mathewhe/aqua_rat huggingface dataset:
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 10 hours of the journey.
(A) 380 km
(B) 390 km
(C) 400 km
(D) 410 km
(E) None of these
Rationale: Explanation:
The total distance covered by the car in the first 10 hours = 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 + 48 = sum of 10 terms in AP whose first term is 30 and last term is 48 = 10/2 [30 + 48] = 390 km.
ANSWER IS B
Answer: (B) 390 km
Question: If w,x,y and z are distinct odd positive integers,then the maximum value of the expression (w^2+x^2)*(y^2+z^2) can be divisible by?
(A) 2
(B) 3
(C) 5
(D) 8
(E) 10
Rationale: ANY ODD NUMBER SQUARE WILL GIVE ODD NUMBER ONLY..
SIMILARLY WEN WE ADD 2 ODD NUMBERS WE WILL GET EVEN NUMBER..
WEN WE MULTIPLY 2 EVEN OWE WILL GET EVEN NUBER..
SO THE RESULT OF THE ABOVE EXPRESSION IS AN EVEN NUMBER ONLY..
HENCE IT IS DIVISIBLE BY 2...
ANSWER:A
Answer: (A) 2
Question: If a truck is traveling at a constant rate of 72 kilometers per hour, how many seconds will it take the truck to travel a distance of 600 meters? (1 kilometer = 1000 meters)
(A) 18
(B) 24
(C) 30
(D) 36
(E) 48
Rationale: Speed = 72 Km/hr => 72,000 m/hr
In one minute => 72000/60 = 1200 meters
In one sec => 1200/60 = 20 meters
Time = Total distance need to be covered / Avg. speed
=> 600/ 20 =30 and hence the Answer : C
Answer: (C) 30
Question: The G.C.D. of 1.08, 0.35 and 0.9 is:
(A) 0.01
(B) 0.9
(C) 0.18
(D) 0.108
(E) None
Rationale: EXPLANATION
Given numbers are 1.08, 0.35 and 0.90. H.C.F. of 108, 35 and 90 is 1,
H.C.F. of given numbers = 0.01.
Answer A
Answer: (A) 0.01
Question: A completes 80% of a work in 20 days. Then B also joins and A and B together finish the remaining work in 3 days. How long does it need for B if he alone completes the work?
(A) 35 Days
(B) 36.5 Days
(C) 37 Days
(D) 37.5 Days
(E) 38 Days
Rationale: Work done by A in 20 days = 80/100 = 8/10 = 4/5
Work done by A in 1 day = (4/5) / 20 = 4/100 = 1/25 --- (1)
Work done by A and B in 3 days = 20/100 = 1/5 (Because remaining 20% is done in 3 days by A and B)
Work done by A and B in 1 day = 1/15 ---(2)
Work done by B in 1 day = 1/15 – 1/25 = 2/75
=> B can complete the work in 75/2 days = 37 ½ days
Answer is D.
Answer: (D) 37.5 Days
Question: Eleven bags are bought for Rs.1000 and sold at 10 for Rs.1600. What is the gain or loss in percentage?
(A) 10%
(B) 26%
(C) 25%
(D) 20%
(E) None of these
Rationale: Explanation:
As selling price is Rs.1600 for 10 bags, each bag is sold at Rs.160.
Hence, the profit is Rs.100 after selling 10 bags plus the selling price of 1 bag = 100 + 160 = Rs.260.
%profit = 260/1000 *100
= 26%
ANSWER B
Answer: (B) 26%
Question: Rs.2500 is divided into two parts such that if one part be put out at 5% simple interest and the other at 6%, the yearly annual income may be Rs.125. How much was lent at 5%?
(A) 2333
(B) 2777
(C) 2688
(D) 1000
(E) 2500
Rationale: (x*5*1)/100 + [(2500 - x)*6*1]/100 = 125
X = 2500
Answer: E
Answer: (E) 2500
Question: A train 110 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) 4 sec
(B) 6 sec
(C) 7 sec
(D) 3 sec
(E) 2 sec
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
= 110 * 3/55 =6 sec.
Answer:B
Answer: (B) 6 sec
Question: Two cars, Car1 and Car2 move towards each other from E and Y respectively with respective speeds of 20 m/s and 15 m/s. After meeting each other Car1 reaches Y in 10 seconds. In how many seconds does Car 2 reach E starting from Y?
(A) 15.5 sec
(B) 8.4 sec
(C) 33.6 sec
(D) 31.11 sec
(E) 16.8 sec
Rationale: E--------------------------------------|----------------------------Y
Car A(20mps)------------------------->P<---------------Car B(15mps)
Let 2 cars meet each other at point P in t seconds.
Car1 covers distance= 20t. Car2 covers distance=15t. So, total distance EY= 35t.
From P, Car 1 reaches onto Y in 10 secs. So it covers 15t further.
so, 15t/20 = 10
So t=40/3 sec and total distance = (35*40)/3
Hence Car2 will cover total distance in (35*40)/(3*15) = 31.11 sec approx.
Answer D
Answer: (D) 31.11 sec
Question: 5 people can write 25 book in 20 days working 8 hour a day.then in how many day 125 can be written by 75 people?
(A) 25/3
(B) 19/3
(C) 20/3
(D) 25/3
(E) 22/3
Rationale: work per day epr hour per person= 25/(20*8*5) // eq-1
people= 75; let suppose day=p; per day work for 8 hours
acc. to condition
work per day epr hour per person= 125/(p*8*75) // eq-2
eq-1==eq-2;
p= 20/3
ANSWER:C
Answer: (C) 20/3
Question: in town of 500 people,285 read hindu and 212 read indian express and 127 read times of india 20 read hindu and times of india and 29 read hindu and indian express and 35 read times of india and indian express . 50 read no news paper . then how many read only one paper?
(A) 320
(B) 321
(C) 421
(D) 417
(E) 317
Rationale: HIndu = 285
TOI = 127
IE = 212
now
Hindu and TOI both is = 20
TOI and IE both is = 35
Hindu and IE both is = 29
now suppose Hindu , TOI nd IE all is = x ;
so,only Hindu is = 285-20-29-x = 236-x ;
only TOI is = 127-20-35-x = 72-x ;
only IE is = 212-35-29-x = 148-x ;
now, 236-x + 72-x + 148-x + 20 + 29 + 35 + x + 50 = 500 590 -2x = 500
so, x = 45 this is the value who read all the 3 dailies.
so,result is = 236-45 + 72-45 + 148-45 = 191 + 27 + 103 = 321. ANSWER:B
Answer: (B) 321
Question: JOHN and Roger can finish the work 24 days if they work together. They worked together for 16 days and then Roger left. JOHN finished the remaining work in another 16 days. In how many days JOHN alone can finish the work?
(A) 30 days
(B) 48 days
(C) 70 days
(D) 80 days
(E) 90 days
Rationale: Amount of work done by JOHN and Roger in 1 day = 1/24
Amount of work done by JOHN and Roger in 16 days = 16 Ã— (1/24) = 2/3
Remaining work â€“ 1 â€“ 2/3 = 1/3
JOHN completes 1/3 work in 16 days
Amount of work JOHN can do in 1 day = (1/3)/16 = 1/48
=> JOHN can complete the work in 48 days
Answer : B
Answer: (B) 48 days
Question: A dealer offers a cash discount of 20%. Further, a customer bargains and receives 20 articles for the price of 15 articles. The dealer still makes a profit of 20%. How much percent E above the cost price were his articles marked?
(A) 100%
(B) 80%
(C) 75%
(D) 66+2/3%
(E) 50%
Rationale: Good question...2:11 min
Marked Price (M) = Cost Price (C) + Mark up...(EQN. A)
Selling price = 20% Discount over M = 0.8*M
Given that, a customer bargains and receives 20 articles for the price of 15 articles-->*afurther loss of 25%to the dealer--> BUT aNET PROFIT of 20%over cost price (C)
0.75* 0.8 * M =1.2 * C
Hence, M/C = 2/1 = 200%=E
From Eqn. A , (C + Mark up)/C = 200% -->Mark up / C = 100%
Ans. A
Answer: (A) 100%
Question: A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint. If 2 gallons of the mixture is needed and the individual colors can be purchased only in one gallon or half gallon cans, what is the least amount of paint R, in gallons, that must be purchased in order to measure out the portions needed for the mixture?
(A) 2
(B) 2 1/2
(C) 3
(D) 3 1/2
(E) 4
Rationale: Given W:B = 3:5
That means say 3 gallons of white paint + 5 gallons of black paint = 8 gallons of paint mixture.
But we want least amount of whiteblack paints for minimum of 2 gallons of mixture, so lets reduce keeping same ratio,
1.5 : 2.5 gives 1.5 + 2.5 = 4 gallons of mixture, but we want only 2 gallons, lets further reduce
0.75: 1.25 gives 1+1.5 =2.5 gallons of mixture. This looks ok, but lets reduce further just to be sure
0.375: 0.625 gives 0.5 + 1 = 1.5 gallons of mixture, thats less than 2 gallons of mixture, so not acceptable.
So correct ans is 2.5 gallons. B
Answer: (B) 2 1/2
Question: A group of 3 investors and 3 clients recently frequented the Chinese Luyang Restaurant. The total bill for the meal, including 20% gratuity, came to $720. On average, how much did the meal of each individual cost before gratuity?
(A) $160
(B) $96
(C) $90
(D) $80
(E) $100
Rationale: 3 Investors and 3 clients - so total 6 people
The bill $720 includes 20% gratuity... so the actual cost of dinner was $600
Now, the cost per person will be $600/6 which is $100
Option E
Answer: (E) $100
Question: Working at a constant rate, P can finish a job in 3 hours. Q, also working at a constant rate, can finish the same job in 9 hours. If they work together for 2 hours, how many more minutes will it take P to finish the job, working alone at his constant rate?
(A) 20
(B) 30
(C) 40
(D) 50
(E) 60
Rationale: Each hour they complete 1/3 + 1/9 = 4/9 of the job.
In 2 hours, they complete 2(4/9) = 8/9 of the job.
The time for P to finish is (1/9) / (1/3) = (1/3) hour = 20 minutes
The answer is A.
Answer: (A) 20
Question: In measuring the sides of a rectangle, one side is taken 9% in excess, and the other 8% in deficit. Find the error percent in the area calculated from these measurements.
(A) 0.11%
(B) 0.7%
(C) 0.4%
(D) 0.6%
(E) 0.28%
Rationale: Let x and y be the sides of the rectangle. Then, Correct area = xy.
Calculated area = (12/11) x (23/25) y = (358/357 )(xy)
Error In measurement = (358/357)xy- xy = (1/357)xy
Error percentage = [(1/357)xy (1/xy)100] % = (7/25) % = 0.28%.
Answer is E.
Answer: (E) 0.28%
Question: The speed of a boat in upstream is 85 kmph and the speed of the boat downstream is 155 kmph. Find the speed of the boat in still water and the speed of the stream?
(A) 10 kmph
(B) 11 kmph
(C) 16 kmph
(D) 18 kmph
(E) 35 kmph
Rationale: Speed of the boat in still water = (85+155)/2 = 120 kmph. Speed of the stream = (155-85)/2 = 35 kmph.Answer: E
Answer: (E) 35 kmph
Question: From a group of boys and girls, 15 girls leave. There are then left 2 boys for each girl. After this, 45 boys leave. There are then 5 girls for each boy. Find the number of girls in the beginning.
(A) 36
(B) 40
(C) 56
(D) 65
(E) 28
Rationale: Let the present boys be x boys.
Then the number of girls at present = 5x.
Before the boys had left : Number of boys = x + 45 and
number of girls = 5x.
x + 45 = 2 * 5x ===> x + 45 = 10x ==> 9x = 45, x = 5.
Hence, the number of girls in the beginning = 5x +15 = 25 + 15 = 40
so the correct answer is option B) 40.
Answer: (B) 40
Question: The cost of an item was reduced from its usual selling price of $23.99 to $18.99. Which of the following is closest to the percent decrease in the price of the item?
(A) 17%
(B) 21%
(C) 24%
(D) 25%
(E) 42%
Rationale: The price decreased by 23.99 - 8.99 = $5.
$5 is a bit more than 20% of original price of $24.
Answer: B.
Answer: (B) 21%
Question: A completes a work in 10 days and B complete the same work in 20 days. If both of them work together, then the number of days required to complete the work will be
(A) 8 days
(B) 6.67 days
(C) 10 days
(D) 12 days
(E) 13 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days
Therefore, here, the required number of days = 10 × 20/ 30 = 6.67 days.
Answer : B
Answer: (B) 6.67 days
Question: If two dice are thrown simultaneously, then find the probability that the sum of numbers appeared on the dice is 11?
(A) 5/6
(B) 7/36
(C) 5/36
(D) 2/36
(E) 12/36
Rationale: The sum of numbers appeared is 11.
Therefore, the required probability = n(E)/n(S) = 2/36.
ANSWER:D
Answer: (D) 2/36
Question: The ratio of the volumes of two cubes is 125 : 1000. What is the ratio of their total surface areas?
(A) 81 : 121
(B) 9 : 11
(C) 729 : 1331
(D) 1 : 4
(E) None of these
Rationale: Ratio of the sides = Â³âˆš125 : Â³âˆš1000 = 5 : 10
Ratio of surface areas = 5^2 : 10^2 = 25 : 100 = 1:4
ANSWER: D
Answer: (D) 1 : 4
Question: A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 864 in 4 years. The sum is:
(A) s. 650
(B) s. 690
(C) s. 668
(D) s. 700
(E) s. 760
Rationale: S.I. for 1 year = Rs. (864 - 815) = Rs. 49.
S.I. for 3 years = Rs.(49 x 3) = Rs. 147.
Principal = Rs. (815 - 147) = Rs. 668.
Answer: Option C
Answer: (C) s. 668
Question: If p and q are positive integers, how many integers are larger than pq and smaller than p(q + 4)?
(A) 4p - 1
(B) P + 2
(C) p – 2
(D) 2p – 1
(E) 2p + 1
Rationale: The number of integers between x and y, where x>y is (x-y)-1. For example, the number of integers between 1 and 5 is (5-1)-1=3: 2, 3, and 4.
Thus, the number of integers between pq and p(q+4)=pq+4p is (pq+4p-pq)-1=4p-1.
Answer: A.
Answer: (A) 4p - 1
Question: If the compound interest on a certain sum of money for 2 years at 10% per annum be Rs. 993, what would be the simple interest?
(A) Rs. 600
(B) Rs. 890
(C) Rs. 895
(D) Rs. 900
(E) None
Rationale: Let P = Principal
A - Amount
We have a = P(1 + R/100)3 and CI = A - P
ATQ 993 = P(1 + R/100)3 - P
? P = 3000/-
Now SI @ 10% on 3000/- for 2 yrs = (3000 x 10 x 2)/100
= 600/-
Answer: A.
Answer: (A) Rs. 600
Question: A can do a piece of work in 20 days. B in 15 days A and C in 12 days. In how many days can A finish the work if he is assisted by B on one day and C on the next, alternately?
(A) 9 days
(B) 8 days
(C) 5 days
(D) 54 days
(E) 2 days
Rationale: A + B = 1/20 + 1/15 = 7/60
A + C = 1/20 + 1/12 = 8/60
7/60 + 8/60 = 15/60 = 1/4
4 days * 2 = 8 days
Answer: B
Answer: (B) 8 days
Question: The ratio of spinsters to cats is 2 to 9. If there are 42 more cats than spinsters, how many spinsters are there?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 13
Rationale: Let 2x be the number of spinsters. Then 9x is the number of cats.
9x-2x=42
x=6 and the number of spinsters is 2(6)=12.
The answer is D.
Answer: (D) 12
Question: How many numbers up to 200 are divisible by 2 and 3 both?
(A) 22
(B) 33
(C) 77
(D) 28
(E) 22
Rationale: Explanation:
200/6 = 33 2/6 => 33 Numbers
Answer:B
Answer: (B) 33
Question: In how many a committee of 5 members can be selected from 6 men 5 ladies consisting of 3 men and 2 ladies
(A) 230
(B) 451
(C) 120
(D) 200
(E) 120
Rationale: (3 men out of 6) and (2 ladies out of 5) are to be chosen
Required number of ways
=(6C3 * 5C2)
= 200
Ans: D
Answer: (D) 200
Question: A car owner buys petrol at Rs.7.50, Rs. 8 and Rs. 8.50 per litre for three successive years. What approximately is the average cost per litre of petrol if he spends Rs. 4000 each year?
(A) Rs. 7.50
(B) Rs. 7.98
(C) Rs. 8
(D) Rs. 9
(E) None
Rationale: Total quantity of petrol
consumed in 3 years
= 4000	+	4000	+	4000 litres
7.50	8	8.50
= 4000 2	+	1	+	2 litres
15	8	17
= 76700 litres
51
Total amount spent = Rs. (3 x 4000) = Rs. 12000.
Average cost = Rs. 12000 x 51 = Rs.	6120 = Rs. 7.98
76700	767
B)
Answer: (B) Rs. 7.98
Question: How many two-digit numbers are there whose remainder when divided by 15 is 1, and whose remainder when divided by 6 is 5?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: 2 digit numbers whose remainder when divided by 10 is 1 are
11 , 21 , 31 , 41 , 51 , 61 , 71 , 81 , 91
Out of above , numbers whose remainder when divided by 6 is 5 are
11 , 41 and 71
Answer E
Answer: (E) 7
Question: If x and y are positive integers, and x^3*y^4 = 27783, which of the following is the value of xy?
(A) 6
(B) 10
(C) 14
(D) 15
(E) 21
Rationale: 27783 = 3*9261 = 3^2*3087 = 3^3*1029 = 3^4*343 = 3^4*7^3
xy = 3*7 = 21
The answer is E.
Answer: (E) 21
Question: Find out the C.I on Rs.5000 at 4% p.a. compound half-yearly for 1 1/2 years.
(A) 306.03
(B) 306.01
(C) 306.04
(D) 306.0
(E) 306.06
Rationale: A = 5000(51/50)3
= 5306.04
5000
-----------
306.04
Answer: C
Answer: (C) 306.04
Question: A train leaves Mumabai at 9 am at a speed of 40 kmph. After one hour, another train leaves Mumbai in the same direction as that of the first train at a speed of 50 kmph. When and at what distance from Mumbai do the two trains meet?
(A) 2:00pm,400 km
(B) 8:00pm,200 km
(C) 2:00pm,200 km
(D) 2:00pm,900 km
(E) 6:00pm,200 km
Rationale: When the second train leaves Mumbai the first train covers 40 * 1 = 40 km
So, the distance between first train and second train is 40 km at 10.00am
Time taken by the trains to meet
= Distance / relative speed = 40 / (50 -40) = 4 hours
So, the two trains meet at 2 p.m. The two trains meet 4 * 50 = 200 km away from Mumbai.
Answer:C
Answer: (C) 2:00pm,200 km
Question: In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs.2.40 per hour for regular work and Rs.3.20 per hours for overtime. If he earns Rs.432 in 4 weeks, then how many hours does he work for?
(A) 160
(B) 175
(C) 180
(D) 195
(E) 185
Rationale: Suppose the man works overtime for x hours.
Now, working hours in 4 weeks = (5 x 8 x 4) = 160.
Therefore, 160 x 2.40 + x x 3.20 = 432
<=> 3.20x = 432 - 384 = 48
x = 15.
Hence, total hours of work = (160 + 15) = 175.
Answer :B
Answer: (B) 175
Question: A polling company surveyed a certain country, and it found that 35% of that country’s registered voters had an unfavorable impression of both of that state’s major political parties and that 20% had a favorable impression only of Party E. If one registered voter has a favorable impression of both parties for every two registered voters who have a favorable impression only of Party B, then what percentage of the country’s registered voters have a favorable impression of both parties (assuming that respondents to the poll were given a choice between favorable and unfavorable impressions only)?
(A) 15
(B) 20
(C) 30
(D) 35
(E) 45
Rationale: S=100
not( E and B ) =35
only E=20
(E and B)/B=1/2
let ( E and B ) =x
only B =2x
so now, 20+35+x+2x=100
x= 15
A ans
Answer: (A) 15
Question: A company seeks to hire a sales manager, a shipping clerk, and a receptionist. The company has narrowed its candidate search and plans to interview all remaining candidates including 7 persons for the position of sales manager, 4 persons for the position of shipping clerk, and 10 persons for the position of receptionist. How many different hirings of these three people are possible?
(A) 7 + 4 + 10
(B) 7 × 4 × 10
(C) 21 × 20 × 19
(D) 7! + 4! + 10!
(E) 7! × 4! × 10!
Rationale: Number of ways one person can be hired for the position of Sales Manager= C71C17=7
Number of ways one person can be hired for the position of Shipping Clerk= C41=4
Number of ways one person can be hired for the position of Receptionist= C101=10
Therefore total number of different hiring possible for the three positions = 7 * 4 * 10
Answer: B
Answer: (B) 7 × 4 × 10
Question: Bird is flying 120 km/hr between B to R. Two trains at B to R at 60 kmph. The distance traveled by the bird before it is killed?
(A) 90 kms.
(B) 100 kms.
(C) 110 kms.
(D) 120 kms.
(E) 130 kms.
Rationale: It will depend on the distance between B and R.
If distance between B and R is 120 kms,
Time taken by trains before collision = 120/(60+60)=1 hr
Distance traveled by bird in 1 hr = 120 kms.
so The distance traveled by the bird before it is killed = 120 kms.
ANSWER:D
Answer: (D) 120 kms.
Question: If the price of a TV is first decreased by 10% and then increased by 30%, then the net change in the price will be :
(A) 4% increase
(B) 17% increase
(C) 10% decrease
(D) 6% increase
(E) None of these
Rationale: Explanation :
Solution: let the original price be Rs. 100.
New final price = 130% of(10% of 100) =Rs. 130/100 * 90/100 * 100 = Rs. 117.
.'. Increase = 17%
Answer :B
Answer: (B) 17% increase
Question: At a local supermarket, a box of cereal usually costs 19 dollars. This week, the supermarket sells the box of cereal for 5 dollars. How much money will you save if you buy this cereal at this supermarket?
(A) 15 dollars
(B) 13 dollars
(C) 14 dollars
(D) 12 dollars
(E) 11 dollar
Rationale: Solution:
In this situation, there is a decrease in the price.
Saving = 19 - 5 = 14 dollars
Option C
Answer: (C) 14 dollars
Question: Rectangular tile each of size 35cm by 30cm must be laid horizontally on a rectangular floor of size 1000cm by 210cm,such that the tiles do not overlap and they are placed with edges jutting against each other on all edges. A tile can be placed in any orientation so long as its edges are parallel to the edges of floor. No tile should overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is:
(A) 600
(B) 400
(C) 200
(D) 500
(E) 100
Rationale: Area of tile = 35*30 = 1050
Area of floor = 1000*210 = 210000
No of tiles = 210000/1050 =200
So, the no of tile = 200
ANSWER:C
Answer: (C) 200
Question: A sum of money at simple interest amounts to Rs. 1560 in 4 years and to Rs. 1590 in 6 years. The sum is:
(A) Rs. 1400
(B) Rs. 1450
(C) Rs. 1500
(D) Rs. 1550
(E) Rs. 1525
Rationale: S.I. for 2 years = Rs. (1590 - 1560) = Rs. 30.
S.I. for 4 years = Rs.(30 x 2) = Rs. 60.
Principal = Rs. (1560 - 60) = Rs. 1500.
Answer: Option C
Answer: (C) Rs. 1500
Question: Find the odd man out. 1, 3, 9, 12, 19, 29
(A) 12
(B) 9
(C) 1
(D) 3
(E) 6
Rationale: Explanation :
12 is an even number.
All other given numbers are odd
Answer : Option A
Answer: (A) 12
Question: There are 50 doors marked with numbers 1 to 50. There are 50 individuals marked 1 to 50.
An operation on a door is defined as changing the status of the door from open to closed or vice versa. All the doors are closed to start with. One at a time, one randomly chosen individual goes and operates the doors. The individual however operates only those doors which are a multiple of the number he/she is carrying. For example, the individual marked with number 5 operates the doors marked with 5, 10, 15, 20, 25, 30, 35, 40, 45, and 50. If every individual in the group gets one turn, then how many doors are open at the end?
(A) 0
(B) 2
(C) 5
(D) 7
(E) 9
Rationale: If a door is closed at the start, it requires an odd number of people to operate to be open at the end. Only the perfect squares have an odd number of factors.
The doors which are open at the end are: 1, 4, 9, 16, 25, 36, 49 for a total of 7 doors.
The answer is D.
Answer: (D) 7
Question: There is a 30% chance that Cara will visit Egypt this year, while there is a 60% chance that she will visit India this year. What is the probability that Cara will visit either Egypt or India this year, but NOT both?
(A) 52%
(B) 54%
(C) 56%
(D) 58%
(E) 60%
Rationale: P(Egypt but not India)=0.3*0.4=0.12
P(India but not Egypt)=0.6*0.7=0.42
P(Egypt or India but not both)=0.12+0.42=0.54
The answer is B.
Answer: (B) 54%
Question: Of the total amount that Jill spent on a shopping trip, excluding taxes, she spent 20 percent on clothing, 50 percent on food, and 30 percent on other items. If Jill paid a 10 percent tax on the clothing, 15 percent tax on the food, and no tax on all other items, then the total tax that she paid was what percent of the total amount that she spent, excluding taxes?
(A) 12.45
(B) 12.5
(C) 12.65
(D) 12.35
(E) 12.25
Rationale: Assume she has $200 to spend.
TAX
Clothing = 20% = $40= $10.00
Food = 50% = $ 100 = $15.00
Items = 30% = $ 60 = $ 0.00
Total tax = $25.00
% of total amount = 25/200 * 100 = 12.25%
Answer E
Answer: (E) 12.25
Question: The positive numbers w, x, y, and z are such that x is 10 percent greater than y, y is 20 percent greater than z, and w is 20 percent less than x. What percent greater than z is w ?
(A) 15.2%
(B) 16.0%
(C) 20.0%
(D) 23.2%
(E) 24.8%
Rationale: My strategy is same as theDobermanbut instead take z=100, which makes life a bit easy. As:
z=100
y=120 (20% greater than z)
z=144(20% greater than y)
Now calculate w 20% less than z = 144*80/100= 115.2
Now by just looking, relation between w and z:
w-z/z*100 = 16 - Answer B
Answer: (B) 16.0%
Question: The sides of a triangle are in the ratio 5: 12: 13 and its perimeter is 300 m, its area is?
(A) 150
(B) 288
(C) 278
(D) 111
(E) 112
Rationale: 5x + 12x + 13x = 300 => x = 10
a = 50, b = 120, c = 130
S = (50 + 120 + 130)/2 = 150
Answer: A
Answer: (A) 150
Question: In right triangle ABC, AC is the hypotenuse. If AC is 50 and AB + BC = 70, what is the area of the triangle ABC?
(A) 225
(B) 450
(C) 25√2
(D) 200
(E) 600
Rationale: Square AB + BC = 70:
(AB)^2 + 2*AB*BC + (BC)^2 = 4900. Since (AC)^2 = (AB)^2 + (BC)^2 = 50^2 = 2500, then (AB)^2 + 2*AB*BC + (BC)^2 = 2500 + 2*AB*BC = 4900.
2500 + 2*AB*BC = 4900.
AB*BC = 1200.
The area = 1/2*AB*BC = 600.
Answer: E.
Answer: (E) 600