mathewhe/aqua_rat huggingface dataset:
Question: If there are twice as many women as men in a group and an equal number of men and women do not own cars - a group that is 40% of the total. What fraction of the total is men who own cars?
(A) 3⁄20
(B) 11⁄60
(C) 2⁄15
(D) 1⁄3
(E) 11⁄20
Rationale: Consider a group of 100 men and 200 women, a total of 300 people. 40% of them, which is 120, form a group of people who don't own a car.
Half of them are men, and the other half are women, more precisely 60.
It means that there are 100 - 60 = 40 men who own a car, and this represents 40/300 = 2/15 of the total.
Answer C
Answer: (C) 2⁄15
Question: In a railway compartment, there are 2 rows of seats facing each other with accommodation for 5 in each, 4 wish to sit facing forward and 3 facing towards the rear while 3 others are indifferent. In how many ways can the 10 passengers be seated?
(A) 172000
(B) 12600
(C) 45920
(D) 43200
(E) None
Rationale: Solution:
The four person who wish to sit facing forward can be seated in: 5P4 ways and 3 who wish to sit facing towards the rear can be seated in: 5P3 ways and the remaining 3 can be seated in the remaining 3 seats in 3P3 ways. Total number of ways =5P4 *5P3 *3P3 = 43200.
Answer: Option D
Answer: (D) 43200
Question: The 8 spokes of a custom circular bicycle wheel radiate from the central axle of the wheel and are arranged such that the sectors formed by adjacent spokes all have different central angles, which constitute an arithmetic series of numbers (that is, the difference between any angle and the next largest angle is constant). If the largest sector has a central angle of 87°, what fraction of the wheel’s area is represented by the smallest sector?
(A) 1/120
(B) 1/100
(C) 1/80
(D) 1/60
(E) 1/40
Rationale: The largest angle is 87.
Let d be the difference between any two angles in the progression.
The sum of all the angles will be:
87 + (87-d) + (87-2d) + ... + (87-7d) = 696 - 28d
The sum of all the central angles in a circle = 360
696 - 28d = 360
d = 336/28 = 12
The smallest sector is (87-7d) = 87-7*12 = 3
3/360 = 1/120
The answer is A.
Answer: (A) 1/120
Question: If the numerator of a fraction be increased by 15% and its denominator be diminished by 8% , the value of the fraction is 15/16. Find the original fraction.
(A) 3/4
(B) 1/4
(C) 1/2
(D) 1
(E) None of them
Rationale: Let the original fraction be x/y.
Then (115%of x)/(92% of y)=15/16 => (115x/92y)=15/16
=((15/16)*(92/115))=3/4
Answer is A.
Answer: (A) 3/4
Question: The average age of a group of 5 members is 20 years. Two years later, a new member joins the group. The average age of the group becomes 21.5 years. What is the age of the new member ?
(A) 20 years
(B) 19 years
(C) 22 years
(D) 23 years
(E) 24 years
Rationale: The average age of the 5 members is 20 years
=> The sum of the ages of the 5 members is 20*5 = 100 years
Once the new member joins, the average age becomes 21.5 years.
Let the age of the new member be x.
Then (110+x)/6 = 21.5
=> x = 19 years
Answer B
Answer: (B) 19 years
Question: A man covered a certain distance at some speed. If he had moved 3 kmph faster, he would have taken 40 minutes less. If he had moved 2 kmph slower, he would have taken 40 minutes more. What is the the distance in km?
(A) 33
(B) 37
(C) 40
(D) 38
(E) 27
Rationale: Let the distance be x km ,
the speed in which he moved = v kmph
Time taken when moving at normal speed - time taken when moving 3 kmph faster = 40 minutes
⇒xv−xv+3=4060⇒x[1v−1v+3]=23⇒x[v+3−vv(v+3)]=23⇒2v(v+3)=9x................(Equation1)
Time taken when moving 2 kmph slower - Time taken when moving at normal speed = 40 minutes
⇒xv−2−xv=4060⇒x[1v−2−1v]=23⇒x[v−v+2v(v−2)]=23⇒x[2v(v−2)]=23⇒x[1v(v−2)]=13⇒v(v−2)=3x................(Equation2)Equation1Equation2⇒2(v+3)(v−2)=3⇒2v+6=3v−6⇒v=12Substituting this value of v in Equation 1⇒2×12×15=9x=>x=2×12×159=2×4×153=2×4×5=40Hence distance = 40 km
Answer :C
Answer: (C) 40
Question: If an article is sold at 5% gain instead of 5% loss,the seller gets Rs 6.72 more. The C.P of the article is?
(A) 132.82
(B) 138.55
(C) 148.81
(D) 150.45
(E) None
Rationale: Sol.
100 * 10/6.72 = 148.81 answer
Answer C
Answer: (C) 148.81
Question: 4 DICE ARE THROWN AND THE SUM OF THE NUMBERS NOTED IS 10. FIND THE PROBABILITY THAT ALL THE NUMBERS LIE BETWEEN 2 AND 5 (both inclusive)?
(A) 11/79
(B) 10/79
(C) 12/79
(D) 13/79
(E) 14/79
Rationale: Sum of numbers noted on 4 dice(with six faces) to be 10 will include combinations:
( 1,1,2,6)(1,1,3,5)(1,1,4,4)(1,1,5,3)(1,1,6,2)(1,2,1,6)(1,2,2,5)(1,2,3,4)(1,2,4,3)(1,2,5,2)(1,2,6,1)(1,3,1,5)(1,3,2,4)(1,3,3,3)(1,3,4,2)(1,3,5,1)(1,4,1,4)(1,4,2,3)(1,4,3,2)(1,4,4,1)(1,5,1,3)(1,5,2,2)(1,5,3,1)(1,6,1,2)(1,6,2,1)
(2,1,1,6)(2,1,2,5)(2,1,3,4)(2,1,4,3)(2,1,5,2)(2,1,6,1)(2,2,1,5)(2,2,2,4)(2,2,3,3)(2,2,4,2)(2,2,5,1)(2,3,1,4)(2,3,2,3)(2,3,3,2)(2,3,4,1)(2,4,1,3)(2,4,2,2)(2,4,3,1)(2,5,1,2)(2,5,2,1)(2,6,1,1)
(3,1,1,5)(3,1,2,4)(3,1,3,3)(3,1,4,2)(3,1,5,1)(3,2,1,4)(3,2,2,3)(3,2,3,2)(3,2,4,1)(3,3,1,3)(3,3,2,2)(3,3,3,1)(3,4,1,2)(3,4,2,1)(3,5,1,1)
(4,1,1,4)(4,1,2,3)(4,1,3,2)(4,1,4,1)(4,2,1,3)(4,2,2,2)(4,2,3,1)(4,3,1,2)(4,3,2,1)(4,4,1,1)
(5,1,1,3)(5,1,2,2)(5,1,3,1)(5,2,1,2)(5,2,2,1)(5,3,1,1)
(6,1,1,2)(6,1,2,1) ------- Total 79
Combinations with all the numbers lie between 2 and 5 are (2,2,2,4)(2,2,3,3)(2,2,4,2)(2,3,2,3)(2,3,3,2)(2,4,2,2)(3,2,2,3)(3,2,3,2)(3,3,2,2)(4,2,2,2) ------Total 10
So probability=10/79
ANSWER:B
Answer: (B) 10/79
Question: If the area of a square with sides of length 4 centimeters is equal to the area of a rectangle with a width of 8 centimeters, what is the length of the rectangle, in centimeters?
(A) 4
(B) 8
(C) 2
(D) 16
(E) 18
Rationale: Let length of rectangle = L
4^2 = L*8
=> L = 16/8 = 2
Answer C
Answer: (C) 2
Question: If the sum of two numbers is 30 and the sum of their squares is 840, then the product of the numbers is
(A) 40
(B) 44
(C) 80
(D) 88
(E) 30
Rationale: Sol.
Let the numbers be x and y.
Then, (x+y) = 30 and x2 + y2 = 840.
Now, 2xy = (x+y)2 - (x2 + y2)
= (30)2 - 840= 900 - 840= 60
xy = 30.
Answer E
Answer: (E) 30
Question: The 40 parents participating in the Smithville PTA have been assigned to at least 1 of 3 committees: festival planning, classroom aid, and teacher relations. 21 parents are assigned to the festival planning committee, 18 parents are assigned to the classroom aid committee, and 19 parents are assigned to the teacher relations committee. If 5 parents are assigned to all 3 committees, how many parents are assigned to exactly 2 committees?
(A) 4
(B) 6
(C) 8
(D) 9
(E) 10
Rationale: The formula is Total = A+B+C - sum of exactly two + 2*all three + neither
21+18+19-x-2*5=40
solving for x you get 8
Answer C
Answer: (C) 8
Question: Write 330,000,000,000 in scientific notation
(A) 3.3 * 10 11
(B) 3.30 * 10 11
(C) 3.300 * 10 11
(D) 3.3000 * 10 11
(E) 30.3000 * 10 11
Rationale: a * 10 n , where a is a real number such that 1 * |a| < 10 and n is an integer.
330,000,000,000 = 3.3 * 100,000,000,000 = 3.3 * 10 11**
correct answer A
Answer: (A) 3.3 * 10 11
Question: If x + y = 13 and x – y = 3, then x^2 - y^2 =
(A) -4
(B) 4
(C) 10
(D) 39
(E) 40
Rationale: The fastest approach has already been shown. Here's one more option.
Given:
x + y = 13
x – y = 3
Add the two equations to get: 2x = 16, which means x = 8
If x = 8, we can plug that value into either equation, to conclude that y = 5
If x = 8 and y = 5, then x² - y² = 39
Answer: D
Answer: (D) 39
Question: The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ Rs. 26.50 per metre is Rs. 6625, what is the length of the plot in metres?
(A) 333
(B) 250
(C) 288
(D) 276
(E) 1999
Rationale: Let length of plot = L meters, then breadth = L - 20 meters
and perimeter = 2[L + L - 20] = [4L - 40] meters
[4L - 40] * 26.50 = 6625
[4L - 40] = 6625 / 26.50 = 250
4L = 290
L = 240/4= 72.5 meters.
Answer: B
Answer: (B) 250
Question: $400 is divided amongst A,B and C so that A may get 2/3 as much as B and C together, B may get 6/9 as much as A and C together, then the share of A is
(A) $100
(B) $150
(C) $160
(D) $200
(E) $250
Rationale: A:(B+C) = 2:3
A's share = 400*2/5 = $160
Answer is C
Answer: (C) $160
Question: In how many W ways can a four-letter password be chosen, using the letters A, B, C, D, E, and/or F, such that at least one letter is repeated within the password?
(A) 720
(B) 864
(C) 900
(D) 936
(E) 1,296
Rationale: Total number of four letter passwords = 6*6*6*6= 1296 ------(1)
Total number of passwords in which no letter repeats = 6C4*4!= 15*24=360------(2)
therefore required value W= (1)-(2)= 1296-360=936.D
Answer: (D) 936
Question: It is currently 8:12 PM. At what time in the morning was it exactly 205,106 minutes ago?
(A) 9:14
(B) 9:16
(C) 9:42
(D) 9:44
(E) 9:46
Rationale: Convert 205,106 minutes to hours by dividing by 60: 205,106/60 = 3,418 R26. That is 3,418 hours and 26 minutes. Convert 3,418 hours to days by dividing by 24: 3,418/24 = 142 R10. That is 142 days and 10 hours. Now, 142 days previous was 8:12 PM. Another 10 hours previous was 10:12 AM. Another 26 minutes previous was 9:46 AM (Subtract the 12 minutes of 10:12 from 26 to get 14. Then subtract 14 from 60 to get 46). E
Answer: (E) 9:46
Question: A sum of money becomes Rs 13,380 in 3 years and Rs 20,070 in 6 years at compound interest. The initial sum is?
(A) Rs 8927
(B) Rs 8922
(C) Rs 89298
(D) Rs 8920
(E) Rs 8921
Rationale: Use the formula Amount = Principal Amount(1 + R/100)n
Where r is rate and t is time in years
=>13,380 = P(1+R/100)2 --(1)
=>20,070 = P(1+R/100)6 --(2)
=> 1.5 = (1+R/100)4
=> P = Rs 8920
ANSWER:D
Answer: (D) Rs 8920
Question: In a factory, an average of 50 TV's are produced per day for the fist 25days of the months. A few workers fell ill for the next 5days reducing the daily avg for the month to 48 sets/day . The average production per day for day last 5days is ?
(A) 20
(B) 36
(C) 48
(D) 38
(E) 59
Rationale: Production during these 5 days = Total production in a month - production in first 25 days.
= 30 x 48 - 25 x 50
= 190
∴ Average for last 5 days = 190 / 5
= 38
D
Answer: (D) 38
Question: A money lender lent a total of $1800 to two of his customers. He charged at the rate of 5%p.a. to one of them and 6% p.a. to the other. If he earned an average of 5.67% on $1800, how much did he lend to each of the two customers?
(A) 700; 1100
(B) 1200; 600
(C) 1000; 800
(D) 1200; 800
(E) None of the above
Rationale: The method given above is the one given in the book.
However the method I used was
(1*x*5)/100 + (1800-x)*6/100 = 1800*5.67/100
Simplifying we get x=594
Though the actual answer is 600
ANSWER:B
Answer: (B) 1200; 600
Question: A brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 28 m * 2 m * 0.75 m?
(A) 28000
(B) 27908
(C) 78902
(D) 25000
(E) 27991
Rationale: 28 * 2 * 0.75 = 20/100 * 10/100 * 7.5/100 * x
28 = 1/100 * x => x
= 28000
Answer: A
Answer: (A) 28000
Question: If 0 < M < Y, M is an odd number and Y is a prime number, which of the following can be the value of M + Y ?
(A) 11.
(B) 13.
(C) 17.
(D) 10.
(E) 7.
Rationale: If m is odd ,implies m(odd)+y(odd/even prime)=(Even/Odd)
If Y is even, the 2 is the even prime , therefore y=2m=1 since 0<M<Y therefore M+Y =3. But 3 is not an option
which implies y is odd,
Now M(odd)+Y(odd)=Even
10 is the only option that is even=D
Answer: (D) 10.
Question: In a rectangular coordinate system, what is the area of a rectangle whose vertices have the coordinates (-4, 1), (1, 1), (1, -3) and (-4, -3)?
(A) 16
(B) 20
(C) 24
(D) 25
(E) 30
Rationale: Length of side 1= 4+1=5
Length of side 2= 3+1= 4
Area of rectangle= 5*4= 20
B is the answer
Answer: (B) 20
Question: A cistern is normally filled in 12 hrs,but takes 2 hrs longer to fill because of a leak on its bottom,if Cistern is full ,how much time citern would empty?
(A) 10 hours
(B) 84 hours
(C) 30 hours
(D) 40 hours
(E) 50 hours
Rationale: If leakage/hour=1/x, then 1/12 -1/x= 1/14, solving 1/x=1/84
So in 84 hours full cistern will be empty.
ANSWER:B
Answer: (B) 84 hours
Question: By using the numbers 1, 2, 3, 5 and 7 only once, how many five digit numbers can be made that are divisible by 25?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: A number to be divisible by 25 must end with 00, 25, 50, or 75.
So, there are the following cases possible:
137-25 --> the first three digits can be arranged in 3=6 ways.
123-75 --> the first three digits can be arranged in 3=6 ways.
Total = 6 + 6 = 12.
Answer: C.
Answer: (C) 12
Question: what is the speed of a stream if a canoes rows upstream at 8km/hr and downstream at 10.5km/hr.
(A) 1.5 kmph
(B) 1.25 kmph
(C) 1.35 kmph
(D) 1.27 kmph
(E) 1.22 kmph
Rationale: Sol.
Speed of stream = 1/2(10.5 -8) kmph = 1.25 kmph.
Answer B
Answer: (B) 1.25 kmph
Question: The speed of a boat in still water is 15 km/hr and the rate of current is 3 km/hr. The distance travelled downstream in 24 minutes is
(A) 17.2 km
(B) 7.2 km
(C) 7.6 km
(D) 17.6 km
(E) 27.2 km
Rationale: speed of a boat in still water = 15 km/hr
Speed of the current = 3 km/hr
Speed downstream = (15+3) = 18 km/hr
Distance travelled downstream in 24 minutes=(24/60)×18=(2×18)/5 = 7.2 km
Answer is B
Answer: (B) 7.2 km
Question: A can give B 100 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?
(A) 111.12 m
(B) 111.22 m
(C) 111.19 m
(D) 118.12 m
(E) 311.12 m
Rationale: A runs 1000 m while B runs 900 m and C runs 800 m.
The number of meters that C runs when B runs 1000 m,
= (1000 * 800)/900 = 8000/9 = 888.88 m.
B can give C = 1000 - 888.88 = 111.12 m.Answer:A
Answer: (A) 111.12 m
Question: A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 650 m long?
(A) 80
(B) 89
(C) 78
(D) 67
(E) 56
Rationale: Speed = 240/24 = 10 m/sec.
Required time = (240 + 650)/10 = 89 sec.
Answer: Option B
Answer: (B) 89
Question: In 1 kg mixture of sand and iron, 20% is iron. How much sand should be added so that the proportion of iron becomes 10%?
(A) 1 kg
(B) 200 gms
(C) 800 gms
(D) 1.8 kg
(E) None of these
Rationale: In 1 kg mixture quantity of iron = 200 gm
Let x gm sand should be added, then
10% of (1000 + x) = 200
\ x = 1000 gm = 1 kg
Answer A
Answer: (A) 1 kg
Question: David and Rachel are getting married. The extended family wants to have its picture taken, but David's father is unwilling to stand next to Rachel's mother. How many options does the photographer have to arrange the 8 family members in a row for the picture?
(A) 9!
(B) 9×8!
(C) 6×7!
(D) 10!/2!
(E) 10!
Rationale: In how many ways David's father and Rachel's mother can stand together? Consider them as one unit: {F, M}. So, we'd have 9 units {F, M}, 1, 2, 3, 4, 5, 6, which can be arranged in 7! ways. David's father and Rachel's mother within their unit can be arranged in 2! ways. Therefore, David's father and Rachel's mother can stand together in 7!*2! ways.
Total - Restriction =
= 8! - 7!*2! =
= 7!(8 - 2!) =
= 6*7!.
Answer: C.
Answer: (C) 6×7!
Question: A horse is tethered to one corner of a rectangular grassy field 40 m by 24 m with a rope 14 m long. Over how much area of the field can it graze?
(A) 154 cm2
(B) 308 m2
(C) 150 m2
(D) 407 m2
(E) None of these
Rationale: Area of the shaded portion
= 1⁄4 × π × (14)2 = 154 m2
Answer A
Answer: (A) 154 cm2
Question: Seven friends are planning to attend a concert. If another friend also goes with them, they will get a group discount on their tickets. If the new total price of the tickets with the group discount is the same as the original total price of the tickets without the group discount, how much is the discount?
(A) 8.5%
(B) 12.5%
(C) 16.5%
(D) 19.5%
(E) 21.5%
Rationale: Let x be the original price of one ticket.
The total original cost is 7x.
The new cost is 8y, where y is the discounted price of one ticket.
7x = 8y
y = 7x/8 = 0.875x which is a discount of 12.5%.
The answer is B.
Answer: (B) 12.5%
Question: In a company with 48 employees, some part-time and some full-time, exactly (1/3) of the part-time employees and (1/4) of the full-time employees take the subway to work. What is the greatest possible number H of employees who take the subway to work?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: P/3 + F/4 = P/3 + (48-P)/4 = 12 + P/2
P/3 + F/3 = (P+F)/3 = 48/3 = 16
P/4 + F/4 = 12
P/3 + F/3 > P/3 + F/4 > P/4 + F/4
--> 16> 12 + P/12 > 12
GREATEST Possible H: 12 + p/12 = 15 --> p = 36 ( integer --> good)
15 or D is the answer
Answer: (D) 15
Question: Mary is expected to pay back a total sum of $819200 to her bank as mortgage. If she is expected to make a payment which is double of the previous months amount, how long will it take her to fully repay the loan if her initial payment was $400.
(A) 13
(B) 15
(C) 12
(D) 10
(E) 11
Rationale: First payment--$400
Total amount to be repaid--$819200
First month payment--$400
Second month payment--$400*2=$800
Third month payment--$800*2=$1600
Fourth month payment--$1600*2=$3200
Fifth month payment--$3200*2=$6400
Sixth month payment--$6400*2=$12800
Seventh month payment--$25600*2=$51200
Eight month payment--$51200*2=$102400
Ninth month payment--$102400*2=$204800
Tenth month payment--$204800*2=$409600
Eleventh month payment--$409600*2=$819200
Answer is E
Answer: (E) 11
Question: What will $500 amount to in three years if it is invested at 20% per year compound interest, with the interest being compounded annually?
(A) $788
(B) $812
(C) $864
(D) $878
(E) $912
Rationale: After one year: 1.2 * $500
After two years: (1.2)^2 * $500
After three years: (1.2)^3 * $500 = $864
The answer is C.
Answer: (C) $864
Question: The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?
(A) 18/35
(B) 18/18
(C) 18/19
(D) 18/17
(E) 18/12
Rationale: If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 3/5 * 4/7 + 2/5 * 3/7
= 12/35 + 6/35 = 18/35
Answer:A
Answer: (A) 18/35
Question: If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60, then the average marks of all the students is
(A) 54.48
(B) 54.68
(C) 54.6
(D) 54.58
(E) None of these
Rationale: Explanation:
(55×50)+(60×55)+(45×60) / 55+60+45
8750 / 160=54.68
Option B
Answer: (B) 54.68
Question: How many numbers amongst the numbers 7 to 56 are there which are exactly divisible by 8 but not by 6?
(A) Nil
(B) 1
(C) 2
(D) 3
(E) More than 3
Rationale: 8,16,24,32,40,48,56 are divisible by 8.
24,48 are divisible by 6 also.
So there are 5 numbers exactly divisible by 8 but not by 6
ANSWER:E
Answer: (E) More than 3
Question: The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle?
(A) 1:96
(B) 1:92
(C) 1:98
(D) 1:94
(E) 1:99
Rationale: Let the length and the breadth of the rectangle be 4x cm and 3x respectively.
(4x)(3x) = 6912
12x2 = 6912
x2 = 576 = 4 * 144 = 22 * 122 (x > 0)
=> x = 2 * 12 = 24
Ratio of the breadth and the areas = 3x : 12x2 = 1 : 4x
= 1:96.
Answer:A
Answer: (A) 1:96
Question: The speed of a boat in upstream is 80 kmph and the speed of the boat downstream is 100 kmph. Find the speed of the boat in still water and the speed of the stream?
(A) 90, 10 kmph
(B) 35, 27 kmph
(C) 50, 60 kmph
(D) 45, 55 kmph
(E) 45, 65 kmph
Rationale: Speed of the boat in still water = (80+100)/2 = 90 kmph. Speed of the stream = (100-80)/2 = 10 kmph
ANSWER:A
Answer: (A) 90, 10 kmph
Question: The tax on a commodity is diminished by 20% but its consumption is increased by 10%. Find the decrease percent in the revenue derived from it?
(A) 20%
(B) 18%
(C) 15%
(D) 12%
(E) 14%
Rationale: 100 * 100 = 10000
80 * 110 = 8800
10000------- 1200
100 ------- ? = 12%
ANSWER:D
Answer: (D) 12%
Question: The ratio of numbers is 3:4 and their H.C.F is 8. Their L.C.M is:
(A) 12
(B) 96
(C) 24
(D) 48
(E) 98
Rationale: Let the numbers be 3x and 4x.
Then their H.C.F = x. So, x = 8.
So, the numbers are 24 and 32.
L.C.M of 24 and 32 = 96.
ANSWER:B
Answer: (B) 96
Question: If set A={2,2,2,....,n times} , set B={3,3,3,3....m times} and set C={12,12,12...k time} , then in terms of m,n and k , how many possible subsets from sets A,B, and C can be created ?
(A) a) k(n+m+mn)+ k
(B) b) (1+n+m+mn)(k+1)
(C) c) k^2(mn+n/m)
(D) d) kmn(k+m+n)
(E) e) None of the above.
Rationale: a) how many 2's are included?
b) how many 3's are included?
and
c) how many 11's are included?
For the number of 2, we could have zero 2's, or one 2, or two 2's, all the way up to n 2's. That's (n + 1) possibilities for the 2's. Similarly, (m + 1) possibilities for the 3's and (k + 1) possibilities for the 11's. We simply multiply these three numbers.
NOTICE that one set, the set that includes no 2's, no 3's, and no 11's, is included. This is known in mathematics as thenull set, sometimes called the empty set, a set with no members. Technically, this is a subset of every possible set, but that's a technical detail of set theory that goes well beyond what the GMAT would expect students to know. Even the the calculation is not that difficult, some of the technical aspects of this question are not in line with the GMAT's expectations.
The number of subsets is (m + 1)(n + 1)(k + 1). The answer is not given in that form. Instead, the first two factors have been FOILed together:
(mn + m + n + 1)(k + 1).
Mike
C
Answer: (C) c) k^2(mn+n/m)
Question: A can run a kilometer race in 4 1/2 min while B can run same race in 5 min. How many meters start can A give B in a kilometer race, so that the race mat end in a dead heat?
(A) 220
(B) 277
(C) 298
(D) 100
(E) 271
Rationale: A can give B (5 min - 4 1/2 min) = 30 sec start.
The distance covered by B in 5 min = 1000 m.
Distance covered in 30 sec = (1000 * 30)/300 = 100 m.
A can give B 100m start.
Answer:D
Answer: (D) 100
Question: A password of a computer used four digits where they are from 0 and 9. What is the probability that the password solely consists of prime numbers and zero?
(A) 1/32
(B) 1/16
(C) 1/8
(D) 2/5
(E) 1/2
Rationale: We have four digits can be used for password -0,2,3,5,7.
Assuming that the numbers can be repeated any number of times in the password, probability of selecting any one of them is 5/10 (out of 10 digits from 0-9)
So, 5/10 * 5/10 * 5/10 * 5/10 =1/16 (B)
Answer: (B) 1/16
Question: If x is an even integer and y is an odd integer, which of the following is an even integer?
(A) x+y
(B) x+2y
(C) 3x+y
(D) x+y^2
(E) x+y+2
Rationale: Plug in an even integer for x; in this case 2
Plug in an odd integer for y; in this case 1
2+1 = 3 Odd
2+(2*1) = 4 Even
(3*2)+1 = 6 + 1 = 7 Odd
2+(1^2) = 2 + 1 = 3 Odd
2+1+2 = 5 Odd
Answer: B
Answer: (B) x+2y
Question: The sum of the present age of Henry and Jill is 48. What is their present ages if 9 years ago Henry was twice the age of Jill?
(A) and 27
(B) and 24
(C) and 22
(D) and 29
(E) of these
Rationale: Let the age of Jill 9 years ago be x, age of Henry be 2x
x+9 + 2x+9 = 48
x = 10
Present ages will be 19 and 29
Answer : D
Answer: (D) and 29
Question: Which number can we add to 722425 to get a number exactly divisible by 456?
(A) 312
(B) 335
(C) 347
(D) 361
(E) 383
Rationale: 722425 / 456 = 1584 with a remainder of 121.
We need to add 456 - 121 = 335
The answer is B.
Answer: (B) 335
Question: The mean of four integers L will not change if all the integers are multiplied by any constant. What is always true about this set of numbers?
I. The mean of the set is 0
II. The sum of the largest member and the smallest member of the set is 0
III. The set contains both positive and negative integers
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II, and III
Rationale: If we consider a set {1,2,3,4}, when multiplied with a constant we take that constant as 1 and multiply resulting set will contain the same numbers as the original. so how can the answer be I only.....A
Answer: (A) I only
Question: In a class there are 10 boys and 25 girls. In how many ways can a boy and a girl be selected?
(A) 400
(B) 250
(C) 600
(D) 530
(E) 630
Rationale: Explanation:
We can select one boy from 10 boys in 10 ways.
We select one girl from 25 girls in 25 ways
We select a boy and girl in 10 * 25 ways i.e., = 250 ways.
Answer: Option B
Answer: (B) 250