mathewhe/aqua_rat huggingface dataset:
Question: A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 350 m long platform?
(A) 11
(B) 77
(C) 36
(D) 47
(E) 99
Rationale: Let the length of the train be x m.
When a train crosses an electric pole, the distance covered is its own length.
So, x = 12 * 36 * 5 /18 m = 120 m.
Time taken to cross the platform = (120 +350)/ 36 * 5/18 = 47 min.
Answer:D
Answer: (D) 47
Question: Among the employees of a certain company, 50 percent of the employees are male and 48 percent are female. In this company 70 percent of the male employees are married and 50 percent of the female employees are married. If one employee in the company is randomly selected, approximately what is the probability that he or she is NOT married?
(A)  0.3
(B)  0.4
(C)  0.5
(D)  0.6
(E)  0.7
Rationale: Much faster: draw 4 quadrants
______________Male (50%)_____Female (50%)
Married :__________70%____________50%
Not Married:_______30%____________50%
Therefore: the probability of picking one random person Not Married (he or she) is: 0,50 x 0,30 + 0,50 x 0,50 = 0,15 + 0,25 (approx.)
Solution: approx. 0,4 (answer B)
Answer: (B)  0.4
Question: The sale price of an article including the sales tax is Rs. 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 12%, then the cost price of the article is:
(A) 500
(B) 277
(C) 266
(D) 288
(E) 261
Rationale: 110% of S.P. = 616
S.P. = (616 * 100)/110 = Rs. 560
C.P = (110 * 560)/112 = Rs. 500.Answer: A
Answer: (A) 500
Question: subash can copy 50 pages in 10 hrs.subash and prakash together can copy 300 pages in 40 hours.in how much time prakash can copy 20 pages.
(A) 8
(B) 10
(C) 12
(D) 14
(E) 16
Rationale: subhas 's 1 hr copy page=50/10=5 page
(subhas+prakash)'s 1 hr copy page=300/40=7.5 page
from above prakash's 1 hr copy page= 2.5 page
so time taken in 20 page's copy =(20/2.5)=8 hrs
ANSWER :A
Answer: (A) 8
Question: When a 186 meters long rod is cut down into small pieces of length 2.0 meters each. Then how many pieces are available ?
(A) 52
(B) 68
(C) 62
(D) 67
(E) 93
Rationale: Answer
No. of pieces = Total length / Length of each piece
= 186/2.0
= 93
Option: E
Answer: (E) 93
Question: The measurement of a rectangular box with lid is 25cmx24cmx18cm. Find the volume of the largest sphere that can be inscribed in the box (in terms of πcm3). (Hint: The lowest measure of rectangular box represents the diameter of the largest sphere)
(A) 288
(B) 2302
(C) 2304
(D) 8640
(E) 964
Rationale: d=24, r=12;
Volume of the largest sphere= 4/3πr3
= 4/3 *π*12*12*12= 2304πcm3 ANSWER:C
Answer: (C) 2304
Question: A basketball team scored x points per game in its first n games of the season, and in all the following games it scored an average (arithmetic mean) of y points per game. What was the average number of points per game in its first n + 6 games?
(A) x + 3y/(n + 3)
(B) x + y/(n + 3)
(C) (x + 3y)/(n + 3)
(D) (nx + 3y)/(n + 6)
(E) (3x + ny)/(n + 3)
Rationale: Total points in first n games = nx
Total marks in next 3 games is 3y
So, Average marks in n + 6 games = (nx+3y)/(n+6)
Hence, correct answer will be (D)
Answer: (D) (nx + 3y)/(n + 6)
Question: Of the films Empty Set Studios released last year, 60% were comedies and the rest were horror films. 75% of the comedies were profitable, but 75% of the horror moves were unprofitable. If the studio made a total of 42 films, and broke even on none of them, how many of their films were profitable?
(A) 18
(B) 19
(C) 20
(D) 21
(E) 41
Rationale: After fiddling some more, this is how I got to answer choice E...but did I get here using voodoo math or is it sound?
(.60*.75) + (.40*.25) = .44 + .10 = .55
55/100 = 11/20
Then subtract from 42:
42 - 11/20 = 41 (answer E)
Answer: (E) 41
Question: There are 40 people and 3 clubs M, S, and Z in a company. 12 people joined M, 14 people joined S and 7 people joined Z. If the members of M did not join any other club, at most, how many people of the company did not
join any club?
(A) 22
(B) 20
(C) 18
(D) 16
(E) 14
Rationale: Answer E.
key is 'atmost' here.
so 12 people joined M.
14 people joined S and 7 people joined Z. to get maximum people who did not join any club, 7 people who joined Z are among 14 people who joined S.
so 14+12 = 26
40-26 = 14
Answer: (E) 14
Question: A mother and father have seven children, and the family receives an invitation with four tickets to the circus. If the family decides to randomly select the four members who get to attend the circus, but determine that the chosen group must include at least one of the mother and father, how many different groups are possible to send to the circus?
(A) 70
(B) 84
(C) 91
(D) 108
(E) 126
Rationale: Condition 1: Atleast one of the mother and father along with seven children must be selected
Then either - Mother or father = 2C1 = 2 ways for one ticket and 7C3 = 35 ways for other three tickets. Total ways here is 2*35 = 70
Condition 2: Both M and F selected and this is 1 way...then we'll have only two tickets for 7 children..then we can select 7C2 = 21.
Total 70+21 = 91.
Option C.
Answer: (C) 91
Question: In how many ways Chief Minister and Minister be elected from a team of 12 members?
(A) 128
(B) 134
(C) 132
(D) 167
(E) 169
Rationale: To do this, if captain is elected first, then we have 12 ways of doing this.
For election of vice-captain, we have only 11 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 12*11 = 132 ways.
C
Answer: (C) 132
Question: What is the rate percent when the simple interest on Rs.800 amount to Rs.160 in 4 Years?
(A) 5%
(B) 6%
(C) 4 1/2%
(D) 3 1/2 %
(E) 4%
Rationale: 160 = (180*4*R)/100
R = 5%
Answer:A
Answer: (A) 5%
Question: A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. Find the length of train ?
(A) 45 m
(B) 50 m
(C) 55 m
(D) 60 m
(E) 65 m
Rationale: Explanation:
First person speed = 2*(5/18) = 5/9 m/sec
Second person speed = 4*(5/18) = 10/9 m/sec
Let the length of train is x metre and speed is y m/sec
then,
x /y−5/9=9
=>9y−5=x
=>9y−x=5.....(i)Also,
x /y−10/9=10
90y−9x=100.....(ii)from (i) and (ii), we get,x=50
So length of train is 50 metre
Option B
Answer: (B) 50 m
Question: If the mean of numbers 28, x, 70, 88 and 104 is 67, what is the mean of 50, 62, 97, 124 and x?
(A) 76.5
(B) 75.6
(C) 73.5
(D) 79
(E) 77
Rationale: Mean = (Sum of all no. in series)/(no. in series)
M1 = 67 = (X+28+70+88+104)/(5)
67 x 5 = 290 + X
X = 45
Therefore mean of 2nd series
M2 = (X+50+62+97+124)/5
M2 = 75.6
Answer = B
Answer: (B) 75.6
Question: A dishonest shopkeeper professes to sell pulses at the cost price, but he uses a false weight of 920gm. for a kg.His gain is …%.
(A) 5.26%
(B) 5.36%
(C) 4.26%
(D) 6.26%
(E) 8.69%
Rationale: His percentage gain is 100*80/920 as he is gaining 80 units for his purchase of 920 units.
so 8.69%.
ANSWER:E
Answer: (E) 8.69%
Question: A bag contains 10 red jellybeans and 10 blue jellybeans. If 3 jellybeans are removed one at a time, at random and are not replaced, what is the probability T that all 3 jellybeans removed from the bag are blue?
(A) 9/100
(B) 2/19
(C) 1/8
(D) 3/20
(E) 3/10
Rationale: Method-1
10 red jellybeans and 10 blue jellybeans
Total Outcomes = No. of ways to choose 3 Jelly bean at random out of a total 20 jellybeans = 20C3 = 1140
Favourable Outcomes = No. of ways to choose 3 Jelly bean such that they are all Blue out of 10 Blue = 10C3 = 120
Probability = Favourable Outcomes / Total Outcomes = 10C3 / 20C3
Probability T= 120 / 1140 = 2/19
Answer: option B
Method-2
Probability of First jelly bean to be Blue = 10/20 [Total 10 Blue out of total 20 jellybeans]
Probability of Second jelly bean to be Blue = 9/19 [Total 9 Blue remaining out of total 19 jellybeans remaining]
Probability of Third jelly bean to be Blue = 8/18 [Total 8 Blue remaining out of total 18 jellybeans remaining]
Required Probability = (10/20)*(9/19)*(8/18) = 2/19
Answer: option B
Answer: (B) 2/19
Question: 817 + 8.017 + 0.817 + 8.0017 = ?
(A) 839.3657
(B) 833.8357
(C) 839.6357
(D) 819.5637
(E) 819.6753
Rationale: 817
8.017
0.817
+ 8.0017
--------
833.8357
---------
Answer is B
Answer: (B) 833.8357
Question: How many five-digit numbers are there, if the two leftmost digits are even, the other digits are odd and the digit 2 cannot appear more than once in the number.
(A) 2200
(B) 2295
(C) 2375
(D) 2380
(E) 2385
Rationale: N=(4*5-1)*5*5*5=2375
where
4 cases of first digit {2,4,6,8}
5 cases of second digit {0,2,4,6,8}
1 case of 22 for two leftmost digit
5 cases of third digit {1,3,5,7,9}
5 cases of fourth digit {1,3,5,7,9}
5 cases of fifth digit {1,3,5,7,9}
C
Answer: (C) 2375
Question: Two numbers A and B are such that the sum of 7% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B.
(A) 2 : 1
(B) 1 : 2
(C) 4 : 9
(D) 1 : 1
(E) 3 : 2
Rationale: Explanation:
7% of A + 4% of B = 2/3(6% of A + 8% of B)
7A/100 + 4B/100 = 2/3(6A/100+8B/100)
⇒7A + 4B = 2/3(6A + 8B)
⇒21A + 12B = 12A + 16B
⇒ 9A = 4B
⇒ AB = 4/9
⇒ A:B=4:9
Answer: Option C
Answer: (C) 4 : 9
Question: Two identical circles intersect such that their centers and the points at which they intersect form a square of side 3 cm. What is the area of the region where the two circles intersect?
(A) 9 - pi
(B) 9pi - 9
(C) 4.5pi - 9
(D) 9 - 2pi
(E) pi^2 - 3
Rationale: Drawing a diagram, we see that the radius of the circle equals the side of the square.
The area of intersection is: pi*r^2/4 - (r^2-pi*r^2/4) = pi*r^2/2 - r^2 = 4.5pi - 9
The answer is C.
Answer: (C) 4.5pi - 9
Question: Q is as much younger than R as he is older than T. If the sum of the ages of R and T is 50 years, what is definitely the difference between R and Q’s age?
(A) 1 year
(B) 2 years
(C) 25 years
(D) Data inadequate
(E) None of these
Rationale: EXPLANATION
Given that:
1. The difference of age b/w R and Q = The difference of age b/w Q and T.
2. Sum of age of R and T is 50 i.e. (R + T) = 50.
Question: R – Q = ?.
Explanation:
R – Q = Q – T
(R + T) = 2Q
Now given that, (R + T) = 50
So, 50 = 2Q and therefore Q = 25.
Question is (R – Q) = ?
Here we know the value(age) of Q (25), but we don’t know the age of R.
Therefore, (R-Q) cannot be determined.
Answer D
Answer: (D) Data inadequate
Question: All the water in container A which was filled to its brim was poured into two containers B and C. The quantity of water in container B was 62.5% less than the capacity of container A. If 149 liters was now transferred from C to B, then both the containers would have equal quantities of water. What was the initial quantity of water in container A?
(A) 1289
(B) 1192
(C) 281
(D) 1184
(E) 282
Rationale: Explanation:
B has 62.5% or (5/8) of the water in A. Therefore, let the quantity of water in container A(initially) be 8k.
Quantity of water in B = 8k - 5k = 3k.
Quantity of water in container C = 8k - 3k = 5k
Container: A B C
Quantity of water: 8k 3k 5k
It is given that if 149 liters was transferred from container C to container B, then both the containers would have equal quantities of water.
5k - 149 = 3k + 149=> 2k = 298 => k = 149
The initial quantity of water in A = 8k = 8 * 149 = 1192 liters.
Answer: Option B
Answer: (B) 1192
Question: On dividing a number by 56, we get 27 as remainder. On dividing the same number by 8, what will be the remainder ?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: Number=56x+27 (∵ since the number gives 27 as remainder on dividing by 56)
=(7×8×x)+(3×8)+3
Hence, if the number is divided by 8, we will get 3 as remainder.
ANSWER:B
Answer: (B) 3
Question: Which of the following CANNOT be the median Q of the four consecutive positive integers w, x, y, and z, where w < x < y < z ?
(A) (w+x)/2 - 1
(B) (w+z)/2
(C) (x+y)/2
(D) (y+z)/2 -1
(E) (w+x+y+z)/4
Rationale: Using the properties of consecutive positive integers we could right away eliminate B,C and E.
(B) - The average of first and last terms is the median
(C) - For even number of integers, the median is the average of middle terms
(E) - The average is equal to median if the integers are consecutive
Remaining answer choices are A and D.
For A, the average of first two consecutive numbers (w,x) will definitely be less than x making it impossible to be a median Q.
Answer (A)
Answer: (A) (w+x)/2 - 1
Question: Machines A and B produce bottles at their respective constant rates. Machine A produces k bottles in 4 hours and machine B produces k bottles in 7 hours. How many hours does it take machines A and B, working simultaneously, to produce 22k bottles?
(A) 48
(B) 52
(C) 56
(D) 60
(E) 64
Rationale: A's rate = k/4
B's rate = k/7
k/4 + k/7 = 11k/28
22k / (11k/28) = 56 hours
The answer is C.
Answer: (C) 56
Question: How many cubes of 20 cm edge can be put in a cubical box of 1 m edge.
(A) 177 cm
(B) 125 cm
(C) 786 cm
(D) 617 cm
(E) 187 cm
Rationale: Number of cubes =100âˆ—100âˆ—100/20âˆ—20âˆ—20=125
Note: 1 m = 100 cm
Answer:B
Answer: (B) 125 cm
Question: A hare and a jackal are running a race. Three leaps of the hare are equal to four leaps of the jackal. For every six leaps of the hare, the jackal takes eleven leaps. Find the ratio of the speed of the hare to the speed of the jackal.
(A) 4:7
(B) 8:11
(C) 5:8
(D) 3:11
(E) 5:2
Rationale: The hare takes 6 leaps and the jackal takes 11 leaps.
1 hare leap = 4/3 jackal leaps
Thus the hare's 6 leaps = 6*(4/3) = 8 jackal leaps.
The ratio of their speeds is 8:11.
The answer is B.
Answer: (B) 8:11
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) 55
(B) 66
(C) 40
(D) 88
(E) 12
Rationale: 800*(25/100) = 200 ---- 5
? ---- 1 => Rs.40
Answer:C
Answer: (C) 40
Question: An artist wishes to paint a circular region on a square poster that is 5 feet on a side. If the area of the circular region is to be 1/2 the area of the poster, what must be the radius of the circular region in feet?
(A) 1/pi
(B) sqrt(2/pi)
(C) 2/sqrt(pi)
(D) sqrt(12.5/pi)
(E) pi/2
Rationale: Area of the poster is 5x5 = 25
1/2 the area = 12.5
pi*r^2 = 12.5
r^2 = 12.5/pi
r = sqrt(12.5/pi) answer (D)
Answer: (D) sqrt(12.5/pi)
Question: Given that r = 98.3, which of the following best approximates the value of r/(2r + 2) ?
(A) 1/4
(B) 1/3
(C) 1/2
(D) 4/7
(E) 2/3
Rationale: r/(2r + 2) = 1/[2+(2/r)] = 1/[2+(2/98.3)]
but 2/98.3 is too small (negligible) in comparison
Hence, 1/[2+(2/98.3)] = 1/2 (approx)
Answer: Option C
Answer: (C) 1/2
Question: r=3^(n+1), then in terms of r, 9^n=
(A) r^2/81
(B) r^2/9
(C) r^2
(D) r/3
(E) r
Rationale: Questions in terms of variables can be easily solved by plugging in some values: Say n = 0
r = 3^1 = 3
and you need the value of 3^n which is 3^0 = 1
So when you put r = 3 in the options, you should get 1. Only option (A) satisfies.
Answer (B)
Answer: (B) r^2/9
Question: 12.5 * 3.2 * 8.8 = ?
(A) 352
(B) 435
(C) 224
(D) 646
(E) 742
Rationale: A
352
? = 12.5 * 3.2 * 8.8 = 352
Answer: (A) 352
Question: The radius of a cylindrical water tank is reduced by 50%. However, the speed by which water is filled into the tank is also decreased by 50%. How much more or less time D will it take to fill the tank now?
(A)  50% less time
(B)  50% more time
(C)  75% less time
(D)  75% more time
(E)  100% more time
Rationale: (VC)Volume of the cylinderical vessal is directly proportional to R^2.
So if radius is 50% less volume will be 1/4th of the original volume.(VC/4)
Now if with velocity V tank can be filled in T1 time of volume VC
So now Velocity is 50% less i..e V/2
So time taken to fill the capacity VC/4 by V/2 velocity is T2.
VT1 = VC
V/2*T2 = VC/4
So T1/T2 = 1/2
So Tank will be filled in less time. that is D=50 % less.A
Answer: (A)  50% less time
Question: There are 720 male and female participants in a meeting. Half the female participants and one-quarterof the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female?
(A) 75
(B) 100
(C) 120
(D) 175
(E) 225
Rationale: Let m be the number of male participants and f be the number of female articipants in the meeting. Thetotal number of participants is given as 720.
Hence, we have m+f= 720
Now, we have that half the female participants and one-quarter of the male participants are Democrats.
Let d equal the number of the Democrats.
Then we have the equation f/2 + m/4 =d
Now, we have that one-third of the total participants are Democrats. Hence, we have the equation
d = 720/3 = 240
Solving the three equations yields the solution
f = 240,m= 480, and d= 240.
The number of female democratic participants equals half the female participants equals
240/2 = 120.
ANSWER:C
Answer: (C) 120
Question: On 8th Dec, 2007 Saturday falls. What day of the week was it on 8th Dec, 2006?
(A) Sunday
(B) Thursday
(C) Tuesday
(D) Friday
(E) KDDSS
Rationale: Explanation:
8th Dec 2007 – 8th Dec 2006 = 52 weeks 1 day. So Dec 8th 2006 is behind one day = Friday
Answer: D
Answer: (D) Friday
Question: Ratio of two numbers x and y is 5:7. If x is increased by 20% and y is increased by 2 then the new ratio becomes 2:3. What is the ratio 3y:(x+6)
(A) 7:8
(B) 8:7
(C) 6:7
(D) 7:6
(E) 2:7
Rationale: Let:
x = 5n
y = 7n
6n/(7n+2) = 2/3
18n = 2*(7n+2)
n = 1
So, x =5; y=7
y/(x+3) = 7/8
Answer = A
Answer: (A) 7:8
Question: Raviraj invested an amount of 100000000 at compound interest rate of 10 pcpa for a period of three years. How much amount will Raviraj get after three years?
(A) 12,310
(B) 13,210
(C) 13,320000
(D) 13,1200000
(E) 133100000
Rationale: Amount = 100000000(1 + 10⁄100)3
= 100000000 × 11⁄10 × 11⁄10 × 11⁄10
= 133100000
Answer E
Answer: (E) 133100000
Question: Maxwell leaves his home and walks toward Brad's house. One hour later, Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 54 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 6 km/h. What is the distance traveled by Maxwell?
(A) 16
(B) 18
(C) 20
(D) 24
(E) 30
Rationale: After the 1st hour, Maxwell has travelled 4 Km. And Brad just left home. So the distance between them = 54 - 4 = 50.
Relative speed = 4 +6 = 10 Kmph.
Now to cover these 50 Kms, they will take 50/10 = 5 Hrs. So in 5 hrs, Maxwell walks 5*4 = 20 Kms.
So total distance travelled by Maxwell = 4 + 20 = 24.
ANSWER:D
Answer: (D) 24
Question: A train 150 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
(A) 7
(B) 6
(C) 8
(D) 2
(E) 4
Rationale: Speed of train relative to man = 60 + 6 = 66 km/hr.
= 66 * 5/18 = 55/3 m/sec.
Time taken to pass the men = 150 * 3/55
= 8 sec.
Answer C
Answer: (C) 8
Question: A batsman makes a score of 86 runs in the 17th inning and thus increases his averages by 3.Find his average after 17th inning?
(A) 19
(B) 29
(C) 38
(D) 49
(E) 59
Rationale: let the average after 17th inning =x
Then average after 16th inning=(x-3)
Therefore 16(x-3)+86=17x
Therefore x=38
ANSWER:C
Answer: (C) 38
Question: Rs.800 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much?
(A) Rs.1056
(B) Rs.1112
(C) Rs.1182
(D) Rs.992
(E) Rs.702
Rationale: Explanation:
(800*3*3)/100 = 72
920 + 72 = 992
ANSWER IS D
Answer: (D) Rs.992
Question: In how many different ways can 3 identical blue pants and 3 identical yellow pants be distributed among 6 children such that each child receives a pair of pants?
(A) 20
(B) 2662
(C) 519
(D) 46
(E) 1
Rationale: 1st Child: 6 has options
2nd Child: 5 has options…
Therefore, for all kids: 6 x 5 x 4 x 3 x 2 = 720 arrangements.
Since the reds are identical, we divide by 3! and since the greens are identical, we divide by another 3!
So, in all, 720/[ 3! X 3! ] = 20 ways.
(e.g. Answer: A)
Answer: (A) 20
Question: The side of a square is increased by 25% then how much % does its area increases?
(A) 56.29 %
(B) 56.25 %
(C) 56.75 %
(D) 58.25 %
(E) 51.25 %
Rationale: a = 100 a2 = 10000
a = 125 a2 = 15625
----------------
10000 --------- 5625
100 -------? => 56.25 %
Answer:B
Answer: (B) 56.25 %
Question: The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?
(A) 4338
(B) 4536
(C) 4538
(D) 4530
(E) 4531
Rationale: Area of the four walls = 2h(l + b)
Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.
Total cost = 906 * 5 = Rs. 4530
Answer: D
Answer: (D) 4530
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
(A) 25
(B) 20
(C) 10
(D) 15
(E) 35
Rationale: M = 15
S = 5
DS = 15 + 5 = 20
Answer: B
Answer: (B) 20
Question: An even positive integer 'x' has 'y' positive integral factors including '1' and the number itself. How many positive integral factors Q does the number 4x have?
(A) 4y
(B) 3y
(C) 16y
(D) 5y
(E) Cannot be determined
Rationale: I tried for x=2,4 and 6. The integral factors Q for x and 4x did not have any specific relation.
My answer is E.
Answer: (E) Cannot be determined
Question: In the coordinate plane, points (x, 6) and (10, y) are on line k. If line k passes through the origin and has slope 1/2, then x * y =
(A) 52
(B) 46
(C) 60
(D) 50
(E) 35
Rationale: Line k passes through the origin and has slope 1/2 means that its equation is y=1/2*x.
Thus: (x, 6)=(12, 6) and (10, y) = (10,5) --> x*y=12*5=60.
Answer: C
Answer: (C) 60
Question: In a group of people, if 30 people were made to stand in each column, 16 columns could be formed. If 32 people were made to stand in a column, how many columns could be formed?
(A) 15
(B) 20
(C) 25
(D) 30
(E) 35
Rationale: 16*30 = 32*n
n = 15
The answer is A.
Answer: (A) 15
Question: Set W consists of all the prime numbers between 10 and 25. What is the range of set W?
(A) 12
(B) 13
(C) 16.6
(D) 17
(E) 23
Rationale: Answer of set W is 12.
Answer: (A) 12
Question: Fake City has a population of 200,221 people and nine districts that are represented by nine members of the city council.They wish to redraw the district lines so that each district consists of the same amount of people. How many people would have to move into Fake City for them to achieve their goal?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: To figure this out, we use the divisibility rule of 9 to get our answer. We add the digits together and get a seven. Since we are adding people to the population, we add two(9 can be divided by 9) to people to the city to get a population of 200,223 people. Answer is option B
Answer: (B) 2
Question: The number of new words that can be formed by rearranging the letters of the word 'LIVE' is?
(A) 15
(B) 20
(C) 25
(D) 32
(E) 23
Rationale: Number of words which can be formed
= 4! - 1 = 24- 1
= 23.
Answer:E
Answer: (E) 23
Question: I have an amazing bath tub having both hot and cold water taps.
The cold water tap can fill my tub in 6 hours while cold water tap can fill the tub in approx 4 hours.
I turned them on simultaneously but forgot to close the lid which remove water out of tub.
The lid can empty the tub in exact 13 hours.
Since both taps are open along with the lib , can you estimate the time needed to fill the bath tub ?
(A) 1 hours
(B) 2 hours
(C) 3 hours
(D) 4 hours
(E) 5 hours
Rationale: Solution:
3 hours
Explanation :
(1/4 + 1/6 - 1/12) ^ (-1)
= (1/3)^(-1) = 3
Answer C
Answer: (C) 3 hours
Question: Three numbers are in the ratio 1:4:6 and their H.C.F is 9. The numbers are:
(A) 1,4,6
(B) 12,24,36
(C) 10, 20, 30
(D) 12, 24, 36
(E) 9,36,54.
Rationale: Let the required numbers be x, 4x and 6x. Then, their H.C.F = x. So, x = 9.
The numbers are 9,36,54.
ANSWER:E
Answer: (E) 9,36,54.
Question: If goods be purchased for Rs.840 and one-fourth be sold at a loss of 20% at what gain percent should the remainder be sold so as to gain 20% on the whole transaction?
(A) 33 1/8%
(B) 33 7/3%
(C) 33 1/3%
(D) 33 1/6%
(E) 32 1/3%
Rationale: 1/4 CP = 210 SP = 21*(80/100) = 168
SP = 840*(120/100) = 1008
1008 - 168 = 840
3/4 SP = 630
Gain = 210
630 --- 210
100 --- ? => 33 1/3%
Answer:C
Answer: (C) 33 1/3%