mathewhe/aqua_rat huggingface dataset:
Question: Two digits in father's age are the same as the digit in the son's age, but in reverse order. In five years father will be twice as old as son will be then. what is the difference in their current age ?
(A) 18
(B) 16
(C) 34
(D) 25
(E) 12
Rationale: Father's age= 10x+y
so son's age= 10y+x..
after 5 years , 10x+y+5=2*(10y+x+5)....
so 5+19y=8x... check for odd values of y, y=1 satisfies the eqn with x=3... so ages are 31 and 13 and ans as found correctly by u is A..18
Answer: (A) 18
Question: If a1 = 1 and an+1= 2an + 5, n = 1, 2 .. , then a20 is equal to ?
(A) a. 5*2^99-6
(B) b.6 * 2^19 - 5
(C) c. 6*2^99+5
(D) d. 6*2^99-5
(E) e. 6*2^99-6
Rationale: Here is my solution:
an+1=2an+5............(1)
lets ADD 5 to both sides....
so (an+1) + 5= 2 (an+5)....................taking 2 as common factor
now a1=1. so for n=1, an+5=6.......
putting n=1. we get both sides as,
a2 + 5= 2 * 6 ..............as ( an+5=6 .......(for n=1)..)
a2= 2 *6 - 5
a2= 2 * 2 *3 - 5
a2= 2^2 *3 - 5................. so with same progression
a20= 2^20 * 3 - 5
a20=2 * 2^19 * 3 - 5
a100= 6 * 2^19 - 5
B
Answer: (B) b.6 * 2^19 - 5
Question: The total number of digit used in numbering the pages of a book having 366 pages, is :
(A) 732
(B) 990
(C) 1098
(D) 1305
(E) None of these
Rationale: Solution
Total number of digits =( No. of digits in 1-digits page nos. + No. of digits in 2-digits page nos. + No. of digits i 3-digits page nos.)
= (1 * 9 + 2 * 90 + 3 * 267) = (9 + 180 + 801) = 990 .
Answer B
Answer: (B) 990
Question: If 15% of 30% of 50% of a number is 126, then what is the number?
(A) 5000
(B) 5600
(C) 5400
(D) 4500
(E) None of these
Rationale: Let the number be a
Given, 15/100 * 30/100 * 50/100 * a = 126
=> 3/20 * 3/10 * 1/2 * a = 126
=> a = 10 * 20 * 10 * 2 = 5600.
ANSWER:B
Answer: (B) 5600
Question: Roja and Pooja start moving in the opposite directions from a pole. They are moving at the speeds of 2 km/hr and 3 km/hr respectively. After 4 hours what will be the distance between them?
(A) 22 km
(B) 20 km
(C) 65 km
(D) 18 km
(E) 16 km
Rationale: Distance = Relative Speed * Time
= (2 + 3) * 4 = 20 km
[ They are travelling in the opposite direction, relative speed
= sum of the speeds].
Answer: B
Answer: (B) 20 km
Question: If the LCM of two numbers a and b is 1104 and their HCF is 4, which of the following MUST be true?
I. a * b = 4416
II. a and b are both divisible by 8
III. a : b = 48 : 23
(A) I only
(B) II only
(C) I and III only
(D) II and III only
(E) I, II, and III
Rationale: LCM (x,y)=1104
HCF (x,y)=4
The product of two numbers is equal to product of their LCM and HCF.
x * y =1104 * 4 =4416 so statement A is true
Since HCF (x,y) is 4 hence maximum common number with which x and y are divisible by is 4
so statement B is false
Now the ratio between x and y may be either 48:23 or 23:48
so statement C is false
Hence answer is 1
ANSWER:A
Answer: (A) I only
Question: A big beautiful cube is formed by rearranging the 160 coloured and 56 non-coloured similar cubes in such a way that the exposure of the coloured cubes to the outside is minimum. The percentage of exposed area to the coloured is :
(A) 25.9%
(B) 44.44%
(C) 35%
(D) 61%
(E) None of these
Rationale: Well the big cube which has the side built with 6 little cubes (6^3) will haveinsidethe cube which has the side built with 4 little cubes (6-2 edges), so 4^3. .. Similarly, the cube which has the side built with 4 little cubes (4^3) will haveinsidethe cube which has the side built with 2 little cubes, (4-2 edges), so 2^3... answer is B
Answer: (B) 44.44%
Question: Three men sit at a table. One dollar is placed in front of each of them. When a buzzer sounds, the first man to touch the money in front of him keeps the money that is in front of him, while the other two receive nothing. If none of the three men touches the money in front of them, then the amount of money doubles for the next round. After eight rounds of this activity, what is the maximum amount of money that any one man could receive?
(A) $4
(B) $5
(C) $101
(D) $115
(E) $128
Rationale: The Optimized scenario
After 1st Round - $1. Let nobody touches the amount will double in next round.
After 2nd Round - $2. Let nobody touches the amount will double in next round.
After 3rd Round - $4. Let nobody touches the amount will double in next round.
After 4th Round - $8. Let nobody touches the amount will double in next round.
After 5th Round - $16. Let nobody touches the amount will double in next round.
After 6th Round - $32. Let nobody touches the amount will double in next round.
After 7th Round - $64. Let Man A touches it and get$64
After 8th Round - $64. Let the same Man A touches it and get another$64.
So, after 8th round, the maximum amount a man receives is $128.
Answer (E)
Answer: (E) $128
Question: A question paper consists of five problems, each problem having three internal choices. In how many ways can a candidate attempt one or more problems?
(A) 1546
(B) 1054
(C) 1023
(D) 1608
(E) 1065
Rationale: Given that, the question paper consists of five problems. For each problem, one or two or three or none of the choices can be attempted.
Hence, the required number of ways = 45 - 1.
= 210 - 1 = 1024 - 1 = 1023
Answer:C
Answer: (C) 1023
Question: If P represents the product of the first 13 positive integers, which of the following must be true?
I. P is an odd number
II. P is a multiple of 16
III. P is a multiple of 27
(A) I only
(B) II only
(C) III only
(D) None of the above
(E) All of the above
Rationale: Answer = B) II only
Answer: (B) II only
Question: The sum of two number is 25 and their difference is 13. Find their product.
(A) 104
(B) product=114
(C) 315
(D) 325
(E) None
Rationale: EXPLANATION
Let the numbers be x and y.
Then, x + y = 25 and x – y = 13.
4xy = (x + y)2 – (x– y)2
= (25)2 – (13)2
= (625 – 169)
= 456
xy = 114.
Answer B
Answer: (B) product=114
Question: Two pipes can fill a tank in 20 minutes and 12 minutes. An outlet pipe can empty the tank in 10 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank?
(A) 24
(B) 26
(C) 28
(D) 30
(E) 32
Rationale: Let V be the volume of the tank.
The rate per minute at which the tank is filled is:
V/20 + V/12 - V/10 = V/30 per minute
The tank will be filled in 30 minutes.
The answer is D.
Answer: (D) 30
Question: Tickets to a certain concert sell for $20 each. The first 10 people to show up at the ticket booth received a 40% discount, and the next 20 received a 15% discount. If 45 people bought tickets to the concert, what was the total revenue from ticket sales?
(A) $600
(B) $760
(C) $850
(D) $980
(E) $1,140
Rationale: Price of 1 ticket = 20$
Revenue generated from sales of first 10 tickets = 10 * (60/100 * 20 )
= 10 * 12 = 120
Revenue generated from sales of next 20 tickets = 20 *(85/100 * 20 )
=20*17 = 340
Revenue generated from sales of last 15 tickets = 20 * 15
= 300
Revenue generated from sales of 45 tickets = 120 + 340 + 300
= 760 $
Answer B
Answer: (B) $760
Question: A can finish a piece of work in 12 days. B can do it in 20 days. They work together for 9 days and then A goes away. In how many days will B finish the work?
(A) 6 days
(B) 4 days
(C) 5 days
(D) 3 days
(E) 7 days
Rationale: 9/12+ (9 + x)/20 = 1 => x = 5 days
Answer: C
Answer: (C) 5 days
Question: Positive integer x has y factors; 3x has 3 factors; Which of the following values can y take?
I. 1
II. 2
III. 3
(A) I or II
(B) I only is true
(C) II only is true
(D) II or III
(E) I or III
Rationale: Squares have odd number of factors.The square which is a multiple of 3 is 9.
3 has factors 1,3 .
Therefore 2 factors
Answer C
Answer: (C) II only is true
Question: A, B and C, each working alone can complete a job in 2, 4 and 6 days respectively. If all three of them work together to complete a job and earn $2500, what will be C's share of the earnings?
(A) $1206.60
(B) $1363.63
(C) $1263.63
(D) $1463.53
(E) $1163.03
Rationale: The dollars earned will be in the same ratio as amount of work done
1 day work of C is 1/6 (or 2/12)
1 day work of the combined workforce is (1/2 + 1/4 + 1/6) = 11/12
C's contribution is 2/9 of the combined effort
Translating effort to $ = 6/11 * 2500 = $1363.63
hence:B
Answer: (B) $1363.63
Question: The product of all the prime numbers less than 15 is closest to which of the following powers of 10?
(A) a) 10^4
(B) b) 10^8
(C) c) 10^7
(D) d) 10^6
(E) e) 10^5
Rationale: Group these numbers so as to get product close to a multiple of 10, so they can be rewritten as (2*5)(3*7)(11*13) or 10*21*143
Now take out power of 10 from each number and rewrite
10*10*100*(1*2.1*1.43) or 10^4*(1*2.1*1.43)== 3.03*10^4
Which is greater than 10^4
A.
Answer: (A) a) 10^4
Question: 140 is what percent of 40?
(A)  5%
(B)  20%
(C)  50%
(D)  350%
(E)  500%
Rationale: 40*x=140 --> x=3.5 --> 3.5 expressed as percent is 350%.
Answer: D.
Answer: (D)  350%
Question: The average runs scored by a batsman in 30 matches is 50. In the next 15 matches the batsman scored an average of 26 runs. Find his average in all the 45 matches?
(A) 31
(B) 42
(C) 29
(D) 97
(E) 27
Rationale: Total score of the batsman in 30 matches = 1500.Total score of the batsman in the next 15 matches = 390.Total score of the batsman in the 30 matches = 1890.Average score of the batsman = 1890/45 = 42.Answer: B
Answer: (B) 42
Question: Depreciation applicable to an equipment is 20%.The value of the equipment 3 years from now will be less by
(A) 48.8%
(B) 47.8%
(C) 46.8%
(D) 49.8%
(E) 45.8%
Rationale: Value after 3 years will be 0.8^3 = 0.512 times the present value.
so it will be less by 48.8%.
ANSWER:A
Answer: (A) 48.8%
Question: A pair of articles was bought for $50 at a discount of 40%. What must be the marked price of each of the article?
(A) $25
(B) $15
(C) $29.65
(D) $35.95
(E) $45.62
Rationale: S.P. of each of the article = 50/2 = $25
Let M.P = $x
60% of x = 25
x = 25*.6 =$15
Answer is B
Answer: (B) $15
Question: When simplified, the product (1 – 1/2) (1 – 1/3) (1 – 1/4)…… (1 – 1/n) gives:
(A) 1/n
(B) 2/n
(C) 2(n – 1)/n
(D) 2/n(n + 1)
(E) 3/n(n + 1)
Rationale: 1/2 x 2/3 x 3/4 x …..x (n – 1)/n
= 1/n
ANSWER:A
Answer: (A) 1/n
Question: A person travels equal distances with speed of 3 km/hr, 4 km/hr and 5 km/hr and takes a total of 47
minutes. Find the total distane
(A) 3 km
(B) 4 km
(C) 6 km
(D) 9 km
(E) None of these
Rationale: Explanation:
Let the distance be 3x km,
then,
x3+x4+x5=476047x60=4760x=1
So total distance = 3*1 = 3 Km
Answer: A
Answer: (A) 3 km
Question: How long does a train 165 meters long running at the rate of 36 kmph take to cross a bridge 660 meters in length?
(A) 33
(B) 72
(C) 55
(D) 82.5
(E) 62
Rationale: Explanation:
T = (660 + 165)/36 * 18/5
T = 82.5
Answer: Option D
Answer: (D) 82.5
Question: What is the greatest prime factor of 1+2+3+。。。+106?
(A) 131
(B) 127
(C) 99
(D) 101
(E) 107
Rationale: find the sum from direct formula = n(n+1)/2 = 106(106+1)/2 = 53*107...
107 is a PRIME number, so ans is 107..
D is the answer
Answer: (D) 101
Question: Sum of the squares of 3 no. is 252 and the sum of their products taken two at a time is 116. Find the sum?
(A) 24
(B) 33
(C) 22
(D) 20
(E) 21
Rationale: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 252 + 2* 116
a + b + c = âˆš484 = 22
Answer C
Answer: (C) 22
Question: How many different ways can 2 students be seated in a row of 3 desks, so that there is always at least one empty desk between the students?
(A)  2
(B)  3
(C)  4
(D)  6
(E)  12
Rationale: 1 ways to seat the students:
with two empty seats between
1 empty w/ one student on the left most
1 empty....right most
two students can be interchanged
1x2=2
A
Answer: (A)  2
Question: After a storm deposits 120 billion gallons of water into the city reservoir, the reservoir is 85% full. If the original contents of the reservoir totaled 220 billion gallons, the reservoir was approximately what percentage full before the storm?
(A) 45%
(B) 48%
(C) 55%
(D) 58%
(E) 65%
Rationale: When the storm deposited 120 billion gallons, volume of water in the reservoir = 220 + 120 = 340 billion gallons
If this is only 85% of the capacity of the reservoir, the total capacity of the reservoir = 340/0.85 = 400 billion gallons
Therefore percentage of reservoir that was full before the storm = (220/400)*100 = 55%
Option C
Answer: (C) 55%
Question: What is the ratio of the volumes of a right cylinder to that of a right cone having equal diameters?
(A) 1:3
(B) 3:1
(C) 2:3
(D) 3:2
(E) None of these
Rationale: SOLUTION :
volume of cylinder : volume of cone
pr2h : 1/3 pr2h = 3 : 1
ANSWER IS B
Answer: (B) 3:1
Question: If Greg buys 6 shirts, 4 trousers and 2 ties, the total cost is $80. If Greg buys 4 shirts, 2 trousers and 2 ties, the total cost is $140. How much will it cost him to buy 3 trousers, 5 shirts and 2 ties?
(A) $60
(B) $64
(C) $75
(D) $110
(E) Cannot be determined
Rationale: Solution: 6x+4y+2z=80 4x+2y+2z=140
adding both the equations= 10x+6y+4z=220
5x+3y+2z=110
ans D
Answer: (D) $110
Question: (X)+1315+9211-1569=11901. Calculate the value of X
(A) 87801
(B) 87811
(C) 87862
(D) 11803
(E) 87803
Rationale: x+1315+9211-1569=11901
=x+1315+9211=11901+1569
=x+10526=13470
=x=98329-10526
=87803
Answer is E
Answer: (E) 87803
Question: Length of a rectangular plot is 20 mtr more than its breadth. If the cost of fencin gthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?
(A) 20 m
(B) 60 m
(C) 50 m
(D) 45 m
(E) 65 m
Rationale: Let breadth = x metres.
Then, length = (x + 20) metres.
Perimeter = 5300 m = 200 m.
26.50
2[(x + 20) + x] = 200
2x + 20 = 100
2x = 80
x = 40.
Hence, length = x + 20 = 60 m
B
Answer: (B) 60 m
Question: 217 x 217 + 183 x 183=?
(A) 79698
(B) 80578
(C) 80698
(D) 81268
(E) None of them
Rationale: =(217)^2 + (183)^2
=(200+17)^2 + (200-17)^2
=2[(200)^2+(17)^2]
=2[40000+289]
=2 x 40289 = 80578
Answer is B
Answer: (B) 80578
Question: How many of the positive factors of 85 , 105 and how many common factors are there in numbers?
(A) 5
(B) 4
(C) 2
(D) 3
(E) 1
Rationale: factors of 85 - 1, 5, 17, 85
factors of 105 - 1, 3, 5, 7, 15, 21, 35, 105
Comparing both, we have two common factors of 85 and 105- 1,5
Answer(C)
Answer: (C) 2
Question: The average weight of A, B and C is 44 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is:
(A) 33 kg
(B) 34 kg
(C) 32 kg
(D) 36 kg
(E) 37 kg
Rationale: Let A, B, C represent their respective weights.
Then, we have: A + B + C = (44 x 3) = 132 .... (i)
A + B = (40 x 2) = 80 .... (ii)
B + C = (43 x 2) = 86 ....(iii)
Adding (ii) and (iii), we get: A + 2B + C = 166 .... (iv)
Subtracting (i) from (iv), we get : B = 34.
B's weight = 34 kg.
B
Answer: (B) 34 kg
Question: If x < y < z and y - x > 5, where x is an even integer and y and z are odd integers, what is the least possible value D of z - x?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: x<y<z
To find the least possible value for z-x; we need to find the values for z and x that can be closest to each other. If x is some even number, then what could be minimum possible odd z.
If x is some even number
y-x>5; y>x+5; minimum value for y=x+5+2=x+7[Note: x+5 is as even+odd=odd and nearest odd greater than x+5 is x+5+2]
Minimum value for z=y+2=x+7+2=x+9 [Note: z=y+2 because both z and y are odd. Difference between two odd numbers is 2]
D=z-x = x+9-x= 9
Ans:D
Answer: (D) 9
Question: John and Lewis leave Chennai for Bangalore simultaneously at 8 P.M in the night driving in two cars at speeds of 50 mph and 70 mph respectively. As soon as Lewis reaches Bangalore he returns back to Chennai along the same route and meets John on the way back. If the distance between the two cities is 210 miles, how far from Chennai did John and Lewis meet?
(A) 200 miles
(B) 140 miles
(C) 150 miles
(D) 149 miles
(E) 50 miles
Rationale: Time taken by Lewis to reach Bangalore = 210/70 = 3 hours
In 3 hours, John travels 50*3 = 150 miles
So distance at which they meet should be greater than 150 miles.
Only C satisfies.
Answer is C.
Answer: (C) 150 miles
Question: There are 10 seats around a circular table. If 8 men and 2 women have to seated around a circular table, such that no two women have to be separated by at least one man. If P and Q denote the respective number of ways of seating these people around a table when seats are numbered and unnumbered, then P : Q equals?
(A) 10:1
(B) 9:1
(C) 72:1
(D) 8:1
(E) None of these
Rationale: Explanation :
Initially we look at the general case of the seats not numbered.The total number of cases of arranging 8 men and 2 women, so that women are together:⇒ 8×!2!The number of cases where in the women are not together:⇒9!−(8!×2!)=QNow, when the seats are numbered, it can be considered to a linear arrangement and the number of ways of arranging the group such that no two women are together is:⇒ 10!−(9!×2!)But the arrangements where in the women occupy the first and the tenth chairs are not favourable as when the chairs which are assumed to be arranged in a row are arranged in a circle, the two women would be sitting next to each other.The number of ways the women can occupy the first and the tenth position:=8!×2!The value of P =10!−(9!×2!)−(8!×2!)Thus P : Q = 10 : 1
Answer : A
Answer: (A) 10:1
Question: If the President and Vice President must sit next to each other in a row with 1 other members of the Board, how many different seating arrangements are possible?
(A) 4
(B) 16
(C) 8
(D) 10
(E) 2
Rationale: We need to take President and VP as one unit. Therefore we have 2 people to arrange=2! ways
Also, we both President and VP can be arranged in 2 ! ways.
Reqd no of ways=2!*2!=4 ways
Answer A
Answer: (A) 4
Question: At 1:00, Annie starts to bicycle along a 58 mile road at a constant speed of 14 miles per hour. Thirty minutes earlier, Scott started bicycling towards Annie on the same road at a constant speed of 12 miles per hour. At what time will they meet?
(A) 2:30
(B) 3:00
(C) 3:30
(D) 4:00
(E) 5:00
Rationale: In the first 30 minutes, Scott can travel 6 miles, so there are 52 miles left.
Together Annie and Scott can complete 26 miles.
52/26 = 2, so they will meet 2 hours after 1:00.
The answer is B.
Answer: (B) 3:00
Question: 8.008/1.001
(A) 0.008
(B) 8
(C) 0.8
(D) 80
(E) 800
Rationale: Answer is 8, move the decimal forward three places for both numerator and denominator or just multiply both by a thousand. The result is 8008/1001= 8
Answer B
Answer: (B) 8
Question: Sandy is younger than Molly by 14 years. If the ratio of their ages is 7:9, how old is Sandy?
(A) 42
(B) 49
(C) 56
(D) 63
(E) 70
Rationale: Let Sandy's age be 7x and let Molly's age be 9x.
9x - 7x = 14
x = 7
Sandy is 49 years old.
The answer is B.
Answer: (B) 49
Question: Linda spent 3/5 of her savings on furniture and the rest on a TV. If the TV cost her $400, what were her original savings?
(A) $900
(B) $300
(C) $600
(D) $1000
(E) $800
Rationale: If Linda spent 3/5 of her savings on furnitute, the rest
5 / 5 - 3 / 5 = 2 / 5 on a TV
But the TV cost her $400. So 2 / 5 of her savings is $400. So her original savings are 5/2 times $400 = $2000/2 = $1000
correct answer D
Answer: (D) $1000
Question: How many ways are there to award a gold, silver and bronze medal to 5 contending teams?
(A) 10 × 9 × 8
(B) 10!/(3!7!)
(C) 5 * 4 * 3
(D) 543
(E) 200
Rationale: we clearly know that there can be only one winning team which deserves the gold medal. we can do the selection in 5 ways
if gold medal is given to 1 of the teams then only possible 4 teams can be considered for silver medal. we can do selection in 4 ways
similarly if gold and silver medals are awarded then only remaining 3 teams can be considered for a bronze medal. we can do the selection in 3 ways
Total number of ways to select the 3 possible medal winners = 5 * 4 * 3
Correct answer - C
Answer: (C) 5 * 4 * 3
Question: The sub-duplicate ratio of 25:16 is
(A) 4:3
(B) 1:2
(C) 1:3
(D) 5:4
(E) 2:3
Rationale: root(25):root(16)=5:4
ANSWER:D
Answer: (D) 5:4
Question: Find large number from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
(A) 1234
(B) 1345
(C) 1350
(D) 1500
(E) 1635
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 15
5x = 1350
x = 270
Large number = 270+1365 = 1635
E
Answer: (E) 1635
Question: One water pump can fill half of a certain empty tank in 5 hours. Another pump can fill half of the same tank in 5.5 hours. Working together, how long will it take these two pumps to fill the entire tank?
(A) 1 7/13
(B) 5 5/8
(C) 3 1/4
(D) 5 5/21
(E) 3 1/2
Rationale: One pump can fill a tank in 5 hours and another in 5.5 hours
so the rate at which both can half fill the tank is (1/5+1/5.5) => 21/55
Thus half of the tank can be filled in 55/21
so for filling the complete tank => 55/21*2 = 110/21 =5 5/21
ANSWER:D
Answer: (D) 5 5/21
Question: Walking at 5/6 of her normal speed, a worker is 12 minutes later than usual in reaching her office. The usual time (in minutes) taken by her to cover the distance between her home and her office is
(A) 36
(B) 42
(C) 48
(D) 54
(E) 60
Rationale: Let V be her normal speed and let T be her normal time.
D = (5/6)V * (T+12)
Since the distance is the same we can equate this to a regular day which is D = V*T
V*T = (5/6)V * (T+12)
T/6 = 10
T=60
The answer is E.
Answer: (E) 60
Question: Janes can eat 25 marshmallows is 20 minutes. Dylan can eat 25 in one hour. In how much time will the two eat 150 marshmallows?
(A) 40 minutes.
(B) 1 hour and 30 minutes.
(C) 1 hour.
(D) 1 hour and 40 minutes.
(E) 2 hours and 15 minutes.
Rationale: Rate =Output/Time
Janes Rate=25/20=5/4
Dylan Rate=25/60=5/12
Combined rate = 5/4+5/12= 20/12
CombinedRate*CombinedTime= CombinedOutput
20/12*t=150
t=90 mins => 1 hr 30 min
Answer: (C) 1 hour.
Question: Three students appear at an examination of Mathematics. The probability of their success are 1/3, 1/4, 3/5 respectively. Find the probability of success of at least two.
(A) 1/3
(B) 2/5
(C) 3/4
(D) 3/5
(E) 4/5
Rationale: The probability of success of at least two students will involve the following possibilities.
The first two students are successful, the last two students are successful, the first and third students are successful and all the three students are successful.
Therefore, the required probability = 1/3 x 1/4 x 2/5 + 1/4 x 3/5 x 2/3 + 1/3 x 3/5 x 3/4 + 1/3 x 1/4 x 3/5 = 1/3
ANSWER:A
Answer: (A) 1/3
Question: Factor: 3y(x – 3) -2(x – 3)
(A) (a) (x – 3)(x – 3)
(B) (b) (x – 3)2
(C) (c) (x – 3)(3y – 2)
(D) (d) 3y(x – 3)
(E) (e) 3y(x – 2)
Rationale: 3y(x – 3) -2(x – 3).
= (x – 3)(3y – 2).
Answer: (C).
Answer: (C) (c) (x – 3)(3y – 2)
Question: If x+|x|+y=2 and x+|y|-y=6 what is x+y=?
(A) 1
(B) -1
(C) 3
(D) 5
(E) 13
Rationale: If x<0 and y<0, then we'll have x-x+y=7 and x-y-y=6. From the first equation y=7, so we can discard this case since y is not less than 0.
If x>=0 and y<0, then we'll have x+x+y=7 and x-y-y=6. Solving gives x=4>0 and y=-1<0 --> x+y=3. Since in PS questions only one answer choice can be correct, then the answer is C (so, we can stop here and not even consider other two cases).
Answer: C.
Adding both eqn we get 2x +IxI+IyI = 13
Now considering X <0 and y>0
2x-x +y = 13
we get x+y =1
Hence answer should be A
Answer: (A) 1
Question: Alex deposited x dollars into a new account that earned 9 percent annual interest, compounded annually. One year later Alex deposited an additional x dollars into the account. If there were no other transactions and if the account contained w dollars at the end of two years, which of the following expresses x in terms of w ?
(A) w/(1+1.08)
(B) w/(1.08+1.16)
(C) w/(1.09+1.09^2)
(D) w/(1.16+1.24)
(E) w/(1.08^2+1.08^2)
Rationale: Account at the end of the first year would be 1.09x dollars. At this time x dollars was deposited, hence the account at the beginning of the second year would be (1.09x+x) dollars. Account at the end of the second year would be (1.09x+x)*1.09=w --> x(1.09^2+1.09)=w --> x=w/(1.09+1.09^2).
Answer: C.
Answer: (C) w/(1.09+1.09^2)