mathewhe/aqua_rat huggingface dataset:
Question: If x and y are integers and |x - y| = 11, what is the minimum possible value of xy?
(A) -10
(B) -18
(C) -28
(D) -30
(E) -32
Rationale: Sometimes the answer choices to a given question provide a big 'hint' as to how you can go about solving it. This prompt can also be solved without any complex math ideas - you just need to do a bit of 'brute force' math and you'll have the answer relatively quickly.
We're told that X and Y are INTEGERS and |X - Y| = 11. We're asked for the MINIMUM possible value of (X)(Y).
Since all of the answer choices are NEGATIVE, this tells us that ONE of the two variables MUST be negative (and the other must be positive), so we should restrict our work to those options.
IF...
X = 10, Y = -1, then XY = -10
X = 9, Y = -2, then XY = -18
X = 8, Y = -3, then XY = -24
X = 7, Y = -4, then XY = -28
X = 6, Y = -5, then XY = -30
X = 5, Y = -6, then XY = -30
X = 4, Y = -7, then XY = -28
From this, we can conclude the XY will start to get bigger as X continues to decrease down to 1, so there's no need to do any additional work.
Final Answer:
D
Answer: (D) -30
Question: In the coordinate plane, points (x, 8) and (20, y) are on line k. If line k passes through the origin and has slope 1/4, then x * y =
(A) 120
(B) 100
(C) 135
(D) 140
(E) 160
Rationale: Line k passes through the origin and has slope 1/4 means that its equation is y=1/4*x.
Thus: (x, 8)=(32, 8) and (20, y) = (20,5) --> x*y=32*5=160.
Answer: E
Answer: (E) 160
Question: In Town X, 60 percent of the population are employed, and 48 percent of the population are employed males. What percent of the employed people in Town X are females?
(A) 16%
(B) 20%
(C) 31%
(D) 40%
(E) 52%
Rationale: We are asked to find the percentage of females in employed people.
Total employed people 60%, out of which 48 are employed males,hence 12% are employed females.
(employed females)/(total employed people)=12/60=1/5=20%
Answer: B.
Answer: (B) 20%
Question: The number of perfect square divisors of 12!
(A) 144
(B) 154
(C) 164
(D) 175
(E) 184
Rationale: the min no divided by 12 and is perfect square is 144
ANSWER:A
Answer: (A) 144
Question: A man is walking at the rate of 5 km/hr crosses a bridge in 15 minutes. The length of the bridge is
(A) 1000 meters
(B) 1050 meters
(C) 1200 meters
(D) 1250 meters
(E) None of these
Rationale: Explanation:
We need to get the answer in meters. So we will first of change distance from km/hour to meter/sec by
multiplying it with 5/18 and also change 15 minutes to seconds by multiplying it with 60.
Answer: D
Answer: (D) 1250 meters
Question: Four people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by:
(A) 1/3
(B) 2/7
(C) 3/7
(D) 4/7
(E) None of them
Rationale: Original share of 1 person = 1/4
New share of 1 person = 1/3
Increase = (1/3 - 1/4	= 1/12)
Therefore, Required fraction = (1/12)/(1/4)	= (1/12)x (4/1)	= 1/3
Answer is A.
Answer: (A) 1/3
Question: If the sum of a number and its square is 306, What is the number?
(A) 16
(B) 77
(C) 25
(D) 17
(E) 171
Rationale: Explanation:
Let the integer be x.
Then, x + x2 = 306
x2 + x - 306 = 0
(x + 18) (x – 17) = 0
x = 17
ANSWER: D
Answer: (D) 17
Question: 2, 3, 6, 15, _ , 123 ?
(A) 42
(B) 38
(C) 28
(D) 29
(E) 11
Rationale: ANSWER: A
Answer: (A) 42
Question: At exactly what time past 4:00 will the minute and hour hands of an accurate working clock be precisely perpendicular to each other for the first time?
(A) 20 13/21 minutes past 7:00
(B) 20 13/17 minutes past 7:00
(C) 21 3/23 minutes past 7:00
(D) 21 9/11 minutes past 4:00
(E) 22 4/9 minutes past 7:00
Rationale: 5.5 is the angle between minute n hour, this is what I was taught...so shouldn't it be solve by dividing 90 with 5.5?
That would have been the case if your initial difference between the hour and the minute hand was = 0 degrees or in other words, both minute and hour hands were at the same location. But as per the question, you are asked for time AFTER 4:00. At 4:00, the angle between the hour and the minute hand is 210 degrees. you need to take this into account as well.
So in order for the difference to decrease to 90 degrees, the minute hand must eat away this difference of 210-90 = 120 degree at the rate of 5.5 degrees per minute ---> 120/5.5 = 21 9/11 minutes.
Thus, D is the correct answer.
Answer: (D) 21 9/11 minutes past 4:00
Question: Right triangle RST can be constructed in the xy-plane such that RS is perpendicular to the y-axis and the right angle is at R. The x and y-coordinates of R, S, and T are to be nonzero integers that satisfy the inequalities −3 ≤ x ≤ 4 and −7 ≤ y ≤ 3. Given these restrictions, how many different triangles can be constructed?
(A) 3780
(B) 4200
(C) 4900
(D) 6160
(E) 7744
Rationale: −3 ≤ x ≤ 4 and −7 ≤ y ≤ 3 gives a rectangle with 8*11 dimensions (8 horizontal and 11 vertical dots). We are given that RS is parallel to x-axis, RT is parallel to y-axis and the right angle is at R.
Choose the (x,y) coordinates for vertex R: 7C1*10C1 (we are told that coordinates of R, S, and T must be nonzero integers, so we are choosing from 7 and 10 instead of 8 and 11 because we should exclude 0);
Choose the x coordinate for vertex S (as y coordinate is fixed by R): 6C1, (7-1=6 as 1 horizontal dot is already occupied by R);
Choose the y coordinate for vertex T (as x coordinate is fixed by R): 9C1, (10-1=9 as 1 vertical dot is already occupied by B).
7C1*10C1*6C1*9C1=3,780.
Answer: A.
Answer: (A) 3780
Question: Working alone at its constant rate, machine K took 3 hours to produce 1/8 of the units produced last Friday. Then machine M started working and the two machines, working simultaneously at their respective constant rates, took 9 hours to produce the rest of the units produced last Friday. How many hours would it have taken machine M, working alone at its constant rate, to produce all of the units produced last Friday?
(A) 8
(B) 12
(C) 18
(D) 24
(E) 30
Rationale: Machine K works at a rate of 1/24 of the units per hour.
The rate of K + M together is 7/8 * 1/9 = 7/72 of the units per hour.
The rate of machine M is 7/72 - 3/72 = 1/18.
It would have taken machine M a total time of 18 hours.
The answer is C.
Answer: (C) 18
Question: If 5 women or 8 girls can do a work in 84 days. In how many days can 10 women and 5 girls can do the same work?
(A) 32 days
(B) 48 days
(C) 52 days
(D) 38 days
(E) 28 days
Rationale: Given that 5 women is equal to 8 girls to complete a work.
So, 10 women = 16 girls.
Therefore 10 women + 5 girls = 16 girls + 5 girls = 21 girls.
8 girls can do a work in 84 days then 21 girls can do a work in (8*84/21) = 32 days.
Therefore 10 women and 5 girls can a work in 32 days
Answer : A.
Answer: (A) 32 days
Question: P, Q and R can do a work in 20, 30 and 60 days respectively. How many days does it need to complete the work if P does the work and he is assisted by Q and R on every third day?
(A) 15 days
(B) 17 days
(C) 25 days
(D) 27 days
(E) 29 days
Rationale: Amount of work P can do in 1 day = 1/20
Amount of work Q can do in 1 day = 1/30
Amount of work R can do in 1 day = 1/60
P is working alone and every third day Q and R is helping him
Work completed in every three days = 2 × (1/20) + (1/20 + 1/30 + 1/60) = 1/5
So work completed in 15 days = 5 × 1/5 = 1
Ie, the work will be done in 15 days
A)
Answer: (A) 15 days
Question: The sum of three integers A, B and C is 60. A is one third of the sum of B and C and B is one fifth of the sum of A and C. What is C?
(A) 40
(B) 45
(C) 35
(D) 50
(E) 55
Rationale: A is one third of the sum of B and C..
or A=1/3(B+C)...
But A+B+C=60
so 1/3(B+C)+B+C=60
4(B+C)/3= 60
B+C =60*3/4 = 45
A=60-45=15
2)B is one fifth of the sum of A and C
or B=1/5(A+C)...
But A+B+C=60
so 1/5(A+C)+A+C=60
A+C=60*5/6=50
but A=15, so C=50-15=35
Answer :C
Answer: (C) 35
Question: Andrew purchased 14kg of grapes at the rate of 54 per kg and 10 kg of mangoes at the rate of 62 per kg. How much amount did he pay to the shopkeeper?
(A) 1000
(B) 1376
(C) 1456
(D) 1900
(E) 1566
Rationale: Cost of 14 kg grapes = 54 × 14 = 756.
Cost of 10 kg of mangoes = 62 x10 = 620.
Total cost he has to pay = 756 + 620 = 1376
B
Answer: (B) 1376
Question: find the number, difference between number and its 3/5 is 64.
(A) 160
(B) 163
(C) 164
(D) 165
(E) 166
Rationale: Explanation:
Let the number = x,
Then, x-(3/5)x = 64,
=> (2/5)x = 64 => 2x = 64*5,
=> x = 160
Answer: Option A
Answer: (A) 160
Question: In a mixture 60 litres, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then the quanity of water to be further added is:
(A) 40
(B) 20
(C) 30
(D) 80
(E) 60
Rationale: Quantity of milk = (60 x 2/3) litres = 40 litres.
Quantity of water in it = (60- 40) litres = 20 litres.
New ratio = 1 : 2
Let quantity of water to be added further be x litres.
Then, milk : water = (40/(20 + x))
Now, (40/(20 + x))= 1/2
= 20 + x = 80
= x = 60.
Therefore, Quantity of water to be added = 60 litres.
Answer is E.
Answer: (E) 60
Question: Find the average of all numbers between 5 and 45 which are divisible by 6
(A) 26
(B) 24
(C) 28
(D) 30
(E) 35
Rationale: Explanation:
Average=(6+12+18+24+30+36+42 / 6)=168/6=28
Option C
Answer: (C) 28
Question: If x/y is an integer, which of the following must also be not an integer?
I. xy
II. y/x
III. x
(A) I alone
(B) II alone
(C) III alone
(D) I and III
(E) All three answers
Rationale: Let's take X = 4/3 and Y = 2/3
Then X/Y = 2 which is an integer.
But XY = 4/3 * 2/3 = 8/9 --> Not an integer.
Y/X = 2/3 divided by 4/3 = 2/4 = 1/2 Not an integer.
X alone is 4/3. Not an integer.
Hence E.
Answer: (E) All three answers
Question: 15 litres of mixture contains 20% alcohol and the rest water. If 3litres of water be mixed with it, the percentage of alcohol in the new mixture would be?
(A) 16.67%
(B) 23%
(C) 18.3%
(D) 19.75%
(E) 21.23%
Rationale: Alcohol in the 15litres of mix. = 20% of 15litres = (20*15/100) = 3litres
water in it = 15-3 = 12litres
new quantity of mix. = 15+3 = 18 litres
Quantity of alcohol in it = 3litres
Percentage of alcohol in new mix. = 3*100/18 = 50/3= 16.67%
Answer is A
Answer: (A) 16.67%
Question: A(n+1)=1+(1/A(n)) and A(1)=1. What is the value of A(7)?
(A) 15/7
(B) 17/9
(C) 19/11
(D) 21/13
(E) 23/15
Rationale: A(n+1)=1+(1/A(n))
A(1) = 1
A(2) = 2
A(3) = 3/2
A(4) = 5/3
A(5) = 8/5
A(6) = 13/8
A(7) = 21/13
The answer is D.
Answer: (D) 21/13
Question: Two fill pipes A and B can fill a cistern in 12 and 16 minutes respectively. Both fill pipes are opened together, but 4 minutes before the cistern is full, one pipe A is closed. How much time will the cistern take to fill ?
(A) 9 1⁄7min.
(B) 3 1⁄3min.
(C) 5 min.
(D) 3 min.
(E) None of these
Rationale: Let cistern will be full in x min. Then,
part filled by B in x min + part filled by A in (x – 4)min = 1
⇒ x/16+x−4/12=1
⇒ x = 64⁄7 = 91⁄7 hours.
Answer A
Answer: (A) 9 1⁄7min.
Question: What approximate value should come in place of the question mark (?) in the following equation?
85.147 + 34.912 × 6.2 + ? = 802.293
(A) 400
(B) 450
(C) 550
(D) 600
(E) 500
Rationale: 85.147 + 34.912 × 6.2 + ? = 802.293
or, ? = 802.293 – 85.147 – 34.912 × 6.2
≈ 800 – 85 – 35 × 6 ≈ 500
Answer E
Answer: (E) 500
Question: What is the sum of the different positive prime factors of 540?
(A) 10
(B) 11
(C) 15
(D) 16
(E) 18
Rationale: 540
54*10 --> 3*3*3*2*2*5 --> 3+5+2=10. Remember its asking for the DIFFERENT positive prime factors of 540.
A
Answer: (A) 10
Question: The number of sailors on a ship is 88% more than the number of officers. The ratio of sailors to officers would be
(A) 33:25
(B) 47:20
(C) 47:25
(D) 22:25
(E) 97:50
Rationale: Sailor = 1/88 * Officer
Sailor/Officer = 1.88/1 = 188/100 = 47/25
Answer will be C
Answer: (C) 47:25
Question: Mysoon collects glass ornaments. Ten more than 1/6 of the ornaments in her collection are handmade, and 1/2 of the handmade ornaments are antiques. If 1/4 of the ornaments in her collection are handmade antiques, how many ornaments are in her collection?
(A) 30
(B) 60
(C) 108
(D) 144
(E) 180
Rationale: The number of ornaments = a
Ten more than 1/6 of the ornaments in her collection are handmade => Handmade = 10+a/6
1/2 of the handmade ornaments are antiques => Handmade ornaments = 1/2*(10+a/6) = 5 + a/12
1/4 of the ornaments in her collection are handmade antiques => Handmade ornaments = a/4
=> 5 + a/12 = a/4 => a = 30
Ans: A
Answer: (A) 30
Question: Indu gave Bindu Rs.1250 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 1250 = D(100/4)2
D = 2
Answer: B
Answer: (B) 2
Question: A ferry can transport 85 tons of vehicles. Automobiles range in weight from 1,800 to 3,200 pounds. What is the greatest number of automobiles that can be loaded onto the ferry?
(A) 23
(B) 41
(C) 48
(D) 90
(E) 86
Rationale: to get maximum vehicles we must take into consideration the minimum weight i.e 1800 pounds here
since , 1 ton = 2000 pounds
85 tons will be 170,000 pounds
from the answer choices:
let max number of vehicles be 86
total weight will be =90*1800 = 162000 pounds , which is lesser than the maximum weight allowed .
Ans: D
Answer: (D) 90
Question: If 1=x. 2=2x 3=4x....
what is 2x*6x+5x/4x-56x
(A) 1
(B) 22
(C) 23
(D) 10
(E) 25
Rationale: Let
1=x
2=2x
3=4x
4=8x
5=16x
6=32x
7=64x
now given
2x*6x+5x/4x-56x
i can write it as
=2x*(2x+4x)+(x+4x)/4x-(64x-8x)
Now by putting the values i get
=2*(2+3)+(8+1)/3-(7-4)
=2*5+9/3-3
=10+9/3-3
=10+3-3
=10
ANSWER:D
Answer: (D) 10
Question: A man purchases 2 watches for $ 400. He sells one at 10% profit and the other at a loss of 15%. He neither gains nor loses on the whole. Thus, the cost price of two watches are :
(A) $ 260 and $ 300
(B) $210 and $ 350
(C) $160 and $240
(D) $400 and $80
(E) $224 and $ 350
Rationale: x + y = 400 --- (1)
1.10x + 0.85y = 400 --- (2)
(2) - (1) --> 0.10x - 0.15y = 0
10x =15y
x/y = 15/10= (2*80)/(3*80) =160/240
Answer: C
Answer: (C) $160 and $240
Question: Insert the missing number
4, -8, 16, -32, 64, (....)
(A) 128
(B) -128
(C) 192
(D) -132
(E) 0
Rationale: 4*-2=-8
-8*-2=16
16*-2=-32
-32*-2=64
64*-2=-128
ANSWER:B
Answer: (B) -128
Question: Evaluate : (313 x 313 + 287 x 287).
(A) 180338
(B) 108338
(C) 180383
(D) 180833
(E) None of them
Rationale: (a^2 + b^2) = 1/2 [(a + b)^2 + (a- b)^2]
(313)^2 + (287)^2 = 1/2 [(313 + 287)^2 + (313 - 287)^2] = ½[(600)^2 + (26)^2]
= 1/2 (360000 + 676) = 180338.
Answer is A.
Answer: (A) 180338
Question: In the Biotechnology class of 2000, there were R graduates. 32 of the graduates found a job, 45 continued on to their second degree and 13 did both. If only 9 people didn't do both, What is R equal to?
(A) 69.
(B) 71.
(C) 73.
(D) 75.
(E) 76.
Rationale: Total = 32 +45 -13 +9 = 73 .... My first post on the forum... I hope I am correct
C is correct choice.
Answer: (C) 73.
Question: In a question on division with zero remainder, a candidate took 12 as divisor instead of 21. The quotient obtained by him was 35. The correct quotient is?
(A) 10
(B) 20
(C) 24
(D) 26
(E) 28
Rationale: Number = (35 * 12) = 420
Correct quotient = 420/21 = 20
B)
Answer: (B) 20
Question: A man's present age is two-fifth of the age of his father. After 8 years, he will be one-half of the age of his father. How old is the father at present
(A) 30
(B) 35
(C) 50
(D) 55
(E) 40
Rationale: fathers age - x
man present age = 2/5x
(2/5x+8) = 1/2(x+8)
==> x =40
ANSWER E
Answer: (E) 40
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) 9
(B) 7
(C) 5
(D) 4
(E) 6
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: E
Answer: (E) 6
Question: A tourist purchased a total of $1,450 worth of traveler’s checks in $10 and $50 denominations, During the trip the tourist cashed 7 checks and then lost all of the rest. If the number of $10 checks cashed was one more or one less than the number of $50 checks cashed, what is the minimum possible value of the checks that were lost?
(A) $1,430
(B) $1,310
(C) $1,290
(D) $1,220
(E) $1,150
Rationale: since total cashed checks = 7 ans $10 check cashed = one less or more than $50 checks
Therefore either $10 checks = 3 and $50 checks = 4 OR $10 checks = 4 and $50 checks = 3
using this information 1st option gives us the maximum cashed value therefore if we negate this value from total value we will get minimum value of which checks have lost
Therfore 1450 - 230 = 1220 hence answer is D
Answer: (D) $1,220
Question: The sum of number of boys and girls in a school is 150. If the number of boys is x, then the number of girls becomes x% of the total number of students. The number of boys is?
(A) 50
(B) 40
(C) 60
(D) 100
(E) 70
Rationale: We have x+x% of 150 = 150
x + x/100 * 150 = 150
5/2 * x = 150
x = 150*2/5 = 60
Answer is C
Answer: (C) 60
Question: The average of 7 numbers is 15. If each number be multiplied by 5. Find the average of new set of numbers?
(A) A)110
(B) B)122
(C) C)90
(D) D)85
(E) E)75
Rationale: Explanation:
Average of new numbers = 15 * 5 = 75
Answer: Option E
Answer: (E) E)75
Question: A farmer with 1,350 acres of land had planted his fields with corn, sugar cane, and tobacco in the ratio of 5:2:2, respectively, but he wanted to make more money, so he shifted the ratio to 2:3:4, respectively. How many more acres of land were planted with tobacco under the new system?
(A) 75
(B) 150
(C) 300
(D) 450
(E) 600
Rationale: Originally (2/9)*1350 = 300 acres were planted with tobacco.
In the new system (4/9)*1350 = 600 acres were planted with tobacco.
Thus 600-300 = 300 more acres were planted with tobacco.
The answer is C.
Answer: (C) 300
Question: The mean daily profit made by a shopkeeper in a month of 30 days was Rs. 350. If the mean profit for the first fifteen days was Rs. 255, then the mean profit for the last 15 days would be
(A) Rs. 200
(B) Rs. 445
(C) Rs. 275
(D) Rs. 425
(E) None of these
Rationale: Average would be : 350 = (255 + x)/2
On solving, x = 445.
Answer: B
Answer: (B) Rs. 445
Question: A positive integer is divisible by 3 if and only if the sum of its digits is divisible by 3. If the six-digit integer is divisible by 3, and n is of the form 1k1,k34, where k represents a digit that occurs twice, how many values could n have?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 10
Rationale: 1k1k34
Taking sum of the numericals = 1 + 1 + 3 + 4 = 9
We require the values of K such that they are also divisible by 3
101034
131334
161634
191934
Answer = 4 =D
Answer: (D) 4
Question: The average price of three items of furniture is Rs. 15000. If their prices are in the ratio 2:4:8, the price of the cheapest item is?
(A) 2379
(B) 2889
(C) 5625
(D) 9000
(E) 28311
Rationale: Let their prices be 3x, 5x and 7x.
Then, 2x + 6x + 8x = (15000 * 3) or x = 2812.5.
Cost of cheapest item = 2x = Rs. 5625.
Answer: C
Answer: (C) 5625
Question: Working at their respective constant rates, Paul, Abdul and Adam alone can finish a certain work in 3, 4, and 5 hours respectively. If all three work together to finish the work, what fraction W of the work will be done by Adam?
(A)  1/4
(B)  12/47
(C)  1/3
(D)  5/12
(E)  20/47
Rationale: Let the total work be 60 units. Pual does 60/3 =20 units of work per hr. abdul does 15 units per hr and adam does 12 units per hr. If all work together they do (20 + 15 + 12) units per hr = 47 units per hr. So the time taken to finish the work = 60/47 hrs.
adam will do 60/47 * 12 units of work in 60/47 hr . fraction of work adam does =work done by adam / total work
W>( 60/47 *12)/60 =12/47
Answer B
Answer: (B)  12/47
Question: if price of t.v set is reduced by 10%, then its sale increases by 85%, find net effect on sale value
(A) 44
(B) 45
(C) 46
(D) 67
(E) 48
Rationale: - a + b + ((-a)(b)/100)
= -10+85+(-10*85)/100
= -10+85-8.5
=67
ANSWER:D
Answer: (D) 67
Question: Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 64 hours and 25 hours respectively. The ratio of their speeds is?
(A) 4:9
(B) 4:3
(C) 4:5
(D) 5:8
(E) 4:2
Rationale: Let us name the trains A and B.
Then, (A's speed) : (B's speed)
= √b : √a = √25 : √64
= 5:8
Answer:D
Answer: (D) 5:8
Question: How many positive integers less than 5,000 are evenly divisible by neither 15 nor 22?
(A) 4,514
(B) 4,475
(C) 4,521
(D) 4,428
(E) 4,349
Rationale: integers less than 5000 divisible by 15 5000/15 =333.something , so 333
integers less than 5000 divisible by 22 5000/22 = 238.## , so 238
we have double counted some, so take LCM of 15 and 22 =105 and divide by 5000, we get 47. so all numbers divisible by 15 and 22 = 333 +238 -47 =524
now subtract that from 4999. 4999- 524 = 4514 answer A.
Answer: (A) 4,514
Question: The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 40% profit?
(A) 2000
(B) 2778
(C) 2299
(D) 2778
(E) 2240
Rationale: Let C.P. be Rs. x.
Then, (1920 - x)/x * 100 = (x - 1280)/x * 100
1920 - x = x - 1280
2x = 3200 => x = 1600
Required S.P. = 140 % of Rs. 1600 = 140/100 * 1600 = Rs. 2240.
Answer:E
Answer: (E) 2240
Question: 97 students take part in a test and the median score is 85. Which of the following descriptions must be correct?
I.At most 49 students’ score are equal to or more than 86.
II. At least 49 students’ score are less than 85.
III. At least 49 students’ score are equal to or more than 85.
(A) I
(B) II
(C) III
(D) III
(E) IIII
Rationale: If we order the scores increasingly, then on the 49th place we have the score of 85. There must be 48 scores (those on the right of the 85 score) greater or equal to 85. So, I is necessarily correct.
The scores on the left of the 49th place, all have to be equal or less than 85. Since we can have the extreme case of all the scores 85, neither II, nor III is correct. The question asks for descriptions thatmustbe correct.
Answer C.
Answer: (C) III
Question: The ‘moving walkway’ is a 300-foot long walkway consisting of a conveyor belt that moves continuously at 3 feet per second. When Bill steps on the walkway, a group of people that are also on the walkway stands 120 feet in front of him. He walks toward the group at a rate of 3 feet per second. Once Bill reaches the group of people, he stops walking and stands with them until the walkway ends. What is Bill’s average rate Q of movement for his trip along the moving walkway?
(A) 2 feet per second
(B) 2.5 feet per second
(C) 3 feet per second
(D) 4 feet per second
(E) 5 feet per second
Rationale: A, B, and C don't make ANY sense! we know for some time...(a majority of the 300ft) Bill will walk at a pace of 6ft per second...and then at some later time he will stop and move at 3 ft per second... The average MUST bebetween3-6 ft per second or the Earth is FLAT!!!.
So we are down to DE, D doesn't make sense on a weighted averages level because we know when Bill gets on the walkway the patrons are already 40% of the way down the 300ft walkway AND they are still moving at half the rate of Bill!! So for Bill to average 4 ft per second he would have had to spend a majority of the 300 ft at 3ft per second because 4 is much closer (when you factor in the size of the values we're dealing with 2 is double 1) to 3 than to 6. We know from the information that isn't possible. Billmust havespent the majority of his time at 6 ft Q per second before he stopped walking. That leaves only answer E as plausible.
Answer: (E) 5 feet per second
Question: If a tire rotates at 400 revolutions per minute when the car is traveling 72km/h, what is the circumference of the tire?
(A) 2
(B) 1
(C) 4
(D) 3
(E) 5
Rationale: 400 rev / minute = 400 * 60 rev / 60 minutes
= 24,000 rev / hour
24,000 * C = 72,000 m : C is the circumference
C = 3 meters
correct answer D
Answer: (D) 3
Question: The difference between the place values of two sevens in the numerical 69758472 is
(A) 0
(B) 6993
(C) 699930
(D) 996330
(E) None of them
Rationale: Required difference = (700000-70)
=699930.
Answer is C
Answer: (C) 699930