mathewhe/aqua_rat huggingface dataset:
Question: Which of the following statements must be true?
I. The product of first 100 prime numbers is even.
II. The sum of first 100 prime numbers is odd.
III. The sum of first five non-negative even numbers is divisible by both 4 and 5.
(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II and III
Rationale: I. Product of first 100 prime number includes 2 , hence result will be even
II. ODD + ODD = Even and Even + Even = Even
100 prime numbers will have all Odd Numbers and 1 even Number ( ie, 2 )
Sum of Odd number of odd numbers will be ODD ( ie, sum of 99 odd numbers = Odd number)
Odd Number + 2 = Odd Number...
III. First 5 non-negative even numbers = {0, 2 , 4 , 6 , 8 }
0 + 2 + 4 + 6 + 8 = 20
Divisible by both 4 and 5
Thus all three are possible, answer will be (E)
Answer: (E) I, II and III
Question: In a certain diving competition, 5 judges score each dive on a scale from 1 to 10. The point value of the dive is obtained by dropping the highest score and the lowest score and multiplying the sum of the remaining scores by the degree of difficulty. If a dive with a degree of difficulty of 3.2 received scores of 7.5, 8.8, 9.0, 6.0, and 8.5, what was the point value of the dive?
(A) 68.8
(B) 73.6
(C) 75.2
(D) 76.8
(E) 79.36
Rationale: Degree of difficulty of dive = 3.2
Scores are 6.0 , 7.5 , 8.8 , 8.5 and 9.0
We can drop 6.0 and 9.0
Sum of the remaining scores = (7.5+8.8+8.5)= 24.8
Point of value of the dive = 24*3.2 =79.36
Answer E
Answer: (E) 79.36
Question: On the xy-coordinate plane, point A lies on the y-axis and point B lies on the x-axis. Points A, B, and C form a right triangle with a 90-degree angle at point C and the triangle has an area of 20. If AC is parallel to the x-axis, and BC is parallel to the y-axis, which of the following could be the coordinates of point C?
(A) (8, -3)
(B) (4, 5)
(C) (-5, 7)
(D) (-2, -20)
(E) (-15, -3)
Rationale: The area of the triangle formed will be:
1/2 * base * height =
1/2 * |(X-coordinate of point C)| * |(Y-coordinate of point C)| = 20
Thus |product of coordinates of point C| = 40
The answer is D.
Answer: (D) (-2, -20)
Question: How many minutes is it before 12 noon if 20 minutes ago it was three times as many minutes after 9 am?
(A) 40
(B) 39
(C) 42
(D) 55
(E) 29
Rationale: A
40 minutes, or 11.20 am
Answer: (A) 40
Question: A track covers a distance of 550 metres in 1 minute whereas a bus covers a distance of 33 kms in 45 minute. The ratio of their speeds is:
(A) 4:3
(B) 3:5
(C) 3:4
(D) 50:3
(E) None
Rationale: Solution: Speed of track = 550 per minute.
Speed of bus = 33 kms /45 = 33000/45 = 733.33 m/minute
Ratio of their speeds = 550/733.33 = 3:4.
Answer: Option C
Answer: (C) 3:4
Question: A reduction of 20% in the price of salt enables a lady to obtain 10kgs more for Rs.100, find the original price per kg?
(A) Rs.2.7
(B) Rs.2.4
(C) Rs.2.5
(D) Rs.2.1
(E) Rs.2.9
Rationale: 100*(20/100) = 20 --- 10
? --- 1 => Rs.2
100 --- 80
? --- 2 => Rs.2.5
Answer:C
Answer: (C) Rs.2.5
Question: The volume of a cube is 1728 cc. Find its surface.
(A) 864
(B) 556
(C) 255
(D) 287
(E) 267
Rationale: a3 = 1728 => a = 12
6a2 = 6 * 12 * 12 = 864
Answer:A
Answer: (A) 864
Question: A person took some amount with some interest for 2 years, but increase the interest for 1%, he paid Rs.120/- extra, then how much amount he took?
(A) Rs.5500/-
(B) Rs.6000/-
(C) Rs.4000/-
(D) Rs.7000/-
(E) None of these
Rationale: Explanation:
2 years = Rs.120/-
year = 120/2
Rate of Interest = 1%
100/1% × 120/2 = Rs.6000/-
P = Rs.6000/-
Answer: Option B
Answer: (B) Rs.6000/-
Question: A factory has 500 workers, 13 percent of whom are women. If 50 additional workers are to be hired and all of the present workers remain, how many of the additional workers must be women in order to raise the percent of women employees to 20 percent?
(A)  3
(B)  10
(C)  45
(D)  30
(E)  35
Rationale: Currently the factory has 0.13*500=65 women.
After 50 additional workers are hired, there will be total of 550 workers and we need 0.2*550=110 of them to be women, so we need 110-65=45 more women.
Answer: C.
Answer: (C)  45
Question: If an object travels 300 feet in 6 seconds, what is the object's approximate speed in miles per hour? (Note: 1 mile = 5280 feet)
(A) 30
(B) 31
(C) 32
(D) 33
(E) 34
Rationale: 1 mile = 5280 feet
=> 1 feet = 1/5280 miles
If the object travels 300 feet in 6 sec
then it travels 300/6 * 60 * 60 feet in 1 hour (1 hr = 60 min * 60 sec)
= 3600 * 50 feet in 1 hour
= 180000 feet in 1 hr
= 180000/5280 miles in 1 hour
= 18000/528 miles/hr ~ 34 miles/hr
Answer - E
Answer: (E) 34
Question: How many times will the digit 6 be written when listing the integers from 1 to 1000?
(A) 150
(B) 280
(C) 310
(D) 420
(E) 300
Rationale: Many approaches are possible. For example:
Consider numbers from 0 to 999 written as follows:
1. 000
2. 001
3. 002
4. 003
...
...
...
1000. 999
We have 1000 numbers. We used 3 digits per number, hence used total of 3*1000=3000 digits. Now, why should ANY digit have preferences over another? We used each of 10 digits equal # of times, thus we used each digit (including 6) 3000/10=300 times.
Answer: E.
Answer: (E) 300
Question: A man caught some fish. The 2 heaviest fish had a combined weight
which was 25% of the total weight of all the fish. The 5 lightest fish had
a combined weight which was 45% of the total weight of all the fish. He
put the 2 heaviest fish in the freezer and ate the 5 lightest fish for lunch.
His cat took all the remaining fish. How many fish did his cat take?
(A) 8
(B) 6
(C) 4
(D) 3
(E) 2
Rationale: Let W be the total weight of all fish the man caught. The fish taken by the cat
had weight 30%W. If the cat took 4 fish or more, then their average weight must have
been at most 7.5%W which is less than the average weight of the 5 lightest fish. If the
cat took 1 or 2 fish, then their average weight must have been at least 15%W which is
more than the average weight of the 2 heaviest fish. Thus, the cat took 3 fish
correct answer D
Answer: (D) 3
Question: Kim has 4 pairs of shoes; each pair is a different color. If Kim randomly selects 2 shoes without replacement from the 8 shoes, what is the probability that she will select 2 shoes of the same color?
(A) 1/7
(B) 1/8
(C) 1/9
(D) 1/10
(E) 1/25
Rationale: Total pairs = 8C2 = 28; Same Color Pairs= 4C1*1C1=4; Prob = 1/7
Ans A
Answer: (A) 1/7
Question: Find the cost of fencing around a circular field of diameter 28 m at the rate of Rs.1.50 a meter?
(A) 138
(B) 132
(C) 278
(D) 279
(E) 222
Rationale: 2 * 22/7 * 14 = 88
88 * 1 1/2
= Rs.132
Answer: B
Answer: (B) 132
Question: In traveling from a dormitory to a certain city, a student went 1/5 of the way by foot, 2/3 of the way by bus, and the remaining 11 kilometers by car. What is the distance, in kilometers, from the dormitory to the city?
(A) 30
(B) 45
(C) 60
(D) 90
(E) 63
Rationale: I believe there is a better way to do it.
Basically one of the options should satisfy the given criteria.
60 did
1/5 *60 =12
2/3*60=40
so total distance
52 + remaining 11 =63
Answer E
Answer: (E) 63
Question: Bruce and Anne can clean their house in 4 hours working together at their respective constant rates. If Anne’s speed were doubled, they could clean their house in 3 hours working at their respective rates. How many hours does it currently take Anne to clean the house on her own?
(A) 6
(B) 7
(C) 8
(D) 12
(E) 14
Rationale: Lets suppose Anne and Bruce take A and B hrs working separately
So in 1 hour they can together finish 1/A + 1/B portion of the work which equals 1/4 (As the work is completed in 4 hours)
After anne doubles her rate of work the portion completed by the both is 1/A +2/B which is equal to 1/3 (As the work is completed in 3 hours)
Solving these 2 equations we can find B as 12
ANSWER:D
Answer: (D) 12
Question: In how many different number of ways 4 men and 3 women can sit on a bench such that women always sit together.
(A) 710
(B) 720
(C) 724
(D) 728
(E) 740
Rationale: 720
B)
Answer: (B) 720
Question: 2, 6, 12, 20, 30, 42, 56, (...)
(A) 72
(B) 61
(C) 64
(D) 70
(E) 65
Rationale: The pattern is 1×2, 2×3, 3×4, 4×5, 5×6, 6×7, 7×8.
Hence, next number is 8×9 = 72
Answer is A.
Answer: (A) 72
Question: Two trains of equal are running on parallel lines in the same direction at 45 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is?
(A) 45
(B) 88
(C) 66
(D) 55
(E) 22
Rationale: Let the length of each train be x m.
Then, distance covered = 2x m.
Relative speed = 45 - 36 = 9 km/hr.
= 9 * 5/18 = 5/2m/sec.
2x/36 = 5/2 => x = 45.
Answer:A
Answer: (A) 45
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 2.9 km and 1.6 km respectively. The time taken by the slower train to cross the faster train in seconds is?
(A) 99
(B) 277
(C) 48
(D) 96
(E) 108
Rationale: Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 2.9 + 1.6 = 4.5 km = 4500 m.
Required time = 4500 * 3/125 = 108 sec.
Answer:E
Answer: (E) 108
Question: There is enough provisions for 700 men in an army camp for 25 days. If there were 300 men less, how long will the provision last?
(A) 30days
(B) 40days
(C) 50days
(D) 59days
(E) 65days
Rationale: Exp: We have, M1D1 = M2D2
700*25= 300* D2
D2 = 700*25/300 = 59 days.
Answer: D
Answer: (D) 59days
Question: At a speed of 50 miles per hour, a certain car uses 1 gallon of gasoline every 30 miles. If the car starts with a full 15 gallon tank of gasoline and travels for 5 hours at 50 miles per hour, the amount of gasoline used would be what fraction of a full tank?
(A) 3/25
(B) 11/36
(C) 5/9
(D) 2/3
(E) 25/36
Rationale: Gas used = (5 hours)*(50 miles/hour)*(1 gallon/30 miles) = 8+1/3 gallons
Portion used = (8+1/3) / 15 = 5/9
Ans C
Answer: (C) 5/9
Question: Raja is able to sell a hand-carved statue for $805 which was a 15% profit over his cost. How much did the statue originally cost him?
(A) $700
(B) $512.40
(C) $555.40
(D) $574.90
(E) $588.20
Rationale: Cost price = 805/115*100 = 700
Answer : A
Answer: (A) $700
Question: A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
(A) 70
(B) 80
(C) 90
(D) 100
(E) 110
Rationale: Explanation:
Let number of notes of each denomination be x.
Then x + 5x + 10x = 480
16x = 480
x = 30.
Hence, total number of notes = 3x = 90.
C)
Answer: (C) 90
Question: If p, q, and r are consecutive integers such that p > q > r and the sum of p, q, and r is a multiple of 10, which of the following could be the value of p?
(A) 0
(B) 1
(C) 9
(D) 10
(E) 12
Rationale: We're given a very specific set of restrictions in this prompt:
1) P, Q and R are CONSECUTIVE INTEGERS
2) P > Q > R
3) P+Q+R = a multiple of 10
We're asked which of the 5 answer COULD be the value of P given these restrictions. Rather than staring at the screen or doing layered math, we canbrute forcethe answers until we find one that fits these restrictions..
Answer A: P = 0
In this case, the numbers would be 0, -1, and -2. The sum = -3 which is NOT a multiple of 10. Eliminate A.
Answer B: P = 1
In this case, the numbers would be 1, 0, and -1. The sum = 0 which IS a multiple of 10. B IS the answer.
Final Answer:
B
Answer: (B) 1
Question: In one hour, a boat goes 19 km/hr along the stream and 9 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
(A) 12 kmph
(B) 13 kmph
(C) 14 kmph
(D) 15 kmph
(E) 16 kmph
Rationale: Explanation:
Let the speed downstream be a km/hr and the speed upstream be b km/hr, then
Speed in still water =1/2(a+b) km/hr
Rate of stream = 1/2(a−b) km/hr
Speed in still water = 1/2(19+9) kmph = 14 kmph.
Answer: Option C
Answer: (C) 14 kmph
Question: The product of all the prime numbers less than 10 is closest to which of the following powers of 10 ?
(A)  10^9
(B)  10^8
(C)  10^2
(D)  10^6
(E)  10^5
Rationale: P = 2*3*5*7
~ 10^ 2
Answer : C
Answer: (C)  10^2
Question: Ayesha’s father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born.What is the difference between the ages of her parents
(A) 2 years
(B) 4 years
(C) 6 years
(D) 8 years
(E) 9 years
Rationale: Solution
Mother's age when Ayesha's brother was born =36 years.
Father's age when Ayesha's brother was born =(38 + 4) years = 42 years.
∴ Required difference = (42-36) years = 6 years.. Answer C
Answer: (C) 6 years
Question: The average weight of 5 person's increases by 10.0 kg when a new person comes in place of one of them weighing 40 kg. What might be the weight of the new person?
(A) 76 kg
(B) 76.5 kg
(C) 90 kg
(D) Data inadequate
(E) None of these
Rationale: Explanation:
Total weight increased = (5 x 10.00) kg = 50 kg.
Weight of new person = (40 + 50) kg = 90 kg.
Answer: C
Answer: (C) 90 kg
Question: A bag contains 4 red, 4 blue and 2 green balls. If 2 ballsare picked at random, what is the probability that both are red?
(A) 2/15
(B) 2/21
(C) 5/26
(D) 3/29
(E) 4/27
Rationale: P(Both are red),
=4C210C2=4C210C2
=6/45=2/15
A
Answer: (A) 2/15
Question: Three numbers are in the ratio 1: 2 : 3 and their H.C.F. is 12. The numbers are?
(A) 5, 10, 15
(B) 10, 20, 30
(C) 12, 24, 36
(D) 11, 21, 31
(E) 21, 24, 32
Rationale: Let the required numbers be z, 2z and 3z. Then, their H.C.F. = z. So, z = 12.The numbers are 12, 24 and 36. answer :C
Answer: (C) 12, 24, 36
Question: The average of a set of five distinct integers is 390. If each number is less than 2,000, and the median of the set is the greatest possible value, what is the sum of the two smallest numbers?
(A) -4,494
(B) -3,997
(C) -3,494
(D) -4,044
(E) The answer cannot be determined from the information given
Rationale: Sum of the set = 390*5=1950 Each number is less than 2000 and median of the set is the greatest possible value.
Therefore last 3 numbers can be 1999,1998 and 1997. Their sum=5994.
Therefore sum of two smallest numbers= 1950-5994= -4044
Answer=D
Answer: (D) -4,044
Question: In a garden, there are 10 rows and 13 columns of mango trees. The distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden. The length of the garden is
(A) 20 m
(B) 22 m
(C) 24 m
(D) 26 m
(E) 28 m
Rationale: Explanation:
Each row contains 13 plants.
There are 12 gapes between the two corner trees (12 x 2) metres and 1 metre on each side is left.
Therefore Length = (24 + 2) m = 26 m.
Answer: D
Answer: (D) 26 m
Question: Apple costs L rupees per kilogram for first 30kgs and Q rupees per kilogram for each additional kilogram. If the price of 33 kilograms is 333 and for 36kgs of Apples is 366 then the cost of first 15 kgs of Apples is
(A) 3.69
(B) 3.66
(C) 3.6
(D) 150
(E) 3.61
Rationale: Ans: By framing equations we get
30L+3Q=333
30L+6Q=366
Eliminate Q by multiplying the first equation by 2 and subtracting second equation from the first
60L+6Q =666
30L+6Q =366
30L = 300 => L = 10
Then we get L =10
Cost of 15 kgs of apples =15 x 10 = 150
Answer:D
Answer: (D) 150
Question: A set of numbers has the property that for any number x in the set, x+5 is also in the set. If -5 is in the set, which of the following must also be in the set
1. -10
2. 10
3. 0
(A) 1 only
(B) 2 only
(C) 1 and 3 only
(D) 2 and 3 only
(E) 1,2 and 3
Rationale: If X is in the set than X+ 5 is also in the set
If -5 in the set than
-5+5= 0 is also in the set
Since + 5 is Present, 5 + 5= 10 Is also present in the set .
Therefore Ans C
Answer: (C) 1 and 3 only
Question: Magnabulk Corp sells boxes holding i magnets each. The boxes are shipped in crates, each holding b boxes. What is the price charged per magnet, in cents, if Magnabulk charges m dollars for each crate?
(A) 100bi/m
(B) bi/(100m)
(C) 100bi/m
(D) m/(bi)
(E) bi/m
Rationale: We're given some facts to work with:
1) Magnabulk Corp sells boxes holding I magnets each.
2) The boxes are shipped in crates, each holding B boxes.
3) Magnabulk charges M DOLLARS for each crate
We're asked for the price charged per magnet, in CENTS....
IF....
I = 2
B = 3
M = 12
(2 magnets per crate)(3 crates) = 6 magnets
$12 for 6 magnets = $2 per magnet = 200 cents per magnet
So we're looking for an answer that equals 200 when I=2, B=3 and M=12. There's only one answer that matches...
Answer is C
Answer: (C) 100bi/m
Question: If the average leaves of three teams of 10,20,30 employees respectively is 10,15,20 what is the average leaves of all the employees?
(A) 11.56
(B) 14.89
(C) 16.66
(D) 12.76
(E) 13.87
Rationale: Average leaves of group 1 =10
employees in group 1 = 10
Total leaves of group 1 = 10*10
Average leaves of group 2 = 15
employees in group 2 = 20
Total leaves of group 2 = 15*20
Average leaves of group 3 = 20
employees in group 3 = 30
Total leaves of group 3 = 20*30
Total employees = 10 +20+ 30 = 60
Average leaves of all the employees
=((10*10)+(15×20)+(20×30))/60
=50/3
=16.66
Answer is C.
Answer: (C) 16.66
Question: Three friends A, B and C decide to run around a circular track. They start at the same time and run in the same direction. A is the quickest and when A finishes a lap, it is seen that C is as much behind B as B is behind A. When A completes 3 laps, C is the exact same position on the circular track as B was when A finished 1 lap. Find the ratio of the speeds of A, B and C?
(A) 5 : 4 : 2
(B) 4 : 3 : 2
(C) 5 : 4 : 3
(D) 3 : 2 : 1
(E) None of these
Rationale: DETAILED SOLUTION
Let track length be equal to T. When A completes a lap, let us assume B has run a distance of (t - d). At this time, C should have run a distance of (t - 2d).
After three laps C would have traveled a distance of 3 * (t - 2d) = 3t - 6d.
After 3 laps C is in the same position as B was at the end of one lap. So, the position after 3t - 6d should be the same as t - d. Or, C should be at a distance of d from the end of the lap. C will have completed less than 3 laps (as he is slower than A), so he could have traveled a distance of either t - d or 2t - d.
=> 3t - 6d = t - d
=> 2t = 5d
=> d = 0.4t
The distances covered by A, B and C when A completes a lap will be t, 0.6t and 0.2t respectively. Or, the ratio of their speeds is 5 : 3 : 1.
In the second scenario, 3t - 6d = 2t - d => t = 5d => d = 0.2t.
The distances covered by A, B and C when A completes a lap will be t, 0.8t and 0.6t respectively. Or, the ratio of their speeds is 5 : 4 : 3.
The ratio of the speeds of A, B and C is either 5 : 3 : 1 or 5 : 4 : 3.
Correct Answer: C
Answer: (C) 5 : 4 : 3
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 290 m long?
(A) 40 sec
(B) 52 sec
(C) 45 sec
(D) 48 sec
(E) 50 sec
Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 290 = 650 m
Required time = 650 * 2/25 = 52 sec
ANSWER:B
Answer: (B) 52 sec
Question: In 1998 the profits of company N were 10 percent of revenues. In 1999, the revenues of company N fell by 30 percent, but profits were 10 percent of revenues. The profits in 1999 were what percent of the profits in 1998?
(A) 70%
(B) 105%
(C) 120%
(D) 124.2%
(E) 138%
Rationale: 0,07R = x/100*0.1R
Answer A
Answer: (A) 70%
Question: Last year, the population of a town was x and if it increases at the same rate, next year it will be y. the present population of the town is
(A) (x+y)/2
(B) (y-x)/2
(C) 2xy/x+y
(D) √xy
(E) None
Rationale: Solution: Let the present population of the town be P.Using compound interest formula
Then, P = x(1+(R/100)); ------(i)
And y = P(1+(R/100)) = P*P/x; -------(ii)
P2 = xy;
Hence, P = √xy.
Answer: Option D
Answer: (D) √xy
Question: Tough and Tricky questions: Number Properties.
If (z + 2)/5 is an integer, what is remainder when z is divided by 5?
(A) 2
(B) 4
(C) 3
(D) 5
(E) 6
Rationale: Assume the answer choices as the value of z
5/5=1
Ans C
Answer: (C) 3
Question: 1399 x 1399
(A) 1957201
(B) 1981709
(C) 18362619
(D) 2031719
(E) None of these
Rationale: 1399 x 1399 = (1399)2
= (1400 - 1)2
= (1400)2 + (1)2 - (1 x 1400 x 1)
= 1957201.
Answer: Option A
Answer: (A) 1957201
Question: Ele, the circus Elephant, is currently three times older than Lyn, the circus Lion. In 6 years from now, Lyn the circus Lion will be exactly half as old as Ele, the circus Elephant. How old is Ele today?
(A) 17
(B) 16
(C) 14
(D) 13
(E) 18
Rationale: Ele, the circus Elephant, is currently three times older than Lyn, the circus Lion.
Ele = 3*Lyn
Usually, ages are integers so there is a good possibility that the age of Ele is 18 (the only option that is a multiple of 3).
Then age of Lyn would be 6. In 6 yrs, Ele would be 24 and Lyn would be 12 - so Lyn would be half as old as Ele.
Answer (E)
Answer: (E) 18
Question: 0.0015÷ ? = 0.003
(A) 0.05
(B) 0.005
(C) 0.5
(D) 5
(E) 50
Rationale: Let 0.0015/X = 0.003
X= 0.0015/0.003
= 0.5
ANSWER:C
Answer: (C) 0.5
Question: As a treat for her two children, a mother runs to the freezer in which she has three cherry ice pops, three orange ice pops, and six lemon ice pops. She chooses two at random to bring outside to the children, but realizes as she runs out the door that she cannot bring them different flavors without one being jealous of the other and getting even more upset. What is the probability that she has to return to the freezer to make sure that they each receive the same flavor?
(A) 11/18
(B) 13/20
(C) 15/22
(D) 17/24
(E) 19/26
Rationale: P(2 cherry) = 3/12 * 2/11 = 6/132
P(2 orange) = 3/12 * 2/11 = 6/132
P(2 lemon) = 6/12 * 5/11 = 30/132
P(2 of the same flavor) = 42/132
P(2 different flavors) = 1 - 42/132 = 90/132 = 15/22
The answer is C.
Answer: (C) 15/22
Question: The area of a rectangular field is equal to 800 square meters. Its perimeter is equal to 120 meters. Find the width of this rectangle.
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25
Rationale: L * W = 800 : area , L is the length and W is the width.
2 L + 2 W = 120 : perimeter
L = 60 - w : solve for L
(60 - W) * W = 800 : substitute in the area equation
W = 20 and L = 40
correct answer D
Answer: (D) 20
Question: If the cost price of 50 articles is equal to the selling price of 32 articles, then the gain or loss percent is?
(A) 22
(B) 56.25
(C) 78
(D) 33
(E) 25
Rationale: Given that, cost price of 50 article is equal to selling price of 32 articles.
Let cost price of one article = Rs. 1
Selling price of 32 articles = Rs. 50
But Cost price of 32 articles = Rs. 32
Therefore, the trader made profit.\Percentage of profit = 18/32 * 100 = 56.25%
Answer:B
Answer: (B) 56.25
Question: Alice the number theorist knows the rule for testing if a number n is divisible by 3:
n is divisible by 3 if and only if the sum of the digits of n is divisible by 3.
When Alice visits Mars, she finds that the Martians have six hands, and six fingers on each
hand, so that they count in base 36. In base 36, Alice’s divisibility test doesn’t work for testing
divisibility by d = 3. But it does work for one of the d listed below. Which one?
(A) 4
(B) 7
(C) 10
(D) 11
(E) 15
Rationale: First of all, why does the rule work in base 10 for 3? It works because 10-1 = 3*3,
100 -1 = 3 *33, 1000 - 1 = 3 * 333, etc. As a result, the expressions
a0 + a1 *10 + a2 /102 + a3 /103 + ... + ak *10k
and
a0 + a1 + a2 + a3 + ...+ ak
differ by a multiple of 3.
The key point is that 3 |(10 - 1). It is quite easy to see that this is a necessary condition. We
can see that it is sufficient because 100-1 = (10-1) *(10+1), 1000-1 = (10*1)(100+
10 + 1), etc. So, in base 36, we must have d | (36 - 1). Therefore, d must be a divisor of 35,
and the only such divisor listed is 7.
correct answer B
Answer: (B) 7
Question: The perimeter of a square is 64 m. Find the area of the square.
(A) 161 mÂ².
(B) 164 mÂ².
(C) 166 mÂ².
(D) 256 mÂ².
(E) 273 mÂ².
Rationale: Perimeter of square = 64 m
But perimeter of square = 4 Ã— side
Therefore, 4 Ã— side = 64 m
Therefore, side= 64/4 m = 16m
Now, the area of the square = (side Ã— side)
Therefore, area of the square = 16 Ã— 16 mÂ² = 256 mÂ².
ANSWER : OPTION D
Answer: (D) 256 mÂ².
Question: A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.672 find the share of A.
(A) 256
(B) 388
(C) 379
(D) 277
(E) 122
Rationale: Explanation:
(3*8 + 2*4):(4*8 + 5*4)
8:13
8/21 * 672 = 256
Answer: A
Answer: (A) 256