mathewhe/aqua_rat huggingface dataset:
Question: It would take one machine 5 hours to complete a large production order and another machine 4 hours to complete the same order. How many hours would it take both machines, working simultaneously at their respective constant rates, to complete the order?
(A) A 9/20
(B) B 20/9
(C) C 7/19
(D) D 5/21
(E) E 3/4
Rationale: The rate of the first machine is 1/5 job per hour;
The rate of the second machine is 1/4 job per hour;
Thus, the combined rate of the machines is 1/5+1/4=9/20 job per hour, which means that it takes 1/(9/20)=20/9 hours both machines to do the job.
Answer: B.
Answer: (B) B 20/9
Question: Mixture A is 20 percent oil, and mixture B is 60 percent oil. If the two are poured together to create a 4-gallon mixture that contains 40 percent oil, approximately how many gallons of mixture A are in the mixture?
(A) 1.0
(B) 0.8
(C) 0.7
(D) 0.6
(E) 0.5
Rationale: (60-40)/(40-20) = Qa/Qb
20/20 = Qa/Qb
1 = Qa/Qb
Qa = (1/5) * 4 = 4/5 = 0.8 approx
Answer : B
Answer: (B) 0.8
Question: A car started running at a speed of 30 km/hr and the speed of the car was increased by 2 km/hr at the end of every hour. Find the total distance covered by the car in the first 12 hours of the journey.
(A) 342 km
(B) 352 km
(C) 642 km
(D) 742 km
(E) 492 km
Rationale: The total distance covered by the car in the first 12 hours = 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 +48 +50 +52 = sum of 12 terms in AP whose first term is 30 and last term is 52 = 12/2 [30 + 52] = 492 km.
ANSWER:E
Answer: (E) 492 km
Question: If a sum of money borrowed at 5 percent/annum SI amounts to Rs.1020 in 4 yrs, then the sum of money borrowed is?
(A) Rs. 850
(B) Rs. 960
(C) Rs. 1000
(D) Rs. 1200
(E) Rs. 1230
Rationale: Sol We have, A : Rs.1U2D
Let the pr xnpal be R5 x
Then mterest u — 12 : wzo — x
Therefore, by u xglurmula.
_umxx
’ Rx’: (
, _ma>< 1nzn—xv
\4Ve|\a\e,Jc— 5“
:> ~(:51DD—S*(or6x:51UU
or, J: : w 350
. The sum of money burrowed : Rs. 850
A)
Answer: (A) Rs. 850
Question: 3 pig’s and 10 hens are brought for Rs.1200. If the average price of a hen be Rs.30. What is the average price of a pig.
(A) 300
(B) 350
(C) 400
(D) 425
(E) 275
Rationale: Explanation:
Average price of a hen = Rs.30
total price of 10 hens = 10*30 = Rs.300
But total price of 3 pigs and 10 hens = Rs. 1200
Total price of 3 pigs is = 1200 - 300
= 900
Average price of a pig = 900/3
= Rs. 300
Answer: A
Answer: (A) 300
Question: A girl swims downstream 48 km and upstream 18 km taking 6 hours each time; what is the speed of the current?
(A) 2.2
(B) 2.3
(C) 2.1
(D) 2.5
(E) 2.4
Rationale: 48 --- 6 DS = 8
? ---- 1
18 ---- 6 US = 3
? ---- 1 S = ?
S = (8 - 3)/2 = 2.5
Answer:D
Answer: (D) 2.5
Question: Which of the following numbers is divisible by each one of 3, 7, 9 and 11 ?
(A) 2079
(B) 456
(C) 974
(D) 562
(E) 300
Rationale: 639 is not divisible by 7
2079 is divisible by each of 3, 7, 9, 11.
ANSWER A
Answer: (A) 2079
Question: If y ¤ q = y^(2q) for all positive integers, then (3 ¤ 4) ¤ 2 =
(A) 3^8
(B) 3^12
(C) 3^16
(D) 3^24
(E) 3^32
Rationale: y ¤ q = y^(2q)
3 ¤ 4 = 3^(8)
(3 ¤ 4) ¤ 2 = (3^8) ¤ 2 = (3^8)^4 = 3^32
Correct Option: E
Answer: (E) 3^32
Question: Two interconnected, circular gears travel at the same circumferential rate. If Gear A has a diameter of 10 centimeters and Gear B has a diameter of 50 centimeters, what is the ratio of the number of revolutions that Gear A makes per minute to the number of revolutions that Gear B makes per minute?
(A) 1:5
(B) 9:25
(C) 5:1
(D) 25:9
(E) Cannot be determined from the information provided
Rationale: Same circumferential rate means that a point on both the gears would take same time to come back to the same position again.
Hence in other words, time taken by the point to cover the circumference of gear A = time take by point to cover the circumference of gear B
Time A = 2*pi*25/Speed A
Time B = 2*pi*5/Speed B
Since the times are same,
50pi/Speed A = 10pi/Speed B
SpeedA/Speed B = 50pi/30pi = 5/1
Correct Option: C
Answer: (C) 5:1
Question: If x/y = 5/3, then (x + y)/(x - y) = ?
(A) 4
(B) 1/5
(C) -1/6
(D) -1/5
(E) -5
Rationale: Any x and y satisfying x/y = 5/3 should give the same value for (x + y)/(x - y).
Say x=5 and y=3, then (x + y)/(x - y) = (5 + 3)/(5-3) = 4.
Answer: A.
Answer: (A) 4
Question: For all even numbers n, h(n) is defined to be the sum of the even numbers between 4 and n, inclusive. What is the value of h(12)/h(10) ?
(A)  1.8
(B)  3
(C)  6
(D)  1.5
(E)  60
Rationale: CONCEPT: When terms are in Arithmetic Progression (A.P.) i.e. terms are equally spaced then
Mean = Median =(First+Last)/2
and Sum = Mean*Number of terms
h(12) = [(4+12)/2]*5 = 40
h(10) = (4+10)/2]*4 = 28
h(12)/h(10) = (40) / (28) ~ 1.5
Answer : D
Answer: (D)  1.5
Question: Last year, sales at Company X were 10% greater in February than in January, 15% less in March than in Feb, 20% greater in April than in March, 10% less in May than in April, and 5% greater in June than in May. In which month were sales closest to Jan?
(A) Feb
(B) Mar
(C) Apr
(D) May
(E) June
Rationale: Jan = $100
10% greater in February than in January ---> Feb = 1.1 Jan = $110
15% less in March than in Feb ---> Mar = 0.85 Feb = $93.5
20% greater in April than in March ---> Apr = 1.2 Mar = $112
10% less in May than in April ---> May = 0.9 Apr = $101 (we have a winner)
5% greater in June than in May --->Jun = 1.05 May = $106
Ans D
Answer: (D) May
Question: A boat running downstream covers a distance of 12 km in 2 hours while for covering the same distance upstream, it takes 3 hours. What is the speed of the boat in still water?
(A) 8 kmph
(B) 5 kmph
(C) 4 kmph
(D) 6 kmph
(E) 7 kmph
Rationale: Speed downstream =12/2 = 6 kmph
Speed upstream =12/3 = 4 kmph
Speed of the boat in still water = 6+4 / 2= 5 kmph
ANSWER:B
Answer: (B) 5 kmph
Question: The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greater number is:
(A) 101
(B) 107
(C) 111
(D) 185
(E) none
Rationale: EXPLANATION
Let the numbers be 37a and 37b.
Then, 37a x 37b = 4107
ab = 3.
Now, co-primes with product 3 are (1, 3).
So, the required numbers are (37 x 1, 37 x 3) i.e., (37, 111).
Greater number = 111.
Answer C
Answer: (C) 111
Question: A person walking takes 26 steps to come down on a escalator and it takes 30 seconds for him for walking. The same person while running takes 18 second and 34 steps. How many steps are there in the escalator?
(A) 45 steps
(B) 46 steps
(C) 47 steps
(D) 48 steps
(E) 49 steps
Rationale: 26+30n=18+34n
12n=8
n=2/3 substitute n valve
26+30(2/3)=46 steps
ANSWER:B
Answer: (B) 46 steps
Question: The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be:
(A) 12 years
(B) 14 years
(C) 16 years
(D) 18 years
(E) 20 years
Rationale: Let the present age of son =x
present age of father (60 -x)
Then, (60 - x) - 6 = 5(x - 6)
54 - x = 5x - 30
6x = 84
x = 14.
Son's age after 6 years = (x+ 6) = 20 years
Answer :E
Answer: (E) 20 years
Question: A man can row upstream at 8kmph and downstream at 13 kmph. The speed of the stream is
(A) 2.5 km/hr
(B) 4.2 km/hr
(C) 5 km/hr
(D) 10.5 km/hr
(E) None
Rationale: Sol.
Speed of stream = 1/2(13 -8) kmph = 2.5 kmph.
Answer A
Answer: (A) 2.5 km/hr
Question: How much water must be mixed in 300 ml of sugar solution which contains 40% sugar by Weight, such that it becomes a 30% sugar solution?
(A) 50 ml
(B) 75 ml
(C) 90 ml
(D) 100 ml
(E) 120 ml
Rationale: Total Quantity = 300 ml
Sugar by weight = 120 ml
Water= 180 ml
Let x be the amount of water added to the solution
Then 120/(300 + x)=30/100
=>1200 = 900 + 3x
=>x= 100 ml
ANSWER:D
Answer: (D) 100 ml
Question: The harmonic mean of two numbers xx and yy, symbolized as h(x,y)h(x,y), is defined as 2 divided by the sum of the reciprocals of xx and yy, whereas the geometric mean g(x,y)g(x,y) is defined as the square root of the product of xx and yy (when this square root exists), and the arithmetic mean m(x,y)m(x,y) is defined as x+y2x+y2. For which of the following pairs of values for xx and yy is g(x,y)g(x,y) equal to the arithmetic mean of h(x,y)h(x,y) and m(x,y)m(x,y)?
(A) x=−2 y=−1
(B) x=−1, y=2
(C) x=2, y=8
(D) x=8, y=8
(E) x=8, y=64
Rationale: A. x=−2 , y=−1
B. x=−1 , y=2
C. x=2 , y=8
D. x=8 , y=8
E. x=8 , y=64
The arithmetic mean, the geometric mean and the harmonic mean of two equal numbers are equal((x+x)/2=x, sqrt(x*x)=x, (2x*x)/(x+x)=x).
So without tedious calculation, (D) should be answer.
Answer: (D) x=8, y=8
Question: Two pipes A and B can fill a tank in 15 min and 20 min respectively. Both the pipes are opened together but after 4 min, pipe A is turned off. What is the total time required to fill the tank?
(A) 14 min 49 sec
(B) 14 min 70 sec
(C) 14 min 41 sec
(D) 14 min 40 sec
(E) 24 min 40 sec
Rationale: Part filled in 4 minutes = 4(1/15 + 1/20) = 7/15
Remaining part = 1 - 7/15 = 8/15
Part filled by B in 1 minute = 1/20
1/20 : 8/15 :: 1 ; x
x = 8/15 * 1 * 20 = 10 2/3 min = 10 min 40 sec.
The tank will be full in (4 min. + 10 min. 40 sec) = 14 min 40 sec.
Answer:D
Answer: (D) 14 min 40 sec
Question: The first flight out of Phoenix airport had a late departure. If the next three flights departed on-time, how many subsequent flights need to depart from Phoenix on-time, for the airport's on-time departure rate to be higher than 60%?
I will see what is the quickest way to solve it then I will provide the explanation
(A) 6
(B) 7
(C) 9
(D) 4
(E) 11
Rationale: The following approach might be the easiest one and less error prone.
We need on-time departure rate to be higher than 6/10, so it should be at least 7/11, which means that 7 out of 11 flights must depart on time. Since for now 3 out of 4 flights departed on time then 7-3=4 subsequent flights need to depart on-time.
Answer: D
Answer: (D) 4
Question: How many liters of water must be added to 20 liters of milk and water containing 10% water to make it 50% water?
(A) 10
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: By rule of alligation:
50% - 10% = 40%
100% - 50% = 50%
Quantity of pure water : Quantity of the mixture = 4 : 5
There are 20 liters of mixture, so we need to add 16 liters of pure water.
The answer is D.
Answer: (D) 16
Question: If x and y are integers and 3^(x-5) = 3^(y+2), what is y in terms of x?
(A) x - 6
(B) x - 7
(C) x - 2
(D) x + 2
(E) x + 6
Rationale: Answer: A
3^(x-5) = 3^(y+2)
Since the base is the same, I isolated the equations and solved for y.
x-5 = y+2
y=x-7
Ans : B
Answer: (B) x - 7
Question: Each of three investments has a 20% of becoming worthless within a year of purchase, independently of what happens to the other two investments. If Simone invests an equal sum Q in each of these three investments on January 1, the approximate chance that by the end of the year, she loses no more than 1/3 of her original investment is
(A) 90%
(B) 80%
(C) 70%
(D) 60%
(E) 40%
Rationale: The problem asks for the approximate chance that no more than 1/3 of the original investment is lost. We can apply the “1 – x” technique: what’s the chance that more than 1/3 of the original investment is lost? There are two outcomes we have to separately measure:
(a) All 3 investments become worthless.
(b) 2 of the 3 investments become worthless, while 1 doesn’t.
Outcome (a): The probability is (0.2)(0.2)(0.2) = 0.008, or a little less than 1%.
Outcome (b): Call the investments X, Y, and Z. The probability that X retains value, while Y and Z become worthless, is (0.8)(0.2)(0.2) = 0.032. Now, we have to do the same thing for the specific scenarios in which Y retains value (while X and Z don’t) and in which Z retains value (while X and Y don’t). Each of those scenarios results in the same math: 0.032. Thus, we can simply multiply 0.032 by 3 to get 0.096, or a little less than 10%.
The sum of these two probabilities is 0.008 + 0.096 = 0.104, or a little more than 10%. Finally, subtracting from 100% and rounding, we find that the probability we were looking for is approximately 90%.
The correct answer is A.
This problem illustrates the power of diversification in financial investments. All else being equal, it’s less risky to hold a third of your money in three uncorrelated (independent) but otherwise equivalent investments than to put all your eggs in one of the baskets. That said, be wary of historical correlations! Housing price changes in different US cities were not so correlated—and then they became highly correlated during the recent housing crisis (they all fell together), fatally undermining spreadsheet models that assumed that these price changes were independent.
Answer: (A) 90%
Question: Nitin borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of eleven years is Rs. 8160, how much money did he borrow?
(A) 8000
(B) 80288
(C) 2668
(D) 2600
(E) 2781
Rationale: Let the sum be Rs. x. Then,
[(x * 6 * 3)/100] + [(x * 9 * 5)/100] + [(x * 13 * 3)/100] = 8160
18x + 45x + 39x = (8160 * 100)
102x = 816000 => x = 8000.
Answer:A
Answer: (A) 8000
Question: The ratio between the sale price and the cost price of an article is 12:7. What is the ratio between the profit and the cost price of that article?
(A) 2:9
(B) 2:5
(C) 3:6
(D) 5:7
(E) 2:1
Rationale: Let C.P. = Rs. 7x and S.P. = Rs. 12x.
Then, Gain = Rs. 5x
Required ratio = 5x : 7x = 5:7
Answer:D
Answer: (D) 5:7
Question: For the past n days, the average (arithmetic mean) daily production at a company was 60 units. If today's production of 90 units raises the average to 62 units per day, what is the value of n ?
(A) 30
(B) 14
(C) 10
(D) 9
(E) 7
Rationale: (average production for n days) * n = (total production for n days) --> 60n=(total production for n days);
(total production for n days) + 90 = (average production for n+1 days) * (n+1) -->60n + 90 = 62 * (n+1) --> n=14.
Or as 30 extra units increased the average for n+1 days by 2 units per day then 30/(n+1)=2 --> n=14.
Answer: B.
Answer: (B) 14
Question: During a certain week, a seal ate 45% of the first 80 smelt it came across, and 30% of the remaining smelt it came across. If the seal ate 40% of the smelt it came across during the entire week, how many smelt did it eat?
(A) 32
(B) 48
(C) 55
(D) 64
(E) 80
Rationale: Total smelt = x.
Then, 0.45*80+0.3(x-80)=0.4*x --> x=120 --> 0.4*x=48.
Answer: B.
Answer: (B) 48
Question: At present, the ratio between the ages of Arun and Deepak is 4:3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present?
(A) 77 years
(B) 15 years
(C) 66 years
(D) 88 years
(E) 55 years
Rationale: Let the present ages of Arun and Deepak be 4x and 3x years respectively.
Then, 4x + 6 = 26 => x = 5
Deepak's age = 3x = 15 years.
Answer: B
Answer: (B) 15 years
Question: The mean of four integers A will not change if all the integers are multiplied by any constant. What is always true about this set of numbers?
I. The mean of the set is 0
II. The sum of the largest member and the smallest member of the set is 0
III. The set contains both positive and negative integers
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II, and III
Rationale: If we consider a set {1,2,3,4}, when multiplied with a constant we take that constant as 1 and multiply resulting set will contain the same numbers as the original. so how can the answer be I only.....A
Answer: (A) I only
Question: The average of five numbers is 281. The average of the first two numbers is 280 and the average of last two numbers is 178.5. What is the third number?
(A) 27
(B) 88
(C) 16
(D) 19
(E) 11
Rationale: Answer:B
Answer: (B) 88
Question: a is an integer greater than 9 but less than 21, b is an integer greater than 19 but less than 31, what is the range of a/b?
(A) 1/4
(B) 1/2
(C) 2/3
(D) 1
(E) 5/4
Rationale: min value of a/b will be when b is highest and a is lowest ---> a=10 and b=30
So, a/b = 1/3
max value of a/b will be when b is lowest and a is highest ---> a=20 and b=20
So, a/b = 1
Range is 1-(1/3) = 2/3.
Answer should be C
Answer: (C) 2/3
Question: A certain manufacturer increased its gross profit on a product from 10 percent of the cost of the product to 15 percent of the cost by changing the selling price. If the new selling price was $92.00 and the cost of the product remained the same, what was the old selling price?
(A) $77.40
(B) $80.00
(C) $83.64
(D) $87.40
(E) $88.00
Rationale: Given that {cost of the product}*1.15=$92 --> {cost of the product}=$80.
The old price was $80*1.1=$88.
Answer: E.
Answer: (E) $88.00
Question: Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is?
(A) 11
(B) 77
(C) 60
(D) 12
(E) 14
Rationale: Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(100 + 100)/8 = 3x => x = 25/3.
So, speed of the faster train = 50/3 = 50/3 * 18/5 = 60 km/hr.
Answer:C
Answer: (C) 60
Question: A bottle contains a certain solution. In the bottled solution, the ratio of water to soap is 3:5, and the ratio of soap to salt is four times this ratio. The solution is poured into an open container, and after some time, the ratio of water to soap in the open container is quartered by water evaporation. At that time, what is the ratio of water to salt in the solution?
(A) 9:100
(B) 100:9
(C) 12:100
(D) 12:20
(E) 13:100
Rationale: Water:soap = 3:5
Soap:Salt=12:20
=> For 12 soap, salt = 20
=> For 5 Soap, salt = (20/12)*5 = 100/12=25/3
So, water:soap:salt = 3:5:25/3 = 9:15:25
After open container, water:soap:salt = 2.25:15:25
So, water:salt = 2.25:25 = 9:100
ANSWER:A
Answer: (A) 9:100
Question: A sum of 1200 lent at S.I at 10% will become twice in how many years?
(A) 12 years
(B) 14 years
(C) 10 years
(D) 8 years
(E) 7 years
Rationale: Explanation:
To become twice means S.I should be as much as initial sum i.e, 1200
(1200 x 10 x T)/100 = 1200
T = 10 years
Answer: Option C
Answer: (C) 10 years
Question: The banker's discount on a certain sum due 2 years hence is 11/10 of the true discount.The rate percent is
(A) 11%
(B) 10%
(C) 5%
(D) 5.5%
(E) 6%
Rationale: Solution
Let T.D be Rs 1.Then, B.D	=Rs.11 / 10
= Rs.1.10.
Sum	=Rs.(1.10 x 1/ 1.10-1)
= Rs.(110 / 10)
= Rs. 11.
S.I on Rs.11 for 2 years is Rs.1.10.
Rate	=(100 x 1.10 / 11 x 2)%
= 5%
Answer C
Answer: (C) 5%
Question: A is a working partner and B is a sleeping partner in the business. A puts in Rs.15000 and B Rs.25000, A receives 10% of the profit for managing the business the rest being divided in proportion of their capitals. Out of a total profit of Rs.9600, money received by A is?
(A) 1797
(B) 2970
(C) 2782
(D) 4200
(E) 2081
Rationale: 15:25 => 3:5
9600*10/100 = 960
9600 - 960 = 8640
8640*3/8 = 3240 + 960
= 4200
Answer:D
Answer: (D) 4200
Question: A certain bacteria colony doubles in size every day for 20 days, at which point it reaches the limit of its habitat and can no longer grow. If two bacteria colonies start growing simultaneously, how many days will it take them to reach the habitat’s limit?
(A) 6.33
(B) 7.5
(C) 10
(D) 15
(E) 19
Rationale: simultaneous grow = same amount of time
In 20 days we should expect to have P(2)^20
So if we have two things doing the job of getting us there then;
2^x + 2^x = 20
2(2)^x=2
2^(x+1)=2^20
x+1 = 20
x = 19;
ANSWER:E
Answer: (E) 19
Question: A committee is reviewing a total of 20x black-and-white films and 6y color films for a festival. If the committee selects y/x% of the black-and-white films and all of the color films, what fraction E of the selected films are in color?
(A) 1/130
(B) 1/5
(C) 3/13
(D) 10/13
(E) 30/31
Rationale: It's y/xpercentnot y/x.
If x=20 and y=10. Then:
20x=400 black-and-white films;
6y=60 color films.
y/x%=10/20%=0.5% of the black-and-white films, so 2 black-and-white films and all 60 color films, thus total of 62 films were selected.
Color films thus compose E=60/62=30/31 of the selected films.
Answer: E.
Answer: (E) 30/31
Question: A teacher will pick a group of 3 students from a group of 7 students that includes Bart and Lisa. If one of all the possible 3-student groups is picked at random, what is the probability of picking a group that includes both Bart and Lisa?
(A) 1/7
(B) 3/14
(C) 1/4
(D) 1/3
(E) 3/7
Rationale: Probability = Favorable Outcomes / Total Outcomes
Total Outcomes= Total No. of ways of Picking Group of 3 out of 7 = 7C3 = 7! / (4! * 3!) = 35
Favorable Outcomes= Total No. of ways of Picking Group of 3 out of 7 such that B and L are always in the group (i.e. we only have to pick remaining two out of remaining 5 as B and L must be there is group) = 5C1 = 5
Hence,Probability=5/35=1/7
Answer: Option A
Answer: (A) 1/7
Question: A cricketer has a certain average for 10 innings. In the eleventh inning, he scored 108 runs, thereby increasing his average by 6 runs. His new average is :
(A) 45 runs
(B) 46 runs
(C) 48 runs
(D) 49 runs
(E) 47 runs
Rationale: 10(x-8) + 108 = 11x , x = 48 . This is the shortest way
or
10*6=60 runs for 10 innings and 108 in 11th innings then 108-60=48 runs
ANSWER:C
Answer: (C) 48 runs
Question: A thief is spotted by a policeman from a distance of 175 meters. When the policeman starts the chase, the thief also starts running. If the speed of the thief be 8km/hr and that of the policeman 10 km/hr, how far the thief will have run before he is overtaken?
(A) 350m
(B) 200m
(C) 400m
(D) 700m
(E) None of them
Rationale: Relative speed of the policeman = (10-8) km/hr =2 km/hr.
Time taken by police man to cover
(175m/1000) x 1/2 hr = 7/80hr.
In 7/80 hrs, the thief covers a distance of 8 x 7/80 km = 7/10 km = 700 m
Answer is D.
Answer: (D) 700m
Question: What is the 4 digit number in which the 1st digit is 1/3 of the second, the 3rd is the sum of the 1st and 2nd, and the last is three times the second?
(A) 1100
(B) 1200
(C) 1349
(D) 1430
(E) 1340
Rationale: First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9.
First + second = third => we can eliminate 3 & 9 since 3 + 9 = 12.
Last is 3 times the second => we can eliminate option 2 & 6 since 3 * 6 = 18.
Hence the number is 1349
C
Answer: (C) 1349
Question: Consider the set (0.34,0.304,0.034,0.43) The sum of the smallest and largest numbers
in the set is
(A) 0.77
(B) 0.734
(C) 0.077
(D) 0.464
(E) 0.338
Rationale: Since each of the numbers in the set is between 0 and 1, then the tenths digit of each number
contributes more to its value than any of its other digits.
The largest tenths digit of the given numbers is 4, and so 0.43 is the largest number in the set.
The smallest tenths digit of the given numbers is 0, so 0.034 is the smallest number in the set.
Therefore, the sum of the smallest number in the set and the largest number in the set is
0.034 + 0.43 = 0.464
correct answer D
Answer: (D) 0.464
Question: If the perimeter of a rectangular garden is 800 m, its length when its breadth is 100 m is?
(A) 286 m
(B) 899 m
(C) 300 m
(D) 166 m
(E) 187 m
Rationale: 2(l + 100) = 800 => l
= 300 m
Answer: C
Answer: (C) 300 m
Question: Bill has 75 cents in his pocket. He walks up to a food stand and asks how much for a hot dog. The vendor just raised the price of his hot dogs by 10% but believes Bill is down on his luck and so he sells the hot dog to Bill for 75 cents which is exactly 75% of his new price for hot dogs. What is the difference in the new price of hot dogs and the price the vendor sold a hot dog to Bill for?
(A) 8.5%
(B) 17.5%
(C) 12.5%
(D) 14.5%
(E) 15.0%
Rationale: Quantity X Rate = Price
1 X 1 = 1
0.75 X 1.10 = 0.825
Decrease in price = (0.175/1) Ã— 100 = 17.5%
Answer = Option B
Answer: (B) 17.5%
Question: Lake A has a duck population of 30 females and 30 males. Lake B’s duck population consists of the same ratio of females to males. If 6 new female ducks are added to Lake B and no other ducks are added or removed, the new total duck population of Lake B could be which of the following?
(A) 144
(B) 105
(C) 78
(D) 72
(E) 36
Rationale: Lake A has a duck population of 30 females and 36 males --> the ratio is F:M = 30:30 = 1:1.
Lake B’s duck population consists of the same ratio of females to males --> F:M = 1:1.
D
Answer: (D) 72