mathewhe/aqua_rat huggingface dataset:
Question: One man traveled a distance of 61 km in 9hrs. He traveled partly on footat 4 km/hr and partly on bicycle ta 9 km/hr. The distance traveled on foot is?
(A) 8 km
(B) 12 km
(C) 16 km
(D) 18 km
(E) 20 km
Rationale: Let the distance travelled on foot be x km.
Then, distance travelled on bicycle = (61 -x) km.
So, x + (61 -x) = 9
4 9
9x + 4(61 -x) = 9 x 36
5x = 80
x = 16 km.
C
Answer: (C) 16 km
Question: An express traveled at an average speed of 100 km/hr, stopping for 4 min after every 75 km. How long did it take to reach its destination 150 km from the starting point ?
(A) 8 hrs 29 min
(B) 6 hrs 28 min
(C) 2 hrs 28 min
(D) 6 hrs 28 min
(E) 1 hr 34 min
Rationale: Explanation:
Time taken to cover 150 km = 150/100 = 1 hr 30 mins
Number of stoppages = 150/75 - 1 = 1
Total time of stoppages = 4 x 1 = 4 min
Hence, total time taken = 1 hr 34 min.
Answer: E
Answer: (E) 1 hr 34 min
Question: How many quarters are equal to 7 dollars?
(A) 1
(B) 28
(C) 12
(D) 9
(E) 7
Rationale: 7 * 4 = 28 quarters
Answer : B
Answer: (B) 28
Question: If w is three times larger than n , and if 2n+3 is 20% of 25, what is the value of ?
(A) 1
(B) 2
(C) 3
(D) 6
(E) 12
Rationale: Then the wordings of question are misleading. Moreover, it'd also be a bad way to convey w=4n, if it really wanted to convey so.
From other questions that I have seen, proper wordings could be:
If w is three times as large as n
OR simply,
If w is three times n.C
Answer: (C) 3
Question: What is the next number in this sequence: 39, 52, 65, 78, 91 ?
(A) 107
(B) 112
(C) 104
(D) 99
(E) 109
Rationale: By subtracting each number from the one after it, we can determine that the numbers are all multiples of 13. By adding 13 to the last number, you get the answer.
91 + 13 = 104
Answer: C
Answer: (C) 104
Question: If x and y are perfect squares, then which two of the following is not necessarily a perfect square?
(A) x^2
(B) xy
(C) 4x
(D) x+y
(E) x^5
Rationale: If x=y=1^2=1, then each option but C is a perfect square, therefore C is NOT necessarily a perfect square.
Answer: C.
Answer: (C) 4x
Question: If 4x + 22x-1 = 3x+(1/2) = 3x - (1/2)
(A) 1/2
(B) 3/2
(C) 5/2
(D) 2
(E) 7/2
Rationale: 4x+4x/2 = 3x/√3 + 3x.√3
=> 4x.3/2 = 3x.4/√3
=> (4/3)x = 8/(3√3)
=> [4/3]x = [4/3]3/2
=> x = 3/2
ANSWER:B
Answer: (B) 3/2
Question: A farm has chickens, cows and sheep. There are six times the number of chickens and cows than sheep. If there are more cows than chickens or sheep, and together, cows and chickens have a total of 100 feet and heads, how many sheep live at the farm?
(A) 5
(B) 8
(C) 10
(D) 4
(E) 17
Rationale: Chicken - ch
Cows - C
Sheep -S
ch+C=6S
C> ch and c>s
Each cow has 4 legs and 1 head
Each chicken has 2 legs and 1 head
So 5c+3ch=100 (sum of legs and head)
There are 2 possible solutions to this equation
c=11 and ch=9 or
c=14 and ch=10
Since from first equation where ch+c=6s
The sum of ch and c should be divisbile by 6. 20 is not so the only possible solution is c=14 and ch=10. So s=4
Answer : D
Answer: (D) 4
Question: The length of a rectangle is increased by 25% and its breadth is decreased by 20%. What is the effect on its area?
(A) 10000
(B) 10020
(C) 10208
(D) 10029
(E) 10182
Rationale: 100 * 100
= 10000
125 * 80
= 10000
Answer:A
Answer: (A) 10000
Question: Solve This
6 + 7 = 12
8 + 9 = 16
5 + 6 = 10
7 + 8 = 14
Then, 9 + 10 = ??
(A) 11
(B) 12
(C) 13
(D) 14
(E) 18
Rationale: 18
ANSWER:E
Answer: (E) 18
Question: 9.009/1.001
(A) 0.009
(B) 0.09
(C) 0.9
(D) 9
(E) 90
Rationale: Answer is 9, move the decimal forward three places for both numerator and denominator or just multiply both by a thousand. The result is 9009/1001= 9
Answer D
Answer: (D) 9
Question: If t>0.9, which of the following options can be the value of t?
(A) 0.9^2
(B) √(0.9)
(C) 0.09
(D) 0.9
(E) 0.9^3
Rationale: Lets take a few examples
When .2 is squared it gives .04
when .5 is squared it gives .25
When .9 is squared it gives .81
So raising a fraction to its power of 2 or 3 only reduces the value of the fraction
This is because
.2 = 2/10
.2^2= 4/100
.2^3=8/1000
Since the denominator gets an extra 0 each time u increase the power , it is going to drag the value down
But if you just think about the opposite case :
Then we can see , if squaring a fraction diminish its value, then taking the square root of it will again increase its value
that is √(0.04) will give you back 0.2
so √(0.04) > 0.04
so obviously diminishing the power will appreciate the value
So t √(0.9) > 0.9
Hence Correct Answer is (B)
Answer: (B) √(0.9)
Question: Cheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 5 to 7 to 8. If a total of 160 sandwiches were made, how many bologna sandwiches
were made?
(A) 15
(B) 30
(C) 38
(D) 42
(E) 56
Rationale: For deciding such task we should calculate all parts 5 + 7 + 8 = 20 parts
and we should calculate how many sandwiches holds 1 part:
160 / 20 = 8 sandwiches in one part
For bologna we have 8 parts so:
7 * 8 = 56
Answer is E
Answer: (E) 56
Question: A store has 10 bottles of juice, including 5 bottles of apple juice. In the evening, 6 bottles of juice are sold one by one. What is the probability of selling 3 bottles of apple juice among the 6 bottles? Assume that every bottle has an equal chance of being bought.
(A) 4/9
(B) 6/11
(C) 8/15
(D) 10/21
(E) 12/25
Rationale: The total number of ways to sell 6 bottles from 10 is 10C6 = 210.
The number of ways to sell 3 bottles of apple juice is 5C3*5C3 = 10*10 = 100
P(selling 3 bottles of apple juice) = 100/210 = 10/21
The answer is D.
Answer: (D) 10/21
Question: The length of the bridge, which a train 140 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 388
(B) 267
(C) 235
(D) 288
(E) 261
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (140 + X)/30 = 25/2 ==> X = 235 m.
Answer: C
Answer: (C) 235
Question: For any positive integer n, the sum of the first n positive integers equals [n(n+1)]/2.
What is the sum of all the even integers between 99 and 201?
(A) 6540
(B) 7650
(C) 8760
(D) 9870
(E) 10,980
Rationale: 100 + 102 +...+ 200 = 51*100 + (2+4...+100) = 51*100 + 2(1+2+...+50) =
51*100 + 2(50)(51)/2 = 150*51 = 7650
The answer is B.
Answer: (B) 7650
Question: What is the solution of the equations x - y = 0.9 and 11(x + y)-1 = 2 ?
(A) x = 3.2, y = 2.3
(B) x = 1, y = 0.1
(C) x = 2, y = 1.1
(D) x = 1.2, y = 0.3
(E) None
Rationale: Answer
x - y = 0.9 ...(i)
and 11(x + y)-1=2
⇒ 11/ (x + y) = 2
⇒ 2(x + y) =11
⇒ x + y = 11/2 ...(ii)
On solving Eqs.(i) and (ii),we get
x = 3.2
and y = 2.3
Correct Option: A
Answer: (A) x = 3.2, y = 2.3
Question: Two varieties of wheat - A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3 : 7. If 5 kg of the mixture is sold at 25% profit, find the profit made?
(A) Rs. 13.50
(B) Rs. 14.50
(C) Rs. 15.50
(D) Rs. 16.50
(E) None of these
Rationale: Let the quantities of A and B mixed be 3x kg and 7x kg.
Cost of 3x kg of A = 9(3x) = Rs. 27x
Cost of 7x kg of B = 15(7x) = Rs. 105x
Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x
Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66
Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 * 66 = Rs. 16.50
ANSWER:D
Answer: (D) Rs. 16.50
Question: A certain college's enrollment at the beginning of 1992 was 20 percent greater than it was at the beginning of 1991, and its enrollment at the beginning of 1993 was 10 percent greater than it was at the beginning of 1992. The college's enrollment at the beginning of 1993 was what percent greater than its enrollment at the beginning of 1991 ?
(A) 17.5%
(B) 24%
(C) 30%
(D) 32%
(E) 38%
Rationale: Suppose enrollment in 1991 was 100
Then enrollment in 1992 will be 120
And enrollment in 1993 will be 120*1.10=132
Increase in 1993 from 1991 = 132-100= 32
Answer : D
Answer: (D) 32%
Question: At what rate of annual simple interest,a certain sum will amount to four times in 15 year?
(A) 15%
(B) 17.5%
(C) 20%
(D) 25%
(E) 35%
Rationale: r=?
t=15 yrs
SI=p*r*t/100
Amount = SI+p = 4p
(p*r*15/100)+p = 4p
p(15r/100 + 1) = 4p
15r + 100 = 400
15r = 300
r = 20%
ANSWER:C
Answer: (C) 20%
Question: At what angle the hands of a clock are inclined at 15 minutes past 5?
(A) 67.9
(B) 67.5
(C) 67.2
(D) 67.1
(E) 67.92
Rationale: Answer: B) 67.5 degrees
Answer: (B) 67.5
Question: The area of a parallelogram is 147 sq m and its base is thrice the corresponding height. Then the length of the base is?
(A) 14m
(B) 29m
(C) 49m
(D) 7
(E) none
Rationale: b*h=147 b*h=147=>b^2=49m.b=7 Answer: (D)
Answer: (D) 7
Question: Albert buys 4 horses and 9 goats for $ 13,400. If he sells the horses at 10% profit and the goats at 20% profit, then he earns a total profit of $ 1880. The cost of a horse is:
(A) $ 3000
(B) $ 6000
(C) $ 2000
(D) $ 8000
(E) $ 7000
Rationale: C
$ 2000
Let C.P. of each horse be $ x and C.P. of each cow be $ y.
Then, 4x + 9y = 13400 -- (i)
And, 10% of 4x + 20% of 9y = 1880
2/5 x + 9/5 y = 1880 => 2x + 9y = 9400 -- (ii)
Solving (i) and (ii), we get : x = 2000 and y = 600.
Cost price of each horse = $ 2000.
Answer: (C) $ 2000
Question: Free notebooks were distributed in a class among all the students. Each student got notebooks which were one-eighth of the number of student. If number of student been half, then each child would have received 16 notebooks in total. Find the total number of books distributed among students?
(A) 456
(B) 480
(C) 499
(D) 501
(E) 512
Rationale: Let suppose total number of students in class are X.
Then from the question we can conclude it that,
X∗18X=X2∗16=>X=64Total notebooks,=18X2=(18∗64∗64)=512
E
Answer: (E) 512
Question: The sum of three numbers is 98. If the ratio of the first to the second is 2:3. And that of the second to the third is 5:8, then the second number is:
(A) 17
(B) 30
(C) 87
(D) 27
(E) 82
Rationale: Let the three parts A, B, C.
Then, A:B = 2:3 and B:C = 5:8
= (5 * 3/5) : (8 * 3/5) = 3:24/5
A:B:C = 2:3:24/5
= 10:15:24 => B = 98 * 15/49 = 30.
Answer:B
Answer: (B) 30
Question: When tossing two coins once, what is the probability of heads on both the coins?
(A) 2/7
(B) 3/5
(C) 2/6
(D) 1/4
(E) 1/47
Rationale: Explanation :
Total number of outcomes possible when a coin is tossed = 2
Hence, total number of outcomes possible when two coins are tossed, n(S) = 2 × 2 = 4
E = event of getting heads on both the coins = {HH}
Hence, n(E) = 1
P(E)=n(E)/n(S)=1/4
D
Answer: (D) 1/4
Question: A train is 360 meter long is running at a speed of 60 km/hour. In what time will it pass a bridge of 140 meter length?
(A) 87
(B) 69
(C) 30
(D) 72
(E) 21
Rationale: Speed = 60 Km/hr = 60*(5/18) m/sec = 50/3 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (3/50) = 30 seconds
Answer: C
Answer: (C) 30
Question: The average of 13 numbers is 60. Average of the first 7 of them is 56 and that of the last 7 is 61. Find the 8th number?
(A) 39
(B) 83
(C) 45
(D) 53
(E) 64
Rationale: Sum of all the 13 numbers = 13 * 60 = 780
Sum of the first 7 of them = 7 * 56 = 392
Sum of the last 7 of them = 7 * 61 = 427
So, the 8th number = 427 + 392 - 780 = 39.
Answer:A
Answer: (A) 39
Question: five children, Arya, Betsy, Chen, Daniel, Emily, are to be seated in a single row of six chairs. If Betsy cannot sit next to Emily, how many different arrangements of the six children are possible?
(A) 240
(B) 480
(C) 540
(D) 72
(E) 840
Rationale: Since it is more time consuming and error prone to find ways Betsy and E not sitting together, It is better we find ways in which they will be together and then subtract from total ways..
total ways = 5!..
ways B and E will be sitting together..
take both B and E as one, then these two together with other 3 can sit in 4! ways ...
Also B and E can sit within themselves in 2! ways..
so the answer required = 5!-2*4!=72..
D
Answer: (D) 72
Question: A standard Veggiematik machine can chop 36 carrots in 4 minutes. How many carrots can 6 standard Veggiematik machines chop in 3 minutes?
(A) 36
(B) 54
(C) 162
(D) 216
(E) 324
Rationale: Direct Relationship:-
1 standard Veggiematik machine - 36 Carrots - 4 minutes,
1 standard Veggiematik machine - 9 Carrots - 1 minute,
Now
6 standard Veggiematik machine - ? Carrots - 3 minutes,
Hence = 9X6X3 =324 Carrots
Answer C
Answer: (C) 162
Question: The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water?
(A) 9
(B) 4
(C) 8
(D) 5
(E) 3
Rationale: S = 4
M = x
DS = x + 4
US = x - 4
6/(x + 4) + 6/(x - 4) = 2
x = 8
Answer:C
Answer: (C) 8
Question: If A is thrice as fast as B and together can do a work in 15 days. In how many days A alone can do the work?
(A) 36
(B) 20
(C) 28
(D) 54
(E) 45
Rationale: A’s one day’s work= 1/X
B’s one day’s work= 1/3x
A + B’s one day’s work= 1/x + 1/3x = 1/15
= 3+1/3x = 4/3x = 1/15
x = 15*4/3 = 20
ANSWER:B
Answer: (B) 20
Question: a, b, c, d, and e are five consecutive numbers in increasing order of size. Deleting one of the five
numbers from the set decreased the sum of the remaining numbers in the set by 20%. Which one of
the following numbers Q was deleted?
(A)  a
(B)  b
(C)  c
(D)  d
(E)  e
Rationale: a+b+c+d+e => 1+2+3+4+5=15
Q=20%*15= 3 =>C
Answer: (C)  c
Question: A sells a Cricket Bat to B at a profit of 20%. B sells it to C at a profit of 25%. If C pays $222 for it, the cost price of the Cricket Bat for A is:
(A) 150
(B) 148
(C) 130
(D) 160
(E) 210
Rationale: 125% of 120% of A = 222
125/100 * 120/100 * A = 222
A = 222 * 2/3 = 148.
ANSWER B
Answer: (B) 148
Question: Sally has a gold credit card with a certain spending limit, and a platinum card with twice the spending limit of the gold card. Currently, she has a balance on her gold card that is 1/3 of the spending limit on that card, and she has a balance on her platinum card that is 1/9 of the spending limit on that card. If Sally transfers the entire balance on her gold card to her platinum card, what portion of her limit on the platinum card will remain unspent?
(A) 11/30
(B) 29/60
(C) 17/30
(D) 13/18
(E) 11/15
Rationale: Let s assume the platinum card spending limit =x
Gold card spending limit will be =x/2
balance on gold card is =x/2*1/3=x/6
Platinum card unspent limit is= x-1/9x=8/9x
So if gold card balance is transferred then the rest unspent will be
8/9x-x/6=13/18x
So the ans is D
Answer: (D) 13/18
Question: The membership of a committee consists of 3 English teachers, 4 Mathematics teachers, and 2 Social Studies teachers. If 2 committee members are to be selected at random to write the committee’s report, what is the probability that the two members selected will both be social teachers?
(A) 2/3
(B) 1/12
(C) 2/9
(D) 1/2
(E) 1/24
Rationale: Probability of first member an English teacher = 3/9
Probability of second member an English teacher = 2/8
Probability of both being english teacher = 3/9 x 2/8 =1/12 (B)
Answer: (B) 1/12
Question: 32 % of 1500 is
(A) 480
(B) 440
(C) 370
(D) 415
(E) 435
Rationale: 1 % of 1500 is = 1532 % of 1500 is = 32*15 = 480Answer : A
Answer: (A) 480
Question: If 4 men can colour 48 m long cloth in 2 days, then 6 men can colour 36 m long cloth in
(A) 1 day
(B) 2 days
(C) 4 days
(D) 3 days
(E) None
Rationale: The length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m
No. of days required to paint 36 m cloth by 6 men = 36/ 6 × 6 = 1 day.
Option 'A'
Answer: (A) 1 day
Question: A cyclist covers a distnce of 750 m in 2 min 30 sec. What is the speed in km/hr of the cyclist?
(A) 28 km/hr
(B) 18 km/hr
(C) 20 km/hr
(D) 22 km/hr
(E) 24 km/hr
Rationale: Speed = { 750 } m/sec =5 m/sec = { 5 * 18 } km/hr =18km/hr
ANSWER B
Answer: (B) 18 km/hr
Question: A person sold a horse at a gain of 15%. Had he bought it for 25% less and sold it for Rs. 600 less, he would have made a profit of 32%. The cost price of the horse was:
(A) Rs. 3,750
(B) Rs. 3,250
(C) Rs. 2,750
(D) Rs. 2,250
(E) None
Rationale: Solution: Let the original CP = Rs. X.
Hence, SP= X + 15% of X = 115X/100 = Rs. 23X/20.
New, CP = X - 25% of X = 75X/100 = 3X/4.
New SP = 3X/4 + 32% of 3X/4 = Rs. 99X/100.
According to the question,
(23x/20)-(99x/100)= 600
Or, (115x-99x)/100 = 600
16x = 600*100
X = 600*100/16 = Rs. 3750.
Answer: Option A
Answer: (A) Rs. 3,750
Question: pipes P and Q would fill a cistern 18 and 24 minutes respectively. Both pipes being opened, find when the first pipe must be turned off so that the cistern may be just filled in 12 minutes?
(A) 8
(B) 9
(C) 2
(D) 7
(E) 5
Rationale: x/18 + 12/24 = 1
x = 9
Answer: B
Answer: (B) 9
Question: A Ship going at the speed of 18 km/hr crosses a light house in 20 seconds. What is the length of the train?
(A) 120
(B) 150
(C) 100
(D) 240
(E) 200
Rationale: Speed=(18x5/18)=5 m/sec.
Length of the train=(Speed x Time).
Length of the train=5x20m = 100 m.
Answer: C
Answer: (C) 100
Question: The ratio of the incomes of X and Y is 6:4 and the ratio of their expenditure is 5:3. If at the end of the year, each saves $2000 then the income of X is?
(A) $11000
(B) $10000
(C) $12000
(D) $10500
(E) $10600
Rationale: Let the income of X and Y be $6x and $4x
Let their expenditures be $5y and $3y
6x-5y = 2000-------1)
4x-3y = 2000-------2)
From 1) and 2)
2x-2y = 0 => x = y
x = 2000
Income of X 5 * 2000 = $10000
Answer : B
Answer: (B) $10000
Question: There is a square of side 6cm . A circle is inscribed inside the square. Find the ratio of the area of circle to square.
(A) 11/14
(B) 1/14
(C) 13/14
(D) 12/14
(E) 5/14
Rationale: Let the side of square = a unit
so Area of Square = a^2
Diameter of inscribed circle = side of square = a
Radius of circle = a/2
Area of circle = (22/7)(a/2)^2
Ratio of area of circle to square = {(22/7)(a/2)^2}/a^2 = 11/14
ANSWER:A
Answer: (A) 11/14
Question: The length of a room is 8 m and width is 4.75 m. What is the cost of paying the floor by slabs at the rate of Rs. 900 per sq. metre.
(A) 25650
(B) 25750
(C) 26550
(D) 26750
(E) 34200
Rationale: Area = 8 × 4.75 sq. metre.
Cost for 1 sq. metre. = Rs. 900
Hence total cost = 8 × 4.75 × 900
= 8 × 4275 = Rs. 34200
Answer is E.
Answer: (E) 34200
Question: If the height of an equilateral triangle TBC is equal in length to the hypotenuse of an isosceles right triangle DEF, a side of ΔTBC is how many times as long as a leg of the right triangle DEF?
(A) (√2)/(√3)
(B) (√3)/(√2)
(C) √2
(D) (2√2)/(√3)
(E) 2/(√3)
Rationale: Side of the equilateral triangle TBC = 2m ----> height = m * sqtr(2)
Hipotenuse of the right triangle TBC = m * sqrt(3) ----> side = m * sqtr(3) / sqtr(2)
Question is 2m/m * sqtr(3) / sqtr(2) = 2*sqrt(2)/sqrt(3)=D
Answer: (D) (2√2)/(√3)
Question: A certain pilot flew 400 miles to City K at an average speed of 350 miles per hour with the wind and made the trip back at an average speed of 450 miles per hour against the wind. Which of the following is closest to the pilot’s average speed, in miles per hour, for the round-trip?
(A) 390
(B) 290
(C) 300
(D) 310
(E) 320
Rationale: Avg speed = total distance/ total time
total distance = 800
total time = 400/350 + 400/450 = 128/63
=> avg speed = (800*63)/128 = 390(approx)
ans is A
Answer: (A) 390
Question: Ramu rides his bike at an average speed of 45 km/hr and reaches his desitination in four hours. Somu covers the same distance in six hours. If Ramu covered his journey at an average speed which was 9 km/hr less and Somu covered his journey at an average speed which was 10 km/hr more, then the difference in their times taken to reach the destination would be (in minutes)?
(A) 12
(B) 30
(C) 27
(D) 12
(E) 13
Rationale: Distance travelled by Ramu = 45 * 4 = 180 km
Somu travelled the same distance in 6 hours.
His speed = 180/6 = 30 km/hr
Hence in the conditional case, Ramu's speed = 45 - 9 = 36 km/hr and Somu's speed = 30 + 10 = 40km/hr.
Therefore travel time of Ramu and Somu would be 5 hours and 4.5 hours respectively. Hence difference in the time taken = 0.5 hours = 30 minutes.
Answer: B
Answer: (B) 30
Question: A woman named Vaisali started a business investing Rs. 30,000. Roja joined him after six months with an amount of Rs. 90,000 and Sachin joined them with Rs. 60,000 after another six months. The amount of profit earned should be distributed in what ratio among Vaisali, Roja and Sachin respectively, 3 years after A woman started the business ?
(A) 7:6:10
(B) 6 : 15 : 8
(C) 14:15:16
(D) 12:15:16
(E) 42:45:56
Rationale: Explanation :
Akash : Roja : Sachin = (30,000 x 36) : (90,000 x 30) : (60,000 x 24)
= 36 : 90 : 48 = > 6 : 15 : 8
Answer : B
Answer: (B) 6 : 15 : 8
Question: A rope of which a calf is tied is increased from 10 m to 23 m, how much additional grassy ground shall it graze?
(A) 1217
(B) 1348.2
(C) 1210
(D) 1212
(E) 1312
Rationale: π (232 – 102) = 1348.2
Answer:B
Answer: (B) 1348.2
Question: Katie has 9 employees that she must assign to 3 different projects. If 3 employees are assigned to each project and no one is assigned to multiple projects, how many different combinations B of project assignments are possible?
(A) 252
(B) 1,680
(C) 2,340
(D) 362,880
(E) 592,704
Rationale: The ways to select three employees out of 9 for first project = 9C3
The ways to select three employees out of Remaining 6 for Second project = 6C3
Third Project already has the group of three to be assigned to it so need to select that
So total ways to assign 3 employees to each of 3 projects B = 9C3 * 6C3 * 1 = 1,680
Answer: Option B
Answer: (B) 1,680
Question: Jane sold N boxes of cookies. Each cookie costs M dollars to make, and Jane always makes a profit of P dollars per cookie.
If each box of cookies contains Q cookies, what was the selling price for all the cookies?
(A) NP+QM
(B) NM-PQ
(C) NQ+PM
(D) (PQ+MQ)N
(E) NQ(P-M)
Rationale: The selling price= the cost price+ profit
The cost price= NQM
The profit made=NQP
And the total selling price=NQM+NQP
=NQ(M+P)
The answer is D!!!
Answer: (D) (PQ+MQ)N
Question: A boat can move upstream at 15 kmph and downstream at 23 kmph, then the speed of the current is?
(A) 5 kmph
(B) 7 kmph
(C) 8 kmph
(D) 9 kmph
(E) 4 kmph
Rationale: US = 15
DS = 23
M = (23 - 15)/2 = 4
Answer:E
Answer: (E) 4 kmph
Question: Train X crosses a stationary train Y in 60 seconds and a pole in 25 seconds with the same speed. The length of the train X is 300 m. What is the length of the stationary train Y?
(A) 277 m
(B) 420 m
(C) 617 m
(D) 868 m
(E) 651 m
Rationale: Let the length of the stationary train Y be LY
Given that length of train X, LX = 300 m
Let the speed of Train X be V.
Since the train X crosses train Y and a pole in 60 seconds and 25 seconds respectively.
=> 300/V = 25 ---> ( 1 )
(300 + LY) / V = 60 ---> ( 2 )
From (1) V = 300/25 = 12 m/sec.
From (2) (300 + LY)/12 = 60
=> 300 + LY = 60 (12) = 720
=> LY = 720 - 300 = 420 m
Length of the stationary train = 420 m
Answer:B
Answer: (B) 420 m
Question: 16.02 × 0.001 = ?
(A) 0.1602
(B) 0.001602
(C) 1.6021
(D) 0.01602
(E) None of these
Rationale: 16.02 × 0.001 = ?
or,? = 0.01602
Answer D
Answer: (D) 0.01602
Question: In a rectangular coordinate system, points O (2,0), P (2,6), and Q (6,0) represent the sites of three proposed housing developments. If a fire station can be built at any point in the coordinate system, at which point would it be equidistant from all three developments?
(A) (4,3)
(B) (5,2)
(C) (3,3)
(D) (3,4)
(E) (4,2)
Rationale: All points equidistant from O and Q lie on the line x = 4, so the fire station should lie on this line.
All points equidistant from O and P lie on the line y = 3, so the fire station should lie on this line.
These two intersect at (4,3) and that will be the point equidistant from all 3 points.
The answer is A.
Answer: (A) (4,3)
Question: By selling 11 pencils for a rupee a man loses 30%. How many for a rupee should he sell in order to gain 30%?
(A) 8
(B) 7
(C) 6
(D) 11
(E) 9
Rationale: 70% --- 12
130% --- ?
70/130 * 11
= 6
Answer:D
Answer: (D) 11