mathewhe/aqua_rat huggingface dataset:
Question: If the price of petrol increases by 25% and Raj intends to spend only an additional 15% on petrol, by how much will he reduce the quantity of petrol purchased?
(A) 10%
(B) 12%
(C) 8%
(D) 16%
(E) None of these
Rationale: Explanation :
Let the price of 1 litre of petrol be Rs. x and let Raj initially buys 'y' litres of petrol.
Therefore, he would have spent Rs. xy on petrol.
When the price of petrol increases by 25%, the new price per litre of petrol is 1.25x.
Raj intends to increase the amount he spends on petrol by 15%.
i.e., he is willing to spend xy+15% of xy=1.15xy.
Let, the new quantity of petrol that he can get be 'q'.
Then, 1.25x × q=1.15xy.
=>q=1.15xy/1.25x.
=>0.92y.
As the new quantity that he can buy is 0.92y, he gets 0.08y lesser than what he used to get earlier i.e a reduction of 8%.
Answer : C
Answer: (C) 8%
Question: In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
(A) 210
(B) 209
(C) 212
(D) 211
(E) 200
Rationale: In a group of 6 boys and 4 girls, four children are to be selected such that at least one boy should be there.
Hence we have 4 options as given below
We can select 4 boys ...(option 1)
Number of ways to this = 6C4
We can select 3 boys and 1 girl ...(option 2)
Number of ways to this = 6C3 × 4C1
We can select 2 boys and 2 girls ...(option 3)
Number of ways to this = 6C2 × 4C2
We can select 1 boy and 3 girls ...(option 4)
Number of ways to this = 6C1 × 4C3
Total number of ways
= 6C4 + 6C3 × 4C1 + 6C2 × 4C2 + 6C1 × 4C3
= 6C2 + 6C3 × 4C1 + 6C2 × 4C2 + 6C1 × 4C1[∵ nCr = nC(n-r)]
= 15 + 80 + 90 + 24
= 209
B
Answer: (B) 209
Question: During one year, the population of town increased by 5% . If the total population is 9975 at the end of the second year , then what was the population size in the beginning of the first year ?
(A) 12500
(B) 7500
(C) 5000
(D) 20000
(E) 10000
Rationale: Population in the beginning of the first year
= 9975/[1+(5/100)]*[1-(5/100)] = [9975*(20/21)*(20/19)]=10000.
Answer is E.
Answer: (E) 10000
Question: At Didymus Corporation, there are just two classes of employees: silver and gold. The average salary of gold employees is $50,000 higher than that of silver employees. If there are 120 silver employees and 160 gold employees, then the average salary for the company is how much higher than the average salary for the silver employees?
(A) $24,000
(B) $28,000
(C) $32,000
(D) $36,000
(E) $40,000
Rationale: The answer should be -> B. $28,000
Answer: (B) $28,000
Question: In how many ways can a Chief Minister and a Vice Minister be elected from a team of 10 members?
(A) 80
(B) 90
(C) 100
(D) 110
(E) 120
Rationale: There are 10 choices for the Chief Minister.
Then there are 9 choices for the Vice Minister.
The total number of ways is 10*9 = 90.
The answer is B.
Answer: (B) 90
Question: 250% of x is increased by 250% to become 30 . what is the value of x?
(A) 3.42
(B) 3.6
(C) 4.6
(D) 4.8
(E) 6.6
Rationale: Let x = 100 (To make calculation easy.)
250% of 100 = 250
Now,
250 is increased by 250%, then it become = 875
Now comparing,
875 = 30
So, 1 = 30/875
Hence, 100 = (30*100)/875 = 3.42
ANSWER : OPTION A
So, 100 = x = 3.42.
Answer: (A) 3.42
Question: (565945 x 121) = ?
(A) 68463812
(B) 68463813
(C) 68479345
(D) 68463814
(E) 68463814
Rationale: 565945*121=68479345Ans C
Answer: (C) 68479345
Question: Company ABC imported 10,500 widgets made of either brass or aluminum. The widgets are painted blue, red or green. If 10 percent of the widgets are made of brass and of those 30 percent are painted green and 40 percent are painted red how many brass widgets painted blue were imported?
(A) 420
(B) 840
(C) 315
(D) 1680
(E) 2100
Rationale: Answer A.
We are told that 10% of all imported widgets are made of brass and of those, 30% are green and 40% are red. Since we know that there are only three colors, the remaining 30% must be blue. 30% blue of 10% brass widgets leads to 3% blue brass widgets out of the total 10,550 widgets.
10,500 /100 * 3 = 315.
Answer C.
Answer: (C) 315
Question: A, B and C enter into a partnership with a capital in which A's contribution is Rs. 10,000. If out of a total profit of Rs. 1000, A gets Rs. 500 and B gets Rs. 300, then C's capital is :
(A) 4000
(B) 3778
(C) 2667
(D) 2887
(E) 1899
Rationale: Explanation:
A : B : C = 500 : 300 : 200 = 5 : 3 : 2.
Let their capitals be 5x, 3x and 2x respectively.
Then, 5x = 10000
=> x = 2000.
C's capital = 2x = Rs. 4000.
Answer: A) 4000
Answer: (A) 4000
Question: Find out the square of a number which when doubled exceeds its one fifth by 9 ?
(A) 16
(B) 25
(C) 19
(D) 26
(E) 17
Rationale: A
Let the number be p, then the square will be p^2
According to question:
2p = (p/5) + 9
=> 10p = p + 45
=> p = 5
p^2 = 5^2 = 25.
Answer : B
Answer: (B) 25
Question: If 5 (A's capital) = 8 (B's capital) = 10 (C's capital). Then the ratio of their capitals is?
(A) 8:5:4
(B) 8:5:18
(C) 8:5:12
(D) 8:5:14
(E) 8:5:11
Rationale: 5A = 8B = 10 C
A:B:C = 1/5:1/8:1/10
= 8:5:4
Answer: A
Answer: (A) 8:5:4
Question: Four car rental agencies A, B, C and D rented a plot for parking their cars during the night. A parked 15 cars for 12 days, B parked 12 cars for 20 days, C parked 18 cars for 18 days and D parked 16 cars for 15 days. If A paid Rs. 1125 as rent for parking his cars, what is the total rent paid by all the four agencies?
(A) Rs. 4500
(B) Rs. 4800
(C) Rs. 5250
(D) Rs. 6150
(E) None of these
Rationale: The ratio in which the four agencies will be paying the rents = 15 * 12 : 12 * 20 : 18 * 18 : 16 * 15
= 180 : 240 : 324 : 240 = 45 : 60 : 81 : 60
Let us consider the four amounts to be 45k, 60k, 81k and 60k respectively.
The total rent paid by the four agencies = 45k + 60k + 81k + 60k= 246k
It is given that A paid Rs. 1125
45k = 1125 => k = 25
246k = 246(25) = Rs. 6150
Thus the total rent paid by all the four agencies is Rs. 6150.
ANSWER:D
Answer: (D) Rs. 6150
Question: Anne bought doughnuts for a class breakfast party. She bought 5 chocolate doughnuts, 6 coconut doughnuts, and 11 jam-filled doughnuts. How many doughnuts did Anne buy in all?
(A) 22
(B) 36
(C) 39
(D) 21
(E) 11
Rationale: Add the numbers of doughnuts.
5 + 6 +11 =22.
Answer is A.
Answer: (A) 22
Question: Find the average of first 4 multiples of 15?
(A) 10
(B) 12.6
(C) 22.5
(D) 31.3
(E) 37.5
Rationale: average = (15+30+45+60)/4 = 37.5
Answer is E
Answer: (E) 37.5
Question: Two pipes A and B can fill a tank in 24 minutes and 32 minutes respectively. If both the pipes are
opened simultaneously, after how much time should B be closed so that the tank is full in 18
minutes?
(A) 7 minute
(B) 9 minute
(C) 10 minute
(D) 8 minute
(E) 11 minute
Rationale: pipe A will work for 18 minutes. suppose pipe B is closed after x minutes than
we have 18/24+x/32=1
x=8 minute.
ANSWER:D
Answer: (D) 8 minute
Question: The manufacturing cost of a shoe is Rs.230 and the transportation lost is Rs.500 for 100 shoes. What will be the selling price if it is sold at 20% gains
(A) s 282
(B) s 216
(C) s 220
(D) s 210
(E) s 217
Rationale: Explanation :
Total cost of a watch = 230 + (500/100) = 235.
Gain = 20% => SP = 1.2CP = 1.2 X 235 = 282
Answer : A
Answer: (A) s 282
Question: A trained covered x km at 40 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 7x km.
(A) 56
(B) 18
(C) 24
(D) 19
(E) 12
Rationale: Total time taken = x/40 + 2x/20 hours
= 5x/40 = x/8 hours
Average speed = 7x/(x/8) = 56 kmph
Answer: A
Answer: (A) 56
Question: Right triangle ABC is to be drawn in the xy-plane so that the right angle is at A and AB is parallel to the y-axis. If the x- and y-coordinates of A, B, and C are to be integers that are consistent with the inequalities -6 ≤ x ≤ 2 and 4 ≤ y ≤ 9 , then how many different triangles can be drawn that will meet these conditions?
(A) 54
(B) 432
(C) 2,160
(D) 2,916
(E) 148,824
Rationale: We have the rectangle with dimensions 9*6 (9 horizontal dots and 6 vertical). AB is parallel to y-axis and AC is parallel to x-axis.
Choose the (x,y) coordinates for vertex A: 9C1*6C1;
Choose the x coordinate for vertex C (as y coordinate is fixed by A): 8C1, (9-1=8 as 1 horizontal dot is already occupied by A);
Choose the y coordinate for vertex B (as x coordinate is fixed by A): 5C1, (6-1=5 as 1 vertical dot is already occupied by A).
9C1*6C*8C1*5C1=2160.
Answer: C.
Answer: (C) 2,160
Question: Reena took a loan of $. 1200 with simple interest for as many years as the rate of interest. If she paid $ 588 as interest at the end of the loan period, what was the rate of interest?
(A) 3.6
(B) 7
(C) 18
(D) Cannot be determined
(E) None of these
Rationale: Let rate = R% and time = R years.
Then,1200 x R x R/100= 588
12R2 = 588
R2 = 49
R = 7.
Answer:B
Answer: (B) 7
Question: There are r red ball, b blue ball and w white ball in a bag. What is the ratio of the number of blue ball to the total no. of ball in terms of r, b and w.?
(A) r / (r + b + w)
(B) r / (r + b)
(C) (r + b + w)/r
(D) r / (b + w)
(E) r * (r + b + w)
Rationale: The total number of marbles is
r + b + w
The total ratio of blue marbles to the total number of marbles is
r / (r + b + w)
A
Answer: (A) r / (r + b + w)
Question: In how many ways Chief Minister and Minister be elected from a team of 10 members?
(A) 90
(B) 95
(C) 120
(D) 100
(E) 165
Rationale: To do this, if captain is elected first, then we have 10 ways of doing this.
For election of vice-captain, we have only 9 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)
So, the ans is 10*9 = 90 ways.
A
Answer: (A) 90
Question: If 4 women can color 48 m long cloth in 2 days, then 6 women can color 36 m long cloth in
(A) 2 days
(B) 1 day
(C) 4 days
(D) 3 days
(E) 2 1/5 days
Rationale: The length of cloth painted by one woman in one day = 48 / 4 × 2 = 6 m
No. of days required to paint 36 m cloth by 6 women = 36/ 6 × 6 = 1 day.
B
Answer: (B) 1 day
Question: Each person who attended a company meeting was either a stockholder in the company, an employee of the company or both. If 62 percent of these who attended the meeting were stockholders and 49 percent were employees. What percent were stockholders, who were not employees?
(A) 52
(B) 51
(C) 54
(D) 55
(E) 56
Rationale: I came up with the same answer choice B, but my approach was slightly different!
49% were employees which shall cover those who were only employees and those who were both shareholders and employees.
Thus, the number of attendants who were only shareholders is 100% - 49% = 51%.
Answer: (B) 51
Question: One square garden has area of A square feet and the perimeter is p feet. If 3A=3(2p+9), what is the perimeter of the garden, in feet?
(A) 28
(B) 36
(C) 40
(D) 56
(E) 74
Rationale: You can also solve this via using the given numbers in the answer choices!
Of course you need to be aware of the basic properties as outlined by the other posts above (a = x^2 and p = 4x)
Starting with D you will notice that x=14 is way too big for your area (14^2) and will not satisfy: 3A=3(2p+9) or A=2p+9
--> Eliminate D and E
Now pick B (its either too big, then its A, or too small then you know its C or it is B itsself)
And picking B indeed solves the problem! (36/4 --> 9; a= 9^2 = 81 and 81=2x36+9)
Answer: (B) 36
Question: A retailer buys a radio for Rs 225. His overhead expenses are Rs 28. He sellis the radio for Rs 300. The profit percent of the retailer is
(A) 10%
(B) 50%
(C) 25%
(D) 52%
(E) 18.5%
Rationale: Explanation:
cost price = (225 + 28) = 253 sell price = 300
gain = (47/253)*100 = 18.5%. Answer: E
Answer: (E) 18.5%
Question: Which of the following is equivalent to the pair of inequalities x + 2 > 10 and x - 4 <= 5 ?
(A)  2 < x < 16
(B)  2 <= x < 4
(C)  2 < x <= 8
(D)  8 < x <= 9
(E)  4 <= x <= 16
Rationale: Solution:
Let’s isolate x in both inequalities, starting with x + 2 > 10.
x + 2 > 10
x > 8
Next we isolate x in the inequality x – 4  5.
x – 4 <= 5
x <= 9
Bringing these two inequalities together we know:
8 < x <= 9
The answer is D.
Answer: (D)  8 < x <= 9
Question: One used-car salesperson receives a commission of $ 200 plus 4 percent of $ 1,000 less than the car’s final sale price. Another car salesperson earns a straight commission of 6 percent of the car’s final sale price. What is the final sale price of a car if both salespeople would earn the same commission for selling it?
(A) $ 5,000
(B) $ 6,000
(C) $ 8,000
(D) $ 10,000
(E) $ 12,000
Rationale: let s1 and s2 be the commission earned by the two salesperson
as per the question,
s1=200+0.04(x-1000) (where x is the sp of the car)
s2=0.06x
also
s1=s2
or,
200+0.04(x-1000)=0.06x
200+0.04x-40=0.06x
0.02x=160
x=8000
ANSWER:C
Answer: (C) $ 8,000
Question: Given that a is the average (arithmetic mean) of the first six positive multiples of six and b is the median of the first twelve positive multiples of six, what is the ratio of a to b?
(A) 3:4
(B) 10:13
(C) 5:6
(D) 13:10
(E) 7:13
Rationale: The first nine positive multiples of six are {6, 12, 18, 24,30, 36}
The first twelve positive multiples of six are {6, 12, 18, 24, 30,36,42, 48, 54, 60, 66, 72}
Both sets are evenly spaced, thus their median=mean:
a=21 and b=(36+42)/2=39 --> a/b=21/39=7/13.
Answer: E.
Answer: (E) 7:13
Question: The grade point average of the entire class is 90. If the average of one third of the class is 96, what is the average of the rest?
(A) 92
(B) 89
(C) 88
(D) 87
(E) 86
Rationale: Let us take number of students on the class as 'x'.
avg grade point = sum of all grade points/x
sum of all grade points = avg grade point*x = 90x
average of one third of the class = 96 = sum of one third grade points of the class/(x/3)
sum of one third grade points of the class = 96*(x/3) = 32x
sum of rest two third grade points of the class = sum of all grade points - sum of one third grade points of the class
sum of rest two third grade points of the class = 90x-32x = 58x
avg of two third of the class = sum of rest two third grade points of the class/(x*2/3) = 58x/(2x/3) = 29*3 = 87.
Hence, answer is D
Answer: (D) 87
Question: In how many ways can the letters of the word CAVED be arranged in a row so that the vowels appear in alphabetic order?
(A) 60
(B) 30
(C) 120
(D) 240
(E) 180
Rationale: Two letters can be arranged in 2! ways.
only one combination EIU is required.
5 letters can be arranged in 5! ways.
thus 5!/ 2! * 1 = 60.
A
Answer: (A) 60
Question: A and B invests Rs.10000 each, A investing for 8 months and B investing for all the 12 months in the year. If the total profit at the end of the year is Rs.25000, find their shares?
(A) Rs.10000, Rs.15020
(B) Rs.10000, Rs.15700
(C) Rs.10000, Rs.15090
(D) Rs.10000, Rs.15000
(E) Rs.10000, Rs.15200
Rationale: The ratio of their profits A:B
= 8:12 = 2:3
Share of A in the total profit
= 2/5 * 25000
= Rs.10000 Share of A in the total profit = 3/5 * 25000
= Rs.15000
Answer: D
Answer: (D) Rs.10000, Rs.15000
Question: Of the following values of n, the value of (-1/4)^(-n) will be greatest for n =
(A) 3
(B) 0
(C) 2
(D) -2
(E) -3
Rationale: imo -2
(-1/4)^-2=
1/(1/16)=16
oops i meant 2
C
Answer: (C) 2
Question: A is twice as fast as B. If B alone can do a piece of work in 18 days, in what time can A and B together complete the work?
(A) 10
(B) 16
(C) 18
(D) 6
(E) 12
Rationale: A can do the work in 18/2 i.e., 9 days.
A and B's one day's work = 1/9+ 1/18 = (2 + 1)/18 = 1/6
So A and B together can do the work in 6 days.
Answer: D
Answer: (D) 6
Question: A train does a journey without stoppage in 8 hours, if it had travelled 5 km/h faster, it would have done the journey in 6 hours 40 minutes. Find its original speed.
(A) 25 km/h
(B) 40 km/h
(C) 45 km/h
(D) 36.5 km/h
(E) None of these
Rationale: Let original speed = S km/h
Here, distance to be covered is constant
∴ S × 8 = (S + 5)(20⁄3)
⇒ 8S - 20⁄3S = 100⁄3 ⇒ S = 100⁄4 = 25 km/h
Answer A
Answer: (A) 25 km/h
Question: In how many ways can the letters of the word 'LEADER' be arranged ?
(A) 360
(B) 72
(C) 144
(D) 760
(E) 280
Rationale: The word 'LEADER' contains 6 letters, namely 1L, 2E, 1A, 1D and 1R.
∴ Required number of ways = 6!/(1!)(2!)(1!)(1!)(2!) = 360.
Answer is A
Answer: (A) 360
Question: If n is the greatest positive integer for which 2^n is a factor of 8!, then n =?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: 8! = 40320
E. 2^10 = 512 (40320/512) - this is not a factor of 8!
D. 2^8 = 256 (40320/256) - this is not a factor of 8!
C. 2^6 = 64 (720/64) - this is a factor of 8!
C is answer
Answer: (C) 6
Question: In a class ,there are 15 boys and 10 girls .one student is selected at random. The probability that one girl is selected,is:
(A) 10/25
(B) 2/5
(C) 15/25
(D) 3/25
(E) 1/25
Rationale: Total number of students = 10+15= 25
no.of girls in a class = 10
probability of one girl is selected = 10/25= 2/5
Answer is B
Answer: (B) 2/5
Question: What is the tenth digit of (4!*3! + 4!*2!)/3?
(A) 5
(B) 7
(C) 9
(D) 1
(E) 0
Rationale: (4!*3! + 4!*2!)/2
=4!(3! + 2!)/2
=24 (6+2)/2
=96
Units digit of the above product will be equal to 9
Answer C
Answer: (C) 9
Question: The probability that A speaks truth is 15/23 and that of B speaking truth is 17/29. What is the probability that they agree in stating the same fact?
(A) 182/395
(B) 129/289
(C) 197/353
(D) 479/667
(E) None of these
Rationale: If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 15/23 * 17/29 + 14/23 * 16/29
= 255/667 + 224/667 = 479/667
ANSWER:D
Answer: (D) 479/667
Question: If x is a positive integer, what is the units digit of (24)^(2x+1)(33)^(x+1)(17)^(x+2)(9)^(2x)
(A) 4
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: To find the units digit of the above (24)^(2x+1)(33)^(x+1)(17)^(x+2)(9)^(2x) , find the units digit of each term possible .
24^2x . 24 --> Units digit of (24^2)^X = 6^X = 6 multiplied by last digit of 24 = 4
33^x . 33 --> Units digit of 33^x . 3 --> 3,9,7,1 multiplied by 3
17^x. 17^2 --> Units digit of 17^x. 9 (units digit of 7^2)--> 7,9,3,1 multiplied by 9
9^2x --> Units digit of 81^x = 1
If you observe 2nd and 3rd expression above and multiply both you will always get 1 for units digit of 33^x multiplied by 17^x ( because 3*7, 9*9,7*3,1*1 all end in 1 for the same value of x) . Thus you have 3 and 9 from 2nd and third expression above.
So the units digit of the whole expression = Units digit of 4*3*9*1 which is 8 .
Answer Choice D
Answer: (D) 8
Question: In what time will a railway train 60 m long moving at the rate of 36 kmph pass a telegraph post on its way?
(A) 5 sec
(B) 8 sec
(C) 3 sec
(D) 4 sec
(E) 6 sec
Rationale: E
6 sec
T = 60/36 * 18/5 = 6 sec
Answer: (E) 6 sec
Question: A discount electronics store normally sells all merchandise at a discount of 10 percent to 30 percent off the suggested retail price. If, during a special sale, an additional 20 percent were to be deducted from the discount price, what would be the lowest possible price of an item costing $300 before any discount?
(A)  $230.00
(B)  $145.60
(C)  $168.80
(D)  $182.00
(E)  $210.00
Rationale: Since the question is essentially just about multiplication, you can do the various mathstepsin a variety of ways (depending on whichever method you find easiest).
We're told that the first discount is 10% to 30%, inclusive. We're told that the next discount is 20% off of the DISCOUNTED price....
We're told to MAXIMIZE the discount (thus, 30% off the original price and then 20% off of the discounted price). Thatmathcan be written in a number of different ways (fractions, decimals, etc.):
30% off = (1 - .3) = (1 - 30/100) = (.7) and the same can be done with the 20% additional discount...
The final price of an item that originally cost $300 would be.....
($300)(.7)(.8) =
($300)(.56)=168
Final Answer:
C
Answer: (C)  $168.80
Question: A man can row 9 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?
(A) 4.32
(B) 4.42
(C) 4.52
(D) 4.62
(E) 4.72
Rationale: M = 9
S = 1.2
DS = 9 + 1.2 = 10.2
US = 9 - 1.2 = 7.8
x/10.2 + x/7.8 = 1
x = 4.42.Answer: B
Answer: (B) 4.42
Question: The area of a circle is increased by 300%. By what percent has the diameter of the circle increased?
(A)  400%
(B)  200%
(C)  300%
(D)  100%
(E)  800%
Rationale: The area of the circle is increased by 300%, thus the area is increased 4 times.
The area of a circle it proportional to the square of the diameter (area=πd^2/4), therefore the diameter must increase 2 times (diameter increase 2 times = area increase 4 times), which is increase by 100%.
Answer: D.
Answer: (D)  100%
Question: 95,70,54,45, ?
(A) 41
(B) 43
(C) 44
(D) 40
(E) 39
Rationale: 95 - 70 = 25 = 5^2
70 - 54 = 16 = 4^2
54 - 45 = 09 = 3^2
so we can write
45 - x = 04 = 2^2 , where x is the next number
x = 45 - 4 = 41
so the next number will be 41
ANSWER:A
Answer: (A) 41
Question: At present, the ratio between the ages of Arun and Deepak is 4:3. After 2 years, Arun's age will be 26 years. What is the age of Deepak at present?
(A) 16
(B) 17
(C) 10
(D) 18
(E) 15
Rationale: Let the present ages of Arun and Deepak be 4x and 3x years respectively.
Then, 4x + 2 = 26 => x = 8
Deepak's age = 3x = 18 years.
Answer: D
Answer: (D) 18
Question: A batch of widgets costs p + 5 dollars for a company to produce and each batch sells for p(6 – p) dollars. For which of the following values of p does the company make a profit?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: to make profit, selling price should be greater than cost price
p(6-p) - p-5 >0
=> p^2-5*p+5<0
hence p=3
A
Answer: (A) 3
Question: A professional athlete was offered a three-year contract to play with Team K that provided for an annual salary of $100,000 in the first year, an increase in annual salary of 20% over the previous year for the next two years, and a bonus of $75,000 on signing. Team L offered a three-year contract providing for an annual salary of $150,000 in the first year, an increase in annual salary of 10% over the previous year for the next two years, and no signing bonus. If he accepts the offer of Team L and fulfills the three-year contract terms, the athlete will receive how much more money by choosing Team L over Team K ?
(A) $32,500
(B) $57,500
(C) $82,500
(D) $92,000
(E) $100,000
Rationale: Team K's contract = $100,000 + $100,000*1.2 + $100,000*1.2*1.2 + $75,000 = $439,000
Team L's contract = $150,000 + $150,000*1.1 + $150,000*1.1*1.1 = $496,500
The difference = $57,500.
Answer: B.
Answer: (B) $57,500
Question: The sum of four consecutive even integers is 1284. The greatest of them is:
(A) 324
(B) 342
(C) 364
(D) 382
(E) none
Rationale: Sol.
Let the four integers be x, x + 2, x + 4 and x + 6
Then, x + (x + 2) + (x + 4) + (x + 6) = 1284 ⇔ 4x = 1272 ⇔ x = 318
∴ Greatest integer = x + 6 = 324.
Answer A
Answer: (A) 324
Question: The sum of the digits of a two-digit number is 12. The difference of the digits is 6. Find the number?
(A) 11
(B) 39
(C) 88
(D) 66
(E) 51
Rationale: Let the two-digit number be 10a + b
a + b = 12 --- (1)
If a>b, a - b = 6
If b>a, b - a = 6
If a - b = 6, adding it to equation (1), we get
2a = 18 => a =9
so b = 12 - a = 3
Number would be 93.
if b - a = 6, adding it to the equation (1), we get
2b = 18 => b = 9
a = 12 - b = 3.
Number would be 39.
There fore, Number would be 39 or 93.
Answer: B
Answer: (B) 39
Question: A bowl was filled with 10 ounces of water, and 0.0008 ounce of the water evaporated each day during a 50-day period. What percent of the original amount of water evaporated during this period?
(A) 0.004%
(B) 0.04%
(C) 0.40%
(D) 4%
(E) 40%
Rationale: Total amount of water evaporated each day during a 50-day period = .0008 * 50
=.0008 * 100/2
= .08/2
= .04
percent of the original amount of water evaporated during this period = (.04/10) * 100%
= 0.4 %
Answer C
Answer: (C) 0.40%
Question: Find the middle one when The sum of three consecutive even numbers is 36?
(A) 10
(B) 12
(C) 15
(D) 17
(E) 18
Rationale: 3 consecutive numbers can be a - 1, a, a + 1
So sum of numbers = 3a = 36.
Hence a = 12.
B
Answer: (B) 12