mathewhe/aqua_rat huggingface dataset:
Question: A and B invests Rs.3000 and Rs.4000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit?
(A) 9:9
(B) 9:8
(C) 9:3
(D) 9:1
(E) 9:2
Rationale: (3*6 + 6*6): (4*12)
54:48 => 9:8
Answer: B
Answer: (B) 9:8
Question: Calculate the speed of a boat in still water (in km/hr) if in one hour, the boat goes at 13 km/hr downstream and 4 km/hr upstream.
(A) 4.5 kmph
(B) 9.5 kmph
(C) 7.5 kmph
(D) 8.5 kmph
(E) 5.5 kmph
Rationale: Speed in still water = (13 + 4)1/2 kmph = 8.5 kmph.
answer :D
Answer: (D) 8.5 kmph
Question: a number divided by 84 leaves remainder 57 what is the remainder when same number divided by 12
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: add 84+57=141
now 141divided by 12 so we get 9 as reaminder
ANSWER:C
Answer: (C) 9
Question: Rajan borrowed Rs.4000 at 5% p.a compound interest. After 2 years, he repaid Rs.2210 and after 2 more year, the balance with interest. What was the total amount that he paid as interest?
(A) 635.5
(B) 635.57
(C) 635.51
(D) 635.59
(E) 635.54
Rationale: 4000
200 ---- I
200
10 ---- II
---------------
4410
2210
--------
2000
110 ---- III
110
5.50 ---- IV
-----------
2425.50
2210
-----------
4635.50
4000
----------
635.50
Answer:A
Answer: (A) 635.5
Question: A contractor undertakes to built a walls in 50 days. He employs 60 peoples for the same. However after 25 days he finds that only 40% of the work is complete. How many more man need to be employed to complete the work in time?
(A) 25
(B) 90
(C) 35
(D) 20
(E) None of these
Rationale: 60 men complete 0.4 work in 25 days.
Applying the work rule, m1 × d1 × w2 = m2 × d2 × w1
we have,
60 × 25 × 0.6 = m2 × 25 × 0.4
or m2 = 60×25×0.6/25×0.4 = 90 men
AnswerB
Answer: (B) 90
Question: Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $3 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the two discounts rates is 18 percent, what is the discount rate on Pony jeans?
(A) 9%
(B) 56.6%
(C) 11%
(D) 12%
(E) 15%
Rationale: You know that Fox jeans costs $15, and Pony jeans costs $18, you also know that 3 pairs of Fox jeans and 2 pairs of Pony jeans were purchased. So
3(15) = 45 - Fox
2(18) = 36 - Pony
The total discount discount is $3 and you are asked to find the percent discount of pony jeans,
so 45(18 - X)/100 + 36(X)/100 = 3 or 45*18 -45*x + 36*x =3*100 or 9x = -3*100 +45*18
x= 510/9 = 56.6%
B
Answer: (B) 56.6%
Question: Find the compound ratio of (2:5), (6:11) and (11:2) is
(A) 3:2
(B) 2:1
(C) 1:2
(D) 6:5
(E) 2:3
Rationale: Required ratio = 2/5 * 6/11 * 11/2 = 2/1 = 6:5
Answer is D
Answer: (D) 6:5
Question: If two-third of a bucket is filled in 6 minute then the time taken to fill the bucket completely will be .
(A) 90 seconds
(B) 70 seconds
(C) 60 seconds
(D) 9 minutes
(E) 120 seconds
Rationale: 2/3 filled in 6 mint
1/3 filled in 3 mint
thn 2/3+1/3=6 + 3 = 9 minutes
ANSWER:D
Answer: (D) 9 minutes
Question: In a queue if 30 children were made to stand in a column, 16 columns could be formed. If 24 children were made to stand in a column, how many columns could be formed?
(A) 10
(B) 20
(C) 25
(D) 36
(E) 40
Rationale: Sol. Required number = 16 *^30 = 20
B
Answer: (B) 20
Question: A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
(A) 88
(B) 27
(C) 36
(D) 88
(E) 12
Rationale: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 240 + 120 = 360 m.
Time taken = 360/10 = 36 sec.
Answer: C
Answer: (C) 36
Question: [(7 * 9) + (2 * 12) + 3]/[(12 * 3) + (81/9)] = ?
(A) 4
(B) 60
(C) 1.75
(D) 4.5
(E) None of these
Rationale: Explanation:
[(7 * 9) + (2 * 12) + 3]/[(12 * 3) + (81/9)] = (63 + 24 + 3)/(36 + 9) = 90/45 = 2
ANSWER IS E
Answer: (E) None of these
Question: Two family reunions are happening at the same hotel, the Dates reunion and the Hall reunion. All 50 guests at the hotel attend at least one of the reunions. If 50 people attend the Dates reunion and 60 people attend the Hall reunion, how many people attend both reunions?
(A)  2
(B)  5
(C)  10
(D)  16
(E)  60
Rationale: No of people in Dates reunion=50
No of people in Hall reunion=60
Attending both=x
All guests attend at least one.
Therefore, 50=50+60-(Both)
Both=60
Answer E
Answer: (E)  60
Question: What will be the cost of building a fence around a square plot with area equal to 81 sq ft, if the price per foot of building the fence is Rs. 58?
(A) 2088
(B) 2882
(C) 2999
(D) 2667
(E) 2121
Rationale: Let the side of the square plot be a ft.
a2 = 81 => a = 9
Length of the fence = Perimeter of the plot = 4a = 36 ft.
Cost of building the fence = 36 * 58 = Rs. 2088.
Answer: A
Answer: (A) 2088
Question: fill in ht blank:(a) the point with ___ (0,0) is called origin of a rectangular coordinate system,(b) to find the y-intercept of a line, we let ___ equal 0 and solve for ___; to find x- intercept , we let ____ equal 0 and solve for___
(A) (a) the point with line (0,0) is called origin of a rectangular coordinate system, (b) to find the y-intercept of a line, we let x equal 0 and solve for y ; to find x- intercept , we let y equal 0 and solve for y
(B) (a) the point with coordinates (0,0) is called origin of a rectangular coordinate system, (b) to find the y-intercept of a line, we let x equal 0 and solve for y ; to find x- intercept , we let y equal 0 and solve for x
(C) (a) the point with axis (0,0) is called origin of a rectangular coordinate system, (b) to find the y-intercept of a line, we let z equal 0 and solve for x ; to find x- intercept , we let x equal 0 and solve for y
(D) (a) the point with xyz (0,0) is called origin of a rectangular coordinate system, (b) to find the y-intercept of a line, we let x equal 0 and solve for y ; to find x- intercept , we let y equal 0 and solve for x
(E) none of the above
Rationale: (a) the point with coordinates (0,0) is called origin of a rectangular coordinate system, (b) to find the y-intercept of a line, we let x equal 0 and solve for y ; to find x- intercept , we let y equal 0 and solve for xcorrect answer (B)
Answer: (B) (a) the point with coordinates (0,0) is called origin of a rectangular coordinate system, (b) to find the y-intercept of a line, we let x equal 0 and solve for y ; to find x- intercept , we let y equal 0 and solve for x
Question: Six years ago, the ratio of the ages of Kunal and Sagar was 6:5, Four years hence, the ratio of their ages will be 11:10. What is Sagar age at present
(A) 22
(B) 17
(C) 15
(D) 16
(E) 12
Rationale: Let six years ago the age of Kunal and Sagar are 6x and 5x resp.
then,
=>(6x+6)+4(5x+6)+4=1110
=>(6x+6)+4(5x+6)+4=1110
<=>10(6x+10)=11(5x+10)
<=>10(6x+10)=11(5x+10)
<=>5x=10=>x=2
<=>5x=10=>x=2
So Sagar age is (5x+6) = 16
Answer: D
Answer: (D) 16
Question: A can complete a project in 20 days and B can complete the same project in 20 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?
(A) 18 days
(B) 27 days
(C) 26.67 days
(D) 16 days
(E) 15 days
Rationale: Let X = the number of days taken to complete the project.
The amount of work done by A is (x-10) * (1/20).
The amount of work done by B is (x) * (1/30).
(1/20)*(x-10) + (1/20)*(x) = 1
(x/20) + (x/20) - (10/20) = 1
x/10 = 3/2
x = 15
Therefore, the answer is E: 15.
Answer: (E) 15 days
Question: The positive numbers w, x, y, and z are such that x is 40 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 = 23.2 - Answer D
Answer: (D) 23.2%
Question: Ashok secured average of 72 marks in 6 subjects. If the average of marks in 5 subjects is 74, how many marks did he secure in the 6th subject?
(A) 62
(B) 74
(C) 78
(D) 80
(E) None of these
Rationale: Explanation:
Number of subjects = 6
Average of marks in 6 subjects = 72
Therefore total marks in 6 subjects = 72 * 6 = 432
Now, No. of subjects = 5
Total marks in 5 subjects = 74 * 5 = 370
Therefore marks in 6th subject = 432 – 370 = 62
ANSWER A
Answer: (A) 62
Question: A cube has a volume of 64 cubic feet. If a similar cube is twice as long, twice as wide, and twice as high, then the volume, in cubic feet of such cube is?
(A) 24
(B) 48
(C) 64
(D) 80
(E) 512
Rationale: Volume = 64 = side^3
i.e. Side of Cube = 4
New Cube has dimensions 8, 8, and 8 as all sides are twice of teh side of first cube
Volume = 8*8*8 = 512 square feet
Answer: option E
Answer: (E) 512
Question: John traveled 80% of the way from Yellow-town to Green-fields by train at an average speed of 80 miles per hour. The rest of the way John traveled by car at an average speed of v miles per hour. If the average speed for the entire trip was 50 miles per hour, what is v in miles per hour?
(A) 20
(B) 40
(C) 50
(D) 55
(E) 70
Rationale: HiBunuel
THe question seems incorrect. it should not be 80% at the speed of 80. However if it's 20% at the speed of 80, Answer comes out 55.
The question is correct. Here's the explanation:
Let distance be D. We can find the total timeequate it, which comes as:
0.8D / 80 + 0.2D / v = D / 50 => v = 20 (Option A).
Answer: (A) 20
Question: If a person moves 15km straight and turns right and moves 15km straight then how much distance he needs to walk to reach starting point?
(A) 20.2
(B) 21.2
(C) 23.2
(D) 24.2
(E) 26.2
Rationale: person will move along right angled traingle whose smaller sides are 15 km
& 15 km
reqd distance= hypotenuse of triangle = √(15^2+15^2)= 15√2 = 21.2 km
ANSWER:B
Answer: (B) 21.2
Question: The profit earned by selling an article for $ 832 is equal to the loss incurred when the same article is sold for $ 448. What should be the sale price for making 30% profit?
(A) $480
(B) $450
(C) $960
(D) $832
(E) $660
Rationale: Let C.P. = $ x.
Then, 832 - x = x - 448
2x = 1280 => x = 640
Required S.P. = 130% of $ 640 = $ 832.
D
Answer: (D) $832
Question: Tomeka is playing a dice game. If she rolls the same number on her second roll as she rolls on her first, she wins. Each roll is with two, fair, six-sided dice. If Tomeka rolled a seven on her first roll, what is the probability that she will win on her second roll?
(A) 1/4
(B) 1/5
(C) 1/6
(D) 1/9
(E) 1/12
Rationale: There are 6 ways to roll a seven: 1 and 6, 6 and 1, 2 and 5, 5 and 2, 3 and 4, 4 and 3.
There are 6*6=36 ways to roll two six-sided dice.
Thus the probability of winning by rolling a seven on the second roll given a seven on the first roll is 6/36 = 1/6
C
Answer: (C) 1/6
Question: 2/3rd of the boys and 3/4th of the girls of a school participate in a function. If the no.of participating students is 550, out of which 150 are girls, what is the total no.of students in the school?
(A) 300
(B) 400
(C) 800
(D) 900
(E) 1000
Rationale: Let total number of boys be x and total number of girls be y. y=400=>x = 600and^= I50=>y = 200 Now, x + y = 800
C
Answer: (C) 800
Question: If 8 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes?
(A) 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
(B) 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
(C) 8 × 9
(D) 28
(E) 45
Rationale: 1st person will have 7 handshakes, 2nd will have 6, ....7th will have 1 and 8th will have 0
= 7+6+5+4+3+2+1 = 28
if we generalize this: if there are n people then there will be n(n-1)/2 handshakes.
Ans.D)
Answer: (D) 28
Question: If x and y are positive integers such that x/y = 6.8, which of the following numbers could be y?
(A) 1
(B) 3
(C) 2
(D) 6
(E) 10
Rationale: With the given information, we are trying to find the value of y.
To achieve this we must convert the given decimal to a fraction and reduce it to it's lowest integer form.
Take the decimal x/y = 6.8 and because it's in the tens decimal place, put the given value (x/y = 6.8/1) and multiply it by 10.
Take the resulting fraction (x/y = 68/10) and reduce it to it's lowest form.
Both of the numbers are divisible by 2.
The result is x/y = 34/5.
Thus y = 5.
The correct answer is C.
Answer: (C) 2
Question: If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is?
(A) 1/8
(B) 1/2
(C) 1/1
(D) 1/6
(E) 1/3
Rationale: The number of exhaustive outcomes is 36.
Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2
P(E) = 1 - 1/2
= 1/2.
Answer:B
Answer: (B) 1/2
Question: A shopkeeper sells a TV set for 16560 at 10 % discount on its marked price and earns 15 % profit. If no discount is offered, then what will be his present per cent profit?
(A) 27 7⁄9
(B) 22 7⁄9
(C) 25 7⁄9
(D) Data inadequate
(E) None of these
Rationale: Original selling price of TV set
=16560×100/90 = 18400
Cost price of the TV = 16560×100/115 = 14400
at no discount, % profit will be
= (18400−14400)×100/14400 = 27 7/9
Answer A
Answer: (A) 27 7⁄9
Question: Old women said no of days of my grand daughter = no of months my daughters is?
And my age in no of years is= no of weeks of my grand daughter . sum of their ages is 115. Find d old women age?
(A) 71.7 years
(B) 72.7 years
(C) 73.7 years
(D) 74.7 years
(E) 75.7 years
Rationale: age of grand daughter is d days d/365 years
and age of daughter is d months d/12yrs
and age of old women is d/7 years
d/7 + d/12 + d/365 = 115years
4380d +2555d + 84d = 115*365*12*7
7019d = 3525900
d = 3525900/7019 = 502
age of old women is 502/7 =71.7 years
ANSWER:A
Answer: (A) 71.7 years
Question: The ratio by weight, measured in pounds, of books to clothes to electronics in a suitcase initially stands at 7:4:3. Someone removes 8 pounds of clothing from the suitcase, thereby doubling the ratio of books to clothes. How many pounds do the electronics in the suitcase weigh?
(A) 6
(B) 8
(C) 10
(D) 12
(E) 14
Rationale: The weights of the items in the suitcase are 7k, 4k, and 3k.
If removing 8 pounds of clothes doubles the ratio of books to clothes, then 8 pounds represents half the weight of the clothes.
2k = 8 pounds and then k = 4 pounds.
The electronics weigh 3(4) = 12 pounds.
The answer is D.
Answer: (D) 12
Question: 1, 0.5, 0.25, 0.125, 0.0625, ?
(A) 0.015625
(B) 0.03125
(C) 0.0078125
(D) None of these
(E) 0.025874
Rationale: Explanation :
Divide by 2 to get the next term
Answer : Option B
Answer: (B) 0.03125
Question: A and B can together complete a piece of work in 4 days. If A alone can complete the same work in 12
days, in how many days can B alone complete that work ?
(A) 4 days
(B) 5 days
(C) 6 days
(D) 7 days
(E) None of these
Rationale: Explanation:
(A+B)'s 1 day work = 1/4
A's 1 day work = 1/12
B's 1 day work =
(14−112)=3−112=16
So B alone can complete the work in 6 days
Answer: C
Answer: (C) 6 days
Question: What is the rate percent when the simple interest on Rs.800 amount to Rs.160 in 5 Years?
(A) 5%
(B) 7%
(C) 9%
(D) 2%
(E) 4%
Rationale: 160 = (800*5*R)/100
R = 4%
Answer: E
Answer: (E) 4%
Question: The difference of two numbers is 1415. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?
(A) A)270
(B) B)280
(C) C)290
(D) D)300
(E) E)310
Rationale: Let the smaller number be x. Then larger number = (x + 1415).
x + 1415 = 6x + 15
5x = 1400
x = 280
Smaller number = 280.
B)
Answer: (B) B)280
Question: A train traveled the first d miles of its journey it an average speed of 60 miles per hour, the next d miles of its journey at an average speed of y miles per hour, and the final d miles of its journey at an average speed of 160 miles per hour. If the train’s average speed over the total distance was 94 miles per hour, what is the value of y?
(A)  98
(B)  84
(C)  90
(D)  120
(E)  135
Rationale: Average speed=Total distance traveled /Total time taken
3d/d/60+d/y+d/160=94
Solving for d and y,
15y=11y+480
5y=480
y=98
Answer A
Answer: (A)  98
Question: Four faces of a fair die are Yellow, two faces red and one blue.The die is tossed three
times. The probability that the colours, yellow, red and blue appear in the first, second and
third tosses respectively is
(A) 1/36
(B) 1/18
(C) 1/32
(D) 1/27
(E) None of these
Rationale: Probability of getting yellow color = P(Y) = 4/6 = 2/3
Probability of getting red color = P(R) = 2/6 = 1/3
Probability of getting blue color = P(B) = 1/6
So, the probability that the colors yellow, red and blue appear in first, second and third toss respectively= P(Y ∩ R ∩ B) = P(Y) x P(R) x P(B) = 2/3 x 1/3 x 1/6 = 1/27
ANSWER:D
Answer: (D) 1/27
Question: Country X imported approximately $1.44 billion of goods in 1996. If Country X imported $488 million of goods in the first two months of 1997 and continued to import goods at the same rate for the rest of the year, by how much would Country Xs 1997 imports exceed those of 1996?
(A)  $1124 million
(B)  $1120 million
(C)  $1144 million
(D)  $1240 million
(E)  $1488 million
Rationale: Convert units to millions as answer is in millions
1996 Imports = $1.44 bill = $1440 mill
i.e. 1440/12 = $120 mill/month
1997 Imports = $488 mill/2 month
i.e. $244 mill/month
Difference/month = 244-120 = 124
Difference/year = $124 mill * 12 = $1488 mill
ANSWER: E
Answer: (E)  $1488 million
Question: A certain sum amounts to Rs.1725 in 3 years and Rs.1875 in 5 years. Find the rate % per annum?
(A) 6%
(B) 5%
(C) 3%
(D) 9%
(E) 2%
Rationale: 3 --- 1725
5 --- 1875
--------------
2 --- 150
N = 1 I = 75 R = ?
P = 1725 - 225 = 1500
75 = (1500*1*R)/100
R = 5%
Answer: B
Answer: (B) 5%
Question: One pump drains one-half of a pond in 4 hours, and then a second pump starts draining the pond. The two pumps working together finish emptying the pond in one-half hour. How long would it take the second pump to drain the pond if it had to do the job alone?
(A) 1 hour
(B) 1.1 hour
(C) 3 hours
(D) 5 hours
(E) 6 hours
Rationale: First pump drains 1/2 of the tank in 4 hours
so 8 hours it will take to drain the full tank.
Let, 2nd pump drains the full tank in a hours
so both together can drain (1/8+1/a) part in 1 hour
son in 1/2 hour they drain 1/2*(1/8+1/a) part of the tank
given that in 1/2 hour they drain 1/2 of the tank
hence we can say
1/2*(1/8+1/a) = 1/2
solving u get a = 8/7=1.1
Hence answer is B
Answer: (B) 1.1 hour
Question: A solid yellow stripe is to be painted in the middle of a certain highway. If 1 gallon of paint covers an area of t square feet of highway, how many gallons of paint will be needed to paint a stripe of t inches wide on a stretch of highway m miles long? (1 mile = 5,280 feet and 1 foot = 12 inches)
(A) (5,280 mt) / 12 t
(B) (5,280 pt) / 12m
(C) (5,280 pmt) /12
(D) (5,280)(12m) / pt
(E) (5,280)(12p) / mt
Rationale: Given that: 1 gallon of paint covers an area oftsquare feet. Question:how many gallonsof paint will be needed ...
In any case you will have:(total area in square feet)/(gallons per feet)=(total area in square feet)/t, so t must be in the denominator: eliminate all but A and D.
Now, lets see where should be t: (area in square feet)=(width in feet)*(length in feet) --> width=tinchesas1 feet=12 inchesthent inches=t/12 feet, so (area in square feet)=(t/12) * (length in feet), so t must be in the nominator: only A is left.
Answer: A.
Answer: (A) (5,280 mt) / 12 t
Question: 8^100 is divisible by 17. Find the remainder?
(A) 10
(B) 12
(C) 16
(D) 21
(E) 26
Rationale: This is an extremely difficult problem to solve with out Fermat's little theorem. By applying Fermat's little theorem , We know that 816 when divided by 17, the remainder is 1.
So divide 100 by 16 and find the remainder. Remainder = 4
Therefore, 100 = (16 × 6) + 4
Now this problem can be written as 810017 = 816×6+417 = (816)6×8417
Now this problem simply boils down to (1)6×8417 = 8417
84 = 82×82, we need to find the remainder when 64 × 64 is divisible by 17. Or 13 × 13 = 169. When 169 is divided by 17, remainder is 16.
C
Answer: (C) 16
Question: In the Biotechnology class of 2000, there were W 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 W 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: On an order of 5 dozen boxes of a consumer product, a retailer receives an extra dozen free. This is equivalent to allowing him a discount of:
(A) 26 2/3%.
(B) 18 2/8%.
(C) 16 2/3%.
(D) 18 2/3%.
(E) 19 2/3%.
Rationale: Explanation:
Clearly, the retailer gets 1 dozen out of 6 dozens free.
Equivalent discount = 1/6 * 100 = 16 2/3%.
Answer: C
Answer: (C) 16 2/3%.
Question: The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical A present and inversely proportional to the concentration of chemical W present. If the concentration of chemical W is increased by 100 percent, which of the following is closest to the percent change in the concentration of chemical A required to keep the reaction rate unchanged?
(A) 100% decrease
(B) 50% decrease
(C) 40% decrease
(D) 40% increase
(E) 50% increase
Rationale: Let A and W be the concentratrations of the individual chemicals.
Rate of chemical reaction = A^2/W
Since new B is increased by 100%
Rate = A^2/(2W)
For the rate to be constant, new value of A should be square root(2)
So new value of A = 1.414A
That means A is increased by 41.4%
Nearest solution is D
Answer: (D) 40% increase
Question: If 2 cards are selected at random from the deck of 52 cards then What is the probability of one of the selected cards will be Jack and other will be Queen?
A deck of cards has a total of 52 cards, consisting of 4 suits; (spades(Black), hearts(Red), diamond(Red)s, and clubs(Black)); and 13 cards including 1 king, 1 queen and 1 jack in each suit
(A) 8/2652
(B) 1/2652
(C) 28/2652
(D) 6/2652
(E) 18/2652
Rationale: 2 possible cases:
Jack - Queen or Queen - Jack (4 Jacks and 4 queens).
Either way,
the total probability = 2( Jack -Queen) = 2 (4/52 * 4/51) = 18/2652. E is the correct answer.
Answer: (E) 18/2652
Question: At a certain college, 80 percent of the total number of students are freshmen. If 60 percent of the fresh-men are enrolled in the school of liberal arts and, of these, 50 percent are psychology majors, what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts?
(A) 25%
(B) 30%
(C) 24%
(D) 28%
(E) 20%
Rationale: Let's say there is a TOTAL of 100students at this college.
80 percent of the total number of students are freshmen.
# of freshmen = 80% of 100 =80
60 percent of the fresh-men are enrolled in the school of liberal arts...
Number of liberal arts freshmen = 60% of 80 = 48
...and, of these, 50 percent are psychology majors...
Number of liberal arts freshmen who are psychology majors = 50% of 48=24
What percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts?
24/100= 24%
Answer:C
Answer: (C) 24%
Question: If the least common multiple of two prime numbers x and y is 77, where x > y, then the value of 2x + y is
(A) 11
(B) 17
(C) 21
(D) 29
(E) 33
Rationale: LCM (x,y) = 77 and both x an y are prime.
The only values of x and y can be 11 and 7 (x = 11 and y = 7)
2x + y = 2*11 + 7 = 29
Correct Option: D
Answer: (D) 29
Question: Working at their respective constant rates, machine A makes 100 copies in 12 minutes and machine B makes 150 copies in 15 minutes. If these machines work simultaneously at their respective rates for 30 minutes, what is the total number of copies that they will produce?
(A)  250
(B)  425
(C)  550
(D)  700
(E)  750
Rationale: Machine A can produce 100 *30/12= 250 copies
And, Machine B can produce 150* 30/15= 300 Copies
Total producing 550 Copies.
C is the answer
Answer: (C)  550