is $1,625 – $1,150 = $475. So the question is this: what percent change does $475 represent, from a starting point of $1,150? Since $1,150 is a nasty divisor, switch to benchmarks:
10% of $1,150 = $115.
So 20% is just double that, or $230.
And 40% is double that, or $460.
Since $475 is just slightly larger than $460 (but not enough to get you to 50%, which would be $460 + $115), x must be between 40 and 50.
Intuitively, it should make sense that you’d need a much bigger positive percent change in the smallest investment (S) to make up for even a moderate downturn in the larger investments (L and M), so if you were completely stuck for time and needed to guess in a hurry, you should favor C/D/E over A or B.
The correct answer is D.
Question: A plane was originally flying at an altitude of x feet when it ascended 2,000 feet and then descended 5,000 feet. If the plane's altitude after these two changes was 1/2 its original altitude, then the solution of which of the following equations gives the plane's original altitude, in feet ?
A.x + 2000 = 1/3*(x - 3000)
B.1/3*(x - 3000) = x
C.x - 3000 = 1/2*x
D.x - 7000 = 1/3*x
Answer: C.x - 3000 = 1/2*x
Explanation: Plane's original altitude = x
Plane's new altitude after ascending 2000 ft = x+2000
Plane's new altitude after descending 5000 ft from previous altitude = x+2000-5000 = x-3000
So, after two changes plane is at 1/2 its original altitude => x-3000 = x/2
Answer (C)
Question: If a light flashes every 6 seconds, how many times will it flash in 2/5 of an hour?
A.181
B.211
C.241
D.271
Answer: C.241
Explanation: In 2/5 of an hour there are 24*60 = 1440 seconds
The number of 6-second intervals = 1440/6 = 240
After the first flash, there will be 240 more flashes for a total of 241.
The answer is C.
Question: Find a if (ax3 + 3x2 - 3) and (2x3 - 5x + a) when divided by (x-4) leave same rmainder?
A.1
B.3
C.4
D.5
Answer: A.1
Explanation: remainders are,
R1 = f(4) = a(4)3+ 3(4)2-3= 64a+45
R2 = f(4) = 2(4)3- 5(4) + a= a +108
Since R1= R2
64a +45= a+108 => 63a = 63 => a =1
A
Question: Find the percentage gain if a shop owner sells 18 mtr of fabric and gains Cost Price of 3 meters?
A.17.67%
B.19.67%
C.11.67%
D.16.67%
Answer: D.16.67%
Explanation: Let cost of each metre be Rs. 100.
Therefore, cost price of 3m cloth = 3*100 =300
cost price of 18m cloth = 18*100 = 1800
Since the trader made the CP of 3m from the sale of 18m therefore
Profit on sale of 18m = cost price of 3 m cloth = 300
Selling price of 18m = 1800+300 = 2100
Profit % = 16.67%
D
Question: By selling a book for 260, 20% profit was earned. What is the cost price of the book?
A.A)215
B.B)216
C.C)230
D.D)235
Answer: B.B)216
Explanation: SP = 120% of CP; :. CP = 260 × 100/120 = 216
Option 'B'
Question: Find the third proportional to 3 and 9?
A.10
B.12
C.27
D.19
Answer: C.27
Explanation: Formula = Third proportional = (b × b)/a
A = 3 and B = 9
(9 x 9)/ 3 = 81/3 = 27
C
Question: A die is rolled twice. What is the probability of getting a sum equal to 9?
A.2/3
B.2/9
C.1/3
D.1/9
Answer: D.1/9
Explanation: Total number of outcomes possible when a die is rolled = 6 (âˆµ any one face out of the 6 faces)
Hence, total number of outcomes possible when a die is rolled twice, n(S) = 6 Ã— 6 = 36
E = Getting a sum of 9 when the two dice fall = {(3, 6), {4, 5}, {5, 4}, (6, 3)}
Hence, n(E) = 4
P(E) = n(E)/n(S)=4/36=1/9
Answer:D
Question: In the third quarter of 2015, Atlantis Law Firm had 20 lawyers and 400 cases. In the fourth quarter of 2015, the firm had 22 lawyers and 500 cases. By approximately what percent did the ratio of lawyers to cases decrease from the third quarter to the fourth quarter.
A.10.0%
B.11.0%
C.12.0%
D.13.0%
Answer: C.12.0%
Explanation: 3rd quarter: lawyers/cases = 20/400 =100/2000
4th quarter: lawyers/cases = 22/500 =88/2000
ASIDE: It's useful to write both ratios with the same denominator. This allows us to IGNORE the denominator and focus solely on the numerators.
So, our ratio went from 100/2000 to 88/2000
Ignoring the denominators, we went from 100 to 88
The percent change = 100(difference in values)/(original value)
= (100)(100-88)/100
= (100)(12)/100)
=12.0
Answer: C
Question: q, b, and c are positive integers. If q, b, and c are assembled into the six-digit number qbcqbc, which one of the following must be a factor of qbcqbc?
A. 16
B. 13
C. 5
D. 3
Answer: B. 13
Explanation: Plug in some values and check -
qbcqbc = 123123
Not divisible by 16 and 5
let qbcqbc = 125125
Not divisible by 3
Only option (B) and (E) is left in both the cases...
Check once more to marke (B) as correct answer
let qbcqbc = 135135
Again divisible by 13
So, mark answer as (B) 13
Question: In the xy-plane, the point (1, 3) is the center of a circle. The point (-2, 3) lies inside the circle and the point (1, -2) lies outside the circle. If the radius r of the circle is an integer, then r =
A.6
B.5
C.4
D.3
Answer: C.4
Explanation: An easy way to solve this question will be just to mark the points on the coordinate plane.
You'll see that the distance between the center (1, 3) and the point inside the circle (-2, 3) is 3 units
(both points are on y=3 line so the distance will simply be 1-(-2)=3)
So the radius must be more than 3 units.
The distance between the center (1,3) and the point outside the circle (1,-2) is 5 units
(both points are on x=1 line so the distance will simply be 3-(-2)=5)
So the radius must be less than 5 units, which implies 3 < r < 5, thus as r is an integer then r=4.
Answer: C.
Question: A does half as much work as Band C does half as much work as A and B together. If C alone can finish the work in 60 days, then together ,all will finish the work in :
A.13 1/3 days
B.12 1/3 days
C.15 days
D.20 days
Answer: C.15 days
Explanation: C alone can finish the work in 60 days.
(A + B)can do it in 20 days
(A + B)s 1 days wok = 1/20.
As 1 days work : Bs 1 days Work = 1/2 : 1 = 1:2.
Aâ€™s 1 dayâ€™s work = (1/20) * (1/3) = (1/60). [Divide 1/20 in the raio 1:2] Bs 1 days work = (1/20) * (2/3) = 1/30
(A+B+c)S 1 dayâ€™s work = (1/60) + (1/30) + (1/60) = 1/15
All the three together will finish it in 15 days.
ANSWER:C
Question: If A = {1, 3, 5}, B = {3, 5, 6}.Find A ∪ B
A.{1,5}
B.{1,3,5,6}
C.{2,6}
D.{8,9}
Answer: B.{1,3,5,6}
Explanation: A= {1,3,5}
B= {3,5,6} Therefore ,
correct answer :A ∪ B = {1, 3, 5, 6}
B
Question: What is the relationship between the fractions 14/15 and 37/40.
A.14/15 = 37/40
B.14/15 < 37/40
C.14/15 > 37/40
D.cannot bedetermined
Answer: C.14/15 > 37/40
Explanation: Take LCM of both 15, 40 we get 120
(14*8)/(15*8) = 112/120
(37*3)/(40*3) = 111/120
So 14/15>37/40
ANSWER:C
Question: A man can row downstream at 18 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?
A.14, 5
B.14, 9
C.14, 6
D.14, 4
Answer: D.14, 4
Explanation: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 18 --- (1)
and x - y = 10 --- (2)
From (1) & (2) 2x = 28 => x = 14, y = 4.
Answer: D
Question: The current in a river is 10 mph. A boat can travel 50 mph in still water. How far up the river can the boat travel if the round trip is to take 5 hours?
A.120
B.100
C.96
D.85
Answer: A.120
Explanation: Upstream Speed = 50-10=40 mph
Downstream Speed = 50+10 = 60 mph
D/40 + D/60 = 5 hours
Solving for D we get D=120
Answer: A
Question: At 1:00, Annie starts to bicycle along a 45 mile road at a constant speed of 14 miles per hour. Thirty minutes earlier, Scott started bicycling towards Annie on the same road at a constant speed of 12 miles per hour. At what time will they meet?
A.2:00
B.2:30
C.3:00
D.3:30
Answer: B.2:30
Explanation: In the first 30 minutes, Scott can travel 6 miles, so there are 39 miles left.
Together Annie and Scott can complete 26 miles.
39/26 = 1.5, so they will meet 1.5 hours after 1:00.
The answer is B.
Question: Ten cards numbered 1 to 10 are placed in a box and then one card is drawn randomly. If it is known that the number on the drawn card is more than 5, what is the probability that it is an even number?
A.1/2
B.2/5
C.3/5
D.2/7
Answer: C.3/5
Explanation: There are 5 numbers higher than 5 and 3 of them are even.
The probability is 3/5.
The answer is C.
Question: In how many different ways can the letters of the word 'AIRPORT' be arranged in such a way that the vowels always come together?
A.A)360
B.B)720
C.C)480
D.D)5040
Answer: B.B)720
Explanation: The word 'AIRPORT' has 7 different letters.
When the vowels AIO are always together, they can be supposed to form one letter.
Then, we have to arrange the letters RPRT (AIO).
Now, 5 (4 + 1 = 5) letters can be arranged in 5! = 120 ways.
The vowels (AIO) can be arranged among themselves in 3! = 6 ways.
Required number of ways = (120 x 6) = 720.
ANSWER:B
Question: If 5 women or 8 girls can do a work in 84 days.In how many days can 10 women and 5 girls can do the same work?
A.32
B.33
C.34
D.35
Answer: A.32
Explanation: Given that 5 women is equal to 8 girls to complete work/
So,10 women=16 girls.
10 women+5 girls=16 girls+5 girls=21 girls.
8 girls can do a work in 84 days then 21 girls can do a work in (8*84)/21=32 days
Therefore 10 women and 5 girls can a work in 32 days.
Answer is option A
Question: What number is obtained by adding the units digits of 734^100 and 347^83?
A.7
B.8
C.9
D.10
Answer: C.9
Explanation: The units digit of 734^100 is 6 because 4 raised to the power of an even integer ends in 6.
The units digit of 347^83 is 3 because powers of 7 end in 7, 9, 3, or 1 cyclically. Since 83 is in the form 4n+3, the units digit is 3.
Then 6+3 = 9.
The answer is C.
Question: A shopkeeper give 12% additional discount on the discounted price, after giving an initial discount of 20% on the labelled price of a radio. If the final sale price of the radio is Rs.704, then what is its labelled price?
A.Rs.844.80
B.Rs.929.28
C.Rs.1000
D.Rs.1044.80
Answer: C.Rs.1000
Explanation: Solution
Let the labelled price be Rs.x.
88% of 80% of x	= 704
x=(704x100x100 /88x80)
= 1000.
Answer C
Question: Find the compound interest and the amount on Rs.8000 at 5% per annum for 3 years when C.I is reckoned yearly?
A.1261
B.1572
C.1689
D.1687
Answer: A.1261
Explanation: A = 8000(21/20)3
= 9261
= 8000
---------
1261
Answer: A
Question: W and X started a business investing Rs. 30,000 and Rs. 6,000 respectively. Out of a total profit of Rs. 18,000, W’s share is :
A.14000
B.15000
C.16000
D.17000
Answer: B.15000
Explanation: Ratio of their shares = 30000 : 6000 = 5 : 1.
W’s share = Rs. 18000 * 5/6
= Rs. 15000
ANSWER:B
Question: What is the smallest number which when increased by 3 is divisible by 9, 35, 25 and 21?
A.1572
B.1782
C.1992
D.2122
Answer: A.1572
Explanation: When increased by 3, the number must include at least 3^2*5^2*7 = 1575
The answer is A.
Question: 4 dice are thrown simultaneously on the board. Find the probability which show the same face?
A.2/113
B.3/117
C.1/216
D.3/111
Answer: C.1/216
Explanation: The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:
=6×6×6×6=64=6×6×6×6=64
n(S)=64n(S)=64
Let XX be the event that all dice show the same face.
X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}
n(X)=6n(X)=6
Hence required probability,
=n(X)n(S)=664=n(X)n(S)=664
=1/216
C
Question: I sold a book at a profit of 12%. Had I sold it for $18 more, 18% would have been gained. Find the cost price?
A.$100
B.$250
C.$300
D.$200
Answer: C.$300
Explanation: 118% of cost - 112% of cost = $18
6% of cost = $18
cost = 18*100/6 = $300
Answer is C
Question: Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
A.17.9 sec
B.11.8 sec
C.27.7 sec
D.10.8 sec
Answer: D.10.8 sec
Explanation: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 140 + 160 = 300 m.
Required time = 300 * 9/250 = 54/5 = 10.8 sec.
Answer: D
Question: In a group of 100 cars, 37 cars do not have air conditioning. If at least 51 cars have racing stripes, what is the greatest number of cars that could have air conditioning but not racing stripes?
A.45
B.47
C.48
D.49
Answer: D.49
Explanation: Lets assume AC=63(includesonly AC carsandcars with AC and racing stripes)
lets assume RS(racing stripes)>=51(includescars with AC and racing stripesandonly racing stripes).
Now since we want to maximize(only AC) we have to see to it thatcars with AC and racing stripesis minimal(assume 0) But since RS>=51.. we have to assign atleast 14 tocars with AC and racing stripes.
Hence AC=63-14=49.
The answer is D
Question: If x < 0 and 0 < y < 1, which of the following has the greatest value H?
A.x^2
B.(xy)^2
C.(x/y)^2
D.x^2/y
Answer: C.(x/y)^2
Explanation: Given, x < 0 and 0 < y < 1
Let, x = -2 and y = 1/2
A. x^2 = (-2)^2 =4
B. (xy)^2 = (-2*1/2)^2 =1
C. (x/y)^2 = {-2/(1/2)}^2 = (-4)^2 =16
D. x^2/y = (-2)^2 / (1/2) = 4*2 =8
E. x^2*y = (-2)^2*(1/2) =2
Answer: option C
Question: If P's height is 40% less than that of Q, how much percent Q's height is more than that of P?
A.66.66
B.86.88
C.70.05
D.76.66
Answer: A.66.66
Explanation: Q'S height over P's = ((40/(100-40)) * 100
= 66.66%
ANSWER A
Question: The average salary of the employees in a office is Rs.120/month.The avg salary of officers is Rs.420 and of non officers is Rs 110. If the no.of officers is 15,then find the No of nonofficers in the office.
A.400
B.420
C.430
D.450
Answer: D.450
Explanation: Let no. of non- officers be x
15 * 420 + x * 110 = (x + 15) 120
x = 450
D
Question: The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 40 are excluded, the average mark of the remaining will be 90. Find the number of students who wrote the exam.
A.78
B.77
C.25
D.77
Answer: C.25
Explanation: Let the number of students who wrote the exam be x.
Total marks of students = 80 x.
Total marks of (x - 5) students = 90(x - 5)
80x - (5 * 40) = 90(x - 5)
250 = 10x => x = 25
Answer:C
Question: The age of father 8 years ago was thrice the age of his son. Five years hence, father's age will be twice that of his son. The ratio of their present ages is:
A.47 : 11
B.37 : 21
C.27 : 21
D.47 : 21
Answer: D.47 : 21
Explanation: Let the ages of father and son 8 years ago be 3x and x years respectively.
Then, (3x + 8) + 5 = 2[(x + 8) + 5]
3x + 13 = 2x + 26
x = 13.
Required ratio = (3x + 8) : (x + 8) = 47 : 21.
Answer: Option D
Question: How many even integers n, such that 20<=n<=200 are of the form 3k+4, where k is any natural number?
A.26
B.30
C.34
D.38
Answer: B.30
Explanation: The first number is 22 = 16+6(1).
We can continue adding 6 to make a list: 22, 28, 34,...
The last number is 196 = 16+6(30)
There are 30 numbers in the list.
The answer is B.
Question: 50% of a number is more than 20% of 650 by 190. Find the number?
A.640
B.278
C.800
D.267
Answer: A.640
Explanation: (50/100) * X â€“ (20/100) * 650 = 190
1/2 X = 320
X = 640
Answer:A
Question: In a certain candy store, 22% of the customers are caught sampling the candy and are charged a small fine, but 5% of the customers who sample the candy are not caught. What is the total percent of all customers who sample candy?
A.22%
B.23%
C.24%
D.25%
Answer: B.23%
Explanation: Since 5% of the customers who sample the candyare notcaught, then 88% of the customers who sample the candyarecaught:
{% of customers who sample candy}*0.95 = 0.22;
{% of customers who sample candy} = 0.231.
Answer: B.
Question: 1.	How much more would Rs.24000 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.A)Rs.6,338.40
B.B)Rs.6,339.40
C.C)Rs.6,340.40
D.D)Rs.6,341.40
Answer: A.A)Rs.6,338.40
Explanation: 24000(11/10)4 - 24000(6/5)2 = 6,338.40
ANSWER:A
Question: A bag contains 6 black and 8 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
A.2/5
B.3/9
C.4/7
D.2/7
Answer: B.3/9
Explanation: Total number of balls = 6+8 = 14
Number of white balls = 8
probability of drawing a white ball = 8/14 = 4/7
Answer is B
Question: Benny goes to the market for buying some apples to be distributed between her nine kids equally.She takes 360 dollars with her .The cost of each apple is 4 dollars .How many apples does she buy to share them equally between her eighteen kids?
A.8
B.9
C.5
D.7
Answer: C.5
Explanation: cost of each apple = 4 dollars
Apples that Benny can buy with the amount she has=360/4 = 90.
Apples that each kid gets evenly = 90/18 = 5 Apples.
So the answer is C=5
Question: Four person are chosen at random form a group of 3 men, 2 women and 4 children. The chance that exactly 2 of them are children, is:
A.10/21
B.20/22
C.32/45
D.13/98
Answer: A.10/21
Explanation: Number of ways of choosing 4 persons out of 9
=9c4
=126
No.of ways of choosing 2 children out of 4 and 2 persons out of (3+2)= (4c2+5c2)
=60
P(E)=60/126
=10/21
ANSWER A
Question: 3. How many numbers that are not divisible by 6 divide evenly into 264,600?
A.9
B.36
C.51
D.63
Answer: D.63
Explanation: 264600 = 2^3 * 3 * 5^2 * 431
Numbers that will divide 264600 will be made up of multiples of factors of 264600 that do not divide by 6.
Expanding out the factors that are made up of the prime factors I get:
2,4,8,5,25,431
The numbers of multiples of these are: 6C1+6C2+6C3+6C4+6C5+6C6 = 63.
But in addition 1 is also a factor and so is 3 so I would have thought the ans to = 65 but my best guess is:
ANS = D
Question: On the independence day, bananas were be equally distributed among the children in a school so that each child would get two bananas. On the particular day 390 children were absent and as a result each child got two extra bananas. Find the actual number of children in the school?
A.237
B.780
C.197
D.287
Answer: B.780
Explanation: Explanation:
Let the number of children in the school be x. Since each child gets 2 bananas, total number of bananas = 2x.
2x/(x - 390) = 2 + 2(extra)
=> 2x - 780 = x => x = 780.
Answer: B
Question: Johnson has a corporate proposal. The probability that vice-president Adams will approve the proposal is 0.5. If VP Adams approves the proposal, then the probability that vice-president Baker will approve the proposal is 0.8. If VP Adams doesn’t approve the proposal, then the probability that vice-president Baker will approve the proposal is 0.3. What is the probability that at least one of the two VPs, approves Johnson’s proposal?
A.0.12
B.0.7
C.0.28
D.0.48
Answer: B.0.7
Explanation: (1at approves * second rejects ) + (1st rejects * 2nd approves ) + (both approves )
=0.5*0.2+0.4*0.3+0.6*0.8
= 0.10+0.12+0.48
=0.70
B
Question: A certain Social Security recipient will receive an annual benefit of $12,000 provided he has annual earnings of $9,360 or less, but the benefit will be reduced by $1 for every $3 of annual earnings over $9,360. What amount of total annual earnings would result in a 65 percent reduction in the recipient's annual Social Security benefit? (Assume Social Security benefits are not counted as part of annual earnings.)
A.$15,360
B.$17,360
C.$18,000
D.$21,960
Answer: D.$21,960
Explanation: For every $3 earn above $9360, the recipient loses $1 of benefit.
OR
For every $1 loss in the benefit, the recipient earns $3 above $9360
If earning is; 9360+3x
Benefit = 12000-x
Or the vice versa
If benefit is 12000-x, the earning becomes 9360+3x
He lost 50% of the benefit;
Benefit Received= 12000-0.65*12000 = 12000-7800
x=4200
Earning becomes 9360+3x=9360+3*4200=21960
Ans:D
Question: x/(y/z)
In the expression above, x, y, and z are different numbers and each is one of the numbers 1, 5, or 6. What is the least possible value of the expression?
A.6/5
B.2/15
C.5/6
D.3/10
Answer: C.5/6
Explanation: x/(y/z)
= (x*z)/y
The expression will have the least value when numerator (x*z) is the smallest.
= (1*5)/6
=5/6
Answer C
Question: The ratio of the present ages of a man and his wife is 7 : 6. Which of the following can't be a possible ratio of their ages 40 years ago?
A.5: 7
B.6: 7
C.7:7
D.8: 7
Answer: D.8: 7
Explanation: 7x-40/6x-40 = 8/7
Therefore x=-40
Age cannot be negative.
Answer: D