mathewhe/aqua_rat huggingface dataset:
Question: A jar is filled of liquid which is 3 parts water and 5 parts alcohol. How much of this mixture should be drawn out and replaced such that this mixture may contain half
water and half alcohol?
(A) 25%
(B) 20%
(C) 14.29%
(D) 33.33%
(E) None of these
Rationale: Explanation:
Let the jar initially contain 8 litres of mixture:3 litres water and 5 litres alcohol
Let x litres of this mixture is drawn out and is replaced by x litres of water.
Amount of water now in the solution: 3-(3/8)x+x.
Amount of alcohol now in the solution: 5-(5/8)x
Desired ratio: 1/1
=>3-(3/8)x+x=5-(5/8)x
x=8/5 litres
%x=((8/5)/8)*100=20%
ANSWER B
Answer: (B) 20%
Question: Siddharth wants to borrow Rs.7000 at rate of interest 6% p.a. at S.I and lend the same amount at C.I at same rate of interest for two years. What would be his income in the above transaction?
(A) s.21.60
(B) s.21.29
(C) s.22.29
(D) s.21.26
(E) s.25.20
Rationale: Amount of money Siddharth borrowed at S.I at 6% p.a. for two years = Rs.7,000
He lend the same amount for C.I at 6% p.a. for two years.
=> Siddharth's income = C.I - S.I
= p[1 + r/ 100]n - p - pnr/100
= p{ [1 + r/ 100]2 - 1 - nr/100
= 7,000{ [1 + 6/100]2 - 1 - 12/100}
= 7,000 {(1.06)2- 1 - 0.12} = 7,000(1.1236 - 1 - 0.12)
= 7,000 (0.0036) = 7 * 3.6 = Rs.25.20
Answer: E
Answer: (E) s.25.20
Question: A merchant purchased a jacket for $60 and then determined a selling price that equalled the purchase price of the jacket plus a markup that was 25 percent of the selling price. During a sale, the merchant discounted the selling price by 20 percent and sold the jacket. What was the merchant’s gross profit on this sale?
(A) $0
(B) $3
(C) $4
(D) $12
(E) $15
Rationale: Markup = x
x = 0.25(60 + x)
=> 3x/4 = 15
=> x = 20
So SP = 80
But Actual SP = 0.8 * 80 = 64
So profit = $4
Answer - C
Answer: (C) $4
Question: A car traveled 75% of the way from town A to town B at an average speed of 50 miles per hour. The car travels at an average speed of S miles per hour for the remaining part of the trip. The average speed for the entire trip was 60 miles per hour. What is S ?
(A) 150
(B) 200
(C) 250
(D) 300
(E) 237.5
Rationale: Total distance = 100 miles (easier to work with %)
75% of the distance = 75 miles
25% of the distance = 25 miles
1st part of the trip → 75/50 = 1.5
2nd part of the trip → 25/S = t
Total trip → (75+25)/60 = 1.5 + t » 100/60 = 1.5 + t » 2.5 = 1.5 + t » t = 0.1667
Back to 2nd part of the trip formula: 25/S = 0.1667 » S = 150
Ans A
Answer: (A) 150
Question: What is the year next to 1990 which will have the same calendar as that of the year 1990?
(A) 1992
(B) 2001
(C) 1995
(D) 1996
(E) 1997
Rationale: Explanation:
For a year to have the same calendar with 1990 ,total odd days from 1990 should be 0.
Take the year 1992 from the given choices.
Total odd days in the period 1990-1991= 2 normal years
≡ 2 x 1 = 2 odd days
Take the year 1995 from the given choices.
Number of odd days in the period 1990-1994 = 4 normal years + 1 leap year
≡ 4 x 1 + 1 x 2 = 6 odd days
Take the year 1996 from the given choices.
Number of odd days in the period 1990-1995= 5 normal years + 1 leap year
≡ 5 x 1 + 1 x 2 = 7 odd days ≡ 0 odd days
(As we can reduce multiples of 7 from odd days which will not change anything)
Though number of odd days in the period 1990-1995 is 0, there is a catch here.
1990 is not a leap year whereas 1996 is a leap year.
Hence calendar for 1990 and 1996 will never be the same.
Take the year 2001 from the given choices.
Number of odd days in the period 1990-2000= 8 normal years + 3 leap years
≡ 8 x 1 + 3 x 2 = 14 odd days ≡ 0 odd days
Also, both 1990 and 2001 are normal years.
Hence 1990 will have the same calendar as that of 2001
Answer: Option B
Answer: (B) 2001
Question: A meeting has to be conducted with 5 managers. Find the number of ways in which the managers be selected from among 9 managers, if 2 managers will not attend the meeting together?
(A) 35
(B) 91
(C) 120
(D) 126
(E) 150
Rationale: we can either choose all 5 people from 7 manager who have no problems or choose 4 from the 7 and 1 from the 2 managers who have a problem sitting together
so 7C5 + (7C4 * 2C1)
this is 21 + 70
91 ANS:B
Answer: (B) 91
Question: If 4 (P's Capital ) = 6 ( Q's Capital ) = 10 ( R's Capital ) , then out of the total profit of Rs 4030 , R will receive
(A) 600
(B) 780
(C) 800
(D) 900
(E) None of these
Rationale: Explanation :
Let P's capital = p, Q's capital = q and R's capital = r
Then
4p = 6q = 10r
=> 2p = 3q = 5r
=>q = 2p/3
r = 2p/5
P : Q : R = p : 2p/3 : 2p/5
= 15 : 10 : 6
R's share = 4030 * (6/31) = 130*6 = 780. Answer : Option B
Answer: (B) 780
Question: How many positive integers will divide evenly into 370?
(A) 4
(B) 6
(C) 8
(D) 12
(E) 16
Rationale: The question is asking how many factors 370 has.
370 = 2*5*37
The number of factors is 2^3 = 8
The answer is C.
Answer: (C) 8
Question: A composer’s guild is planning its spring concert, and eleven pieces have been submitted for consideration. The director of the guild knows that they will only have time to present three of them. If the pieces can be played in any order, how many combinations of pieces are possible?
(A) 402
(B) 165
(C) 154
(D) 512
(E) 126
Rationale: Combination question..
11C3 = 165..
IMO option B is correct..
Answer: (B) 165
Question: The cash difference between the selling prices of an article at a profit of 8% and 6% is Rs 3. The ratio of two selling prices is
(A) 51:52
(B) 52:53
(C) 53:54
(D) 54:53
(E) None of these
Rationale: Explanation:
Let the Cost price of article is Rs. x
Required ratio = (108% of x) / (106% of x)
=108/106
=54/53 = 54:53.
Answer: D
Answer: (D) 54:53
Question: A car travels from point A to point B. The average speed of the car is 60 km/hr and it travels the first half of the trip at a speed of 48 km/hr. What is the speed of the car in the second half of the trip?
(A) 72
(B) 75
(C) 80
(D) 84
(E) 90
Rationale: Let D be the distance and let V be the speed in the second half.
The total time = T1 + T2
D/60 = D/96 + (D/2) / V
8D/480 - 5D/480 = (D/2) / V
D/160 = D/2V and so V = 80 km/hr
The answer is C.
Answer: (C) 80
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 6 years ago?
(A)  8
(B)  10
(C)  12
(D)  14
(E)  16
Rationale: 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 6 years ago?
i.e. D-6 = 14-6 = 8 years
Answer: Option
A
Answer: (A)  8
Question: The length of a train and that of a platform are equal. If with a speed of 126 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
(A) 227
(B) 299
(C) 1050
(D) 750
(E) 211
Rationale: Speed = [126 * 5/18] m/sec = 35 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 35 è x = 35 * 60 / 2 = 1050
Answer: C
Answer: (C) 1050
Question: which of the following is a prime number ?
(A) 17
(B) 18
(C) 15
(D) 20
(E) 25
Rationale: Clearly, 17 is a prime number.
Option A
Answer: (A) 17
Question: A man's regular pay is $3 per hour up to 40 hours. Overtime is twice the payment for regular time. If he was paid $180, how many hours overtime did he work?
(A) 8
(B) 5
(C) 9
(D) 6
(E) 10
Rationale: At $3 per hour up to 40 hours, regular pay = $3 x 40 = $120 If total pay = $168, overtime pay = $180 - $120 = $60 Overtime rate (twice regular) = 2 x $3 = $6 per hour => number of overtime hours = $60/$6 =10
Ans is E
Answer: (E) 10
Question: A man takes 3 hours 45 minutes to row a boat 25 km downstream of a river and 2 hours 30 minutes to cover a distance of 15 km upstream. Find the speed of the current.
(A) 1 km/hr
(B) 2/3 km/hr
(C) 1/3 km/hr
(D) 4 km/hr
(E) None of these
Rationale: Explanation:
First of all, we know that
speed of current = 1/2(speed downstream - speed upstream) [important]
So we need to calculate speed downstream and speed upstream first.
Speed = Distance / Time [important]
Speed upstream =(25/3 3/4)km/hr
=20/3km/hr
Speed Downstream = (15/2 1/2)km/hr
=6km/hr
So speed of current = 1/2(20/3−6)
=1/3 km/hr
Option C
Answer: (C) 1/3 km/hr
Question: An accurate clock shows 8 o'clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon?
(A) 144°
(B) 150°
(C) 168°
(D) 180°
(E) none
Rationale: Solution
Angle traced by hour hand in
5 hrs 10 min.	= (360/12 x 6)°
= 180°.
Answer D
Answer: (D) 180°
Question: Mr. Wayne bungee jumps from the top of a building straight to the ground at a constant speed. 3 seconds after he starts plummeting he passes the 20th floor. 15 seconds after he starts plummeting he passes the 5th floor. Each floor is 4 meters high. What is Mr. Wayne's speed in meters per second?
(A) 3
(B) 3.75
(C) 4
(D) 4.25
(E) 5
Rationale: IMO: E
15 Floors * 4 Meter/Floor = 60 Meters
Time= 12 sec
Rate * 12 = 60
Rate= 60/12
=5
Answer E
Answer: (E) 5
Question: A person goes to his office at 1/3rd of the speed at which he returns from his office. If the avg speed during the whole trip is 12m/h. what is the speedof the person while he was going to his office?
(A) 8km/h
(B) 10km/h
(C) 12km/h
(D) 13km/h
(E) 14km/h
Rationale: u = k , v= 3k
\inline \therefore \frac{2uv}{u+v}\: \: \Rightarrow \frac{2\times k\times 3k}{(k+3k)}=12
\inline \Rightarrow 1.5k = 12
\inline \Rightarrow k=8km/h
A
Answer: (A) 8km/h
Question: A marketing firm determined that, of 200 households surveyed, 80 used neither Brand R nor Brand B soap, 60 used only Brand R soap, and for every household that used both brands of soap, 3 used only Brand B soap. How many of the 200 households surveyed used both brands of soap?
(A)  15
(B)  20
(C)  30
(D)  40
(E)  45
Rationale: SOLUTION FOR SOAP R AND SOAP B
(D) 40
Answer: (D)  40
Question: David and Rachel are getting married. The extended family wants to have its picture taken, but David's father is unwilling to stand next to Rachel's mother. How many options does the photographer have to arrange the 14 family members in a row for the picture?
(A) 12!
(B) 13×12!
(C) 12×13!
(D) 14!/2!
(E) 14!
Rationale: The number of ways to arrange 14 people is 14!
We need to subtract the arrangement when these two people are together.
Let's think of these two people as a single unit so there are 13 units.
The number of ways to arrange 13 units is 13!
We need to multiply this by 2 since these two people could switch places.
The total number of valid arrangements is 14! - 2*13! = 13!*(14-2) = 12x13!
The answer is C.
Answer: (C) 12×13!
Question: What is the units digit of 33^2 * 17^3 * 39^2?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: The units digit of 33^2 is the units digit of 3*3 = 9 which is 9.
The units digit of 17^3 is the units digit of 7*7*7 = 343 which is 3.
The units digit of 39^2 is the units digit of 9*9 = 81 which is 1.
The units digit of 9*3*1 = 27 is 7.
The answer is D.
Answer: (D) 7
Question: A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg?
(A) 22
(B) 99
(C) 40
(D) 28
(E) 23
Rationale: 800*(25/100) = 200 ---- 5
? ---- 1 => Rs.40
Answer: C
Answer: (C) 40
Question: Saskia needs to catch the 3.15pm train in order to get to her Mixed Martial Arts fight on time. It is 2.55 pm and Saskia is 2 miles from the train station. Saskia can run at an average speed of 10 miles per hour. However Saskia is carrying a sack of bricks which slows her down by 20%. If she runs to the station how many minutes early or late will she be for the train?
(A) 10 minutes early
(B) 5 minutes early
(C) 0 minutes early
(D) 5 minutes late
(E) 10 minutes late
Rationale: Saskia can run at an average speed of 10 miles per hour however she is slowed down by 20% by the sack of bricks and so can only run at 8 miles per hour. (0.2 x 10 = 2; 10 - 2 = 8)
At a speed of 8 miles per hour, Saskia can run 2 miles in 15 minutes. (8 miles / 2 miles = 4; 60 minutes/4 = 15 minutes)
Saskia has 20 minutes until her train but can run the distance in 15 minutes therefore she will be 5 minutes early (20 - 15 = 5 minutes).
ANSWER: B
Answer: (B) 5 minutes early
Question: The H.C.F of two numbers is 15 and their L.C.M is 3300. If one of the numbers is 225, then the other is?
(A) 200
(B) 210
(C) 220
(D) 230
(E) 240
Rationale: Other number = (15 * 3300)/225
= 220.
Answer: C
Answer: (C) 220
Question: A bus from city M is traveling to city N at a constant speed while another bus is making the same journey in the opposite direction at the same constant speed. They meet in point P after driving for 2 hours. The following day the buses do the return trip at the same constant speed. One bus is delayed 24 minutes and the other leaves 36 minutes earlier. If they meet 24 miles from point P, what is the distance Q between the two cities?
(A) 48
(B) 72
(C) 96
(D) 120
(E) 192
Rationale: Hmmm I did this question a while ago and got it wrong so trying again
Rate x time = distance.
For the initial trip lets the distance Q to the midpoint be represented by P.
EQN1: R x 2 = P
For the second trip we know one bus left late and one left early. Together this is just a tricky way of saying one bus left an hour after the other. We know the total trip takes 4 hours (since getting to P is 2 hours). The second trip can be represented by:
Since the trip takes 4 hours if a bus leaves one hour early, the reminaining 3 hours are split between the two buses, ie. 1 + 3/2 = 2.5
EQN2: R x 2.5 = P + 24
EQN2-EQN1 : 0.5R=24
R=48
So the distance is rate x time = 48 x 4 = 192.
ANS = E
Answer: (E) 192
Question: The slant height of a cone is 12 cm and radius of the base is 4cm, find the curved surface of the cone?
(A) 26
(B) 28
(C) 48
(D) 26
(E) 28
Rationale: π * 12 * 4
= 48
Answer:C
Answer: (C) 48
Question: The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 4 years hence?
(A) 50
(B) 60
(C) 68
(D) 80
(E) 90
Rationale: A + B = 60, A = 2B
2B + B = 60 => B = 20 then A = 40.
5 years, their ages will be 44 and 24.
Sum of their ages = 44 + 24 = 68.
ANSWER:C
Answer: (C) 68
Question: What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58?
(A) 3944
(B) 2287
(C) 2977
(D) 2668
(E) 1298
Rationale: Let the side of the square plot be a ft.
a2 = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 * 58 = Rs. 3944.
Answer:A
Answer: (A) 3944
Question: John invests $x at the semi-annual constant compounded rate of 2 percent and also does $40,000 at the quarterly constant compounded rate of 4 percent. If the interests are the same after 1 year, what is the value of x??
(A) 50000
(B) 55000
(C) 60000
(D) 70000
(E) 80804
Rationale: A = P(1+r/n)^nt
A= total amount accrued
P = principal deposited
r = rate of interest in decimal form
n = number of times per year, interest compounded
t = time in number of years.
.
x(1+0.02/2)^2 - x = 40,000(1+0.04/4)^4 - 40,000 [ when the principal is subtracted from the total amount accrued , the resulting difference is the interest portion and question states interests are equal)
=> x[(1.01)^2 - 1] = 40,000[(1.01)^4 - 1]
=> x[(1.01)^2 - 1] = 40,000[(1.01)^2+1][(1.01)^2-1] --> Using a^2-b^2 = a+b X a-b formula and cancel common expression on both sides
=> x = 40,000(1.0201+1) =80804.
Hence answer is E.
Answer: (E) 80804
Question: B and C walk around a circular track. They start at 9 a.m from the same point in the opposite directions. B and C walk at a speed of 5 rounds per hour and 4 rounds per hour respectively. How many times shall they cross each other before 1 p.m
(A) 34
(B) 35
(C) 36
(D) 37
(E) 38
Rationale: Explanation:
Relative speed = (5+4) =9 rounds per hour
So, they cross each other 9 times in an hour hence, they cross 36 times before 1 p.m
Answer: Option C
Answer: (C) 36
Question: On a certain bus, one-fourth of the children are boys that are wearing sneakers. One-third of the children on the bus are girls that are wearing sneakers, which of the following is a possible number of children on the bus?
(A) 11
(B) 16
(C) 29
(D) 30
(E) 36
Rationale: Let No. of Children = x
Boys wearing sneakers = x/4
Boys wearing sneakers = x/3
i.e. Total number of children must be divisible by 4 as well as by 3
i.e. Total number of children must be divisible by LCM of 4 & 3 i.e. 12
Only Option E- 36 satisfies the requirement hence
ANSWER:E
Answer: (E) 36
Question: Sixteen men complete a work in 24 days while 48 children can do it in 16 days. Twelve men started the work, after 14 days 12 children joined them. In how Many days will all of them together complete the remaining work?
(A) 12
(B) 62
(C) 27
(D) 29
(E) 17
Rationale: Explanation:
Let man capacity = 2 units/day. Then total work = 16 × 2 × 24 = 768
Let the children capacity is k units/ days. So total work = 48 × k × 16
Equating above two equations we get k = 1. So children capacity = 1 unit / day.
Twelve men did 14 days of job. So they completed 12 × 2 ×14 = 336.
Remaining work = 768 - 336 = 432.
Now 12 children joined them. So per day capacity of entire team = 12 × 2 + 12 × 1 = 36.
So they complete the remaining work in 432/36 = 12 days.
Answer:A
Answer: (A) 12
Question: If a man walks to his office at ¾ of his usual rate, he reaches office 1/3 of an hour late than usual. What is his usual time to reach office?
(A) 1
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Speed Ratio = 1:3/4 = 4:3
Time Ratio = 3:4
1 -------- 1/3
3 --------- ? è 1 hour
Answer: A
Answer: (A) 1
Question: Rs.500 amounts to Rs.620 in 2 years at simple interest. If the interest is increased by 2%, it would amount to how much?
(A) 120
(B) 25
(C) 614
(D) 530
(E) 210
Rationale: (500*3*2)/100 = 30
500+ 30 = 530
Answer: D
Answer: (D) 530
Question: Yearly subscription to professional magazines cost a company $840.00. To Make a 30% cut in the magazine budget, how much less must be spent?
(A) 654
(B) 655
(C) 656
(D) 588
(E) 658
Rationale: total cost 840
840*30/100=252
so the cut in amount is 252
the less amount to be spend is 840-252=588
ANSWER:D
Answer: (D) 588
Question: What is the sum of the integers from -190 to 191 inclusive?
(A) 0
(B) 191
(C) 375
(D) 875
(E) 965
Rationale: sum/n= average.
sum=(average)(n)
average=a+b/2=190+191/2=0.5
number of items(n)=B-A+1=191-(-190)+1=195+191=382.
sum=average*n=0.5*382=191.
answer is B
Answer: (B) 191
Question: The number of ways in which six boys and six girls can be seated in a row for a photograph so that no two girls sit together is ?
(A) 6! * 7P6
(B) 2(6!)
(C) 6!)2
(D) 6! * 7
(E) 7! * 7
Rationale: We can initially arrange the six boys in 6! ways.
Having done this, now three are seven places and six girls to be arranged. This can be done in ⁷P₆ ways.
Hence required number of ways
= 6! * 7P6
Answer:A:
Answer: (A) 6! * 7P6
Question: V is the volume of a cylinder; the radius of the cylinder is 3.5. The height of the cylinder is 650% more than the radius. Which of the following is true?
(A) 100 < V < 300
(B) 300 < V < 500
(C) 500 < V < 700
(D) 700 < V < 900
(E) 900 < V < 1100
Rationale: As we see the answers are in form of range we can use approximation
Volume of cylinder is πr^2h
Given π= 22/7 and r = 3.5 so r^2 ~ 12 and h = 6.5 * 3.5 ~ 23
So 22/7 * 12 * 23 ~ 868
so answer should be
D. 700 < V < 900
Answer : D
Answer: (D) 700 < V < 900
Question: If there are 7 pairs of twins, and a committee will be formed with 3 members. In how many ways this committee formed in a way that no siblings in a group?
(A) 32
(B) 24
(C) 56
(D) 144
(E) 280
Rationale: Firstly, there are 7 ways to choose 3 groups from the 4 groups. Hence 7C3.
Next, with the 3 groups chosen, there are 2^3 choices of choosing either one of the siblings.
Hence, the total number of ways are 7C3 * (2^3) = 280
E
Answer: (E) 280
Question: Rs 1000 is being charged at 50% per annum. what is the interest for 3rd year at compound interest?
(A) 3277
(B) 2667
(C) 1125
(D) 2867
(E) 9996
Rationale: Explanation:
Total amount for two years = \inline 1000(1.5)^2=2250
Now , interest for third year = \inline \frac{2250\times 50\times 1}{100}=1125
Answer: C) 1125
Answer: (C) 1125
Question: The total weight of six nougat nuggets is 3 oz. What is the average (arithmetic mean) weight of one such nougat nugget?
(A) 0.18 oz.
(B) 0.5 oz.
(C) 1.8 oz.
(D) 5 oz.
(E) 18 oz
Rationale: Average = Total/Number of items
= 3/6 = 0.5.
Hence, B
Answer: (B) 0.5 oz.
Question: A tourist purchased a total of $1,400 worth of traveler’s checks in $10 and $50 denominations, During the trip the tourist cashed 7 checks and then lost all of the rest. If the number of $10 checks cashed was one more or one less than the number of $50 checks cashed, what is the minimum possible value of the checks that were lost?
(A) $1,430
(B) $1,310
(C) $1,290
(D) $1,270
(E) $1,170
Rationale: since total cashed checks = 7 ans $10 check cashed = one less or more than $50 checks
Therefore either $10 checks = 3 and $50 checks = 4 OR $10 checks = 4 and $50 checks = 3
using this information 1st option gives us the maximum cashed value therefore if we negate this value from total value we will get minimum value of which checks have lost
Therfore 1400 - 230 = 1170 hence answer is E
Answer: (E) $1,170
Question: From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first is a red card and the second is a king is?
(A) 1/26
(B) 1/24
(C) 1/20
(D) 1/21
(E) 1/21
Rationale: Let E1 be the event of drawing a red card.
Let E2 be the event of drawing a king .
P(E1 ∩ E2) = P(E1) . P(E2)
(As E1 and E2 are independent)
= 1/2 * 1/13 = 1/26
Answer:A
Answer: (A) 1/26
Question: 223.124 x 11.98 Ã· 6.001 + 11.11 = ?
(A) 983.578
(B) 459.121
(C) 781.189
(D) 656.112
(E) 457.358
Rationale: Explanation:
? = 223.124 x 11.98 Ã· 6.001 + 11.11
â‰ˆ (223.124 x 12/6) + 11.11 â‰ˆ 446.248 + 11.11 â‰ˆ 457.358
Answer: Option E
Answer: (E) 457.358
Question: A shop produces sarongs. The daily average production is given by 5n + 20, where n is the number of workers aside from the owner. In the first k days, 500 units are produced, and then 5 workers are added to the team. After another k days, the cumulative total is 800. How many workers were part of the latter production run?
(A) A)6
(B) B)10
(C) C)11
(D) D)21
(E) E)23.5
Rationale: The daily average production is given by 5n + 20- given
In the first k days, 500 units are produced
= (5n+20)K =500
k = 500/5n+20...................................1
5 workers were added = 5(n+5)+20 = 5n +45
cumulative is 1250 .. thus for the current period = 800 -500 = 300
(5n+45)K= 300
k = 300/5n+45........................................2
equate 1 and 2
500/5n+20 = 300 /5n+45
500(5n+45) = 300(5n+20)
2500n + 22500 = 1500n + 6000
1000n = -16500
n = 16
thus n+5 = 21
hence D
Answer: (D) D)21
Question: If 0 < a < b and k = (2a + 4b)/b , which of the following must be true?
(A) k < 2
(B) k < 6
(C) k < 9
(D) k > 9
(E) k > 11
Rationale: Here's another approach:
k = (2a + 4b)/b
= 2a/b + 4b/b
= 2(a/b) + 4
Since 0 < a < b, we know that a/b is less than 1, which means that 2(a/b) is some number less than 2.
So, we get k = (some number less than 2) + 4
From here, we can see that k must be less than 6
Answer: B
Answer: (B) k < 6
Question: an operation * is defined by the equation:
a*b=a-b/a+b, for all numbers a and b such that a is not equal to -b, if a is not equal to -e and a*e=0, then e=?
(A) a) -a
(B) b) -1/a
(C) c) 1/a
(D) d)0
(E) e)a
Rationale: If a*e=0 and a=-e then a-e = o of a=e, so answer E
Answer: (E) e)a