mathewhe/aqua_rat huggingface dataset:
Question: Two friends Simpson & Stewie decide to get together
So they start driving cars towards each other. They plan to meet halfway. Each is riding at 6 Km/hr. They live 36 kms apart. Stewie has a pet "eagle" and it starts flying the instant they start traveling. The eagle flies back and forth at 18 Km/hr between them until the two meet.
How many kms does the eagle travel ?
(A) 54
(B) 76
(C) 25
(D) 60
(E) 58
Rationale: A
54
It takes 3 hours for the Simpson & Stewie to meet.
so the eagle flies for 3 hours at 18 Km/hr = 54 kms
Answer: (A) 54
Question: Two years ago, Arthur gave each of his five children 20 percent of his fortune to invest in any way they saw Fit. In the first year, three of the children, Alice, Bob, and Carol, each earned a profit of 50 percent on their Investments, while two of the children, Dave and Errol, lost 40 percent on their investments. In the second Year, Alice and Bob each earned a 10 percent profit, Carol lost 60 percent, Dave earned 25 percent in profit, And Errol lost all the money he had remaining. What percentage of Arthur's fortune currently remains?
(A) 93%
(B) 97%
(C) 100%
(D) 107%
(E) 120%
Rationale: Say Arthur's fortune was $100. Then:
A = 20*1.5*1.1 = 33
B = 20*1.5*1.1 = 33
C = 20*1.5*0.4 = 12
D = 20*0.6*1.25 = 15
E = 0
Total 33 + 33 + 12 + 15 = 93.
Answer: A.
Answer: (A) 93%
Question: If 300!/10^n is an integer, what is the largest possible value of n?
(A) 75
(B) 74
(C) 79
(D) 77
(E) 72
Rationale: The question actually asks the highest power of 10 which divides 300! ( For a number to be an integer - Without any remainder all the trailing zeroe's must be divided by the denominator)
10 = 2 x 5
300 factorial will have 74 as -
300/5 = 60
60/5 = 12
12/5 =2
So answer will be (D) 74
Answer: (D) 77
Question: A train running at the speed of 60 km/hr crosses a pole in 12 seconds. What is the length of the train?
(A) 186 m
(B) 176 m
(C) 300 m
(D) 150 m
(E) 200 m
Rationale: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train
= (Speed x Time) = (50/3 * 12) m
= 200 m.
Answer: E
Answer: (E) 200 m
Question: If a certain manager had received a 12.5% raise instead of the 8% raise that she actually received, her salary would have been $60,500. What was her actual salary after the raise?
(A) 55,000
(B) 58,080
(C) 59,290
(D) 59,400
(E) 61,620
Rationale: No need of getting involved with decimals ..just work in fractions ..
salary(let X) included 10% increase can be written as
(1+12.5/100)X=60500
X=60500/1.125------>53777.77
if there is 8% rise in 53777.77
then the salary now is 8% of 53777.77
8*53777.77/100=4302.22
then toal salary after increment=53777.77+4302.22----->58079.99
Ans B
Answer: (B) 58,080
Question: To complete a work A and B takes 8 days, B and C takes 12 days, A,B and C takes 6 days. How much time A and C will take
(A) 24 days
(B) 16 days
(C) 12 days
(D) 8 days
(E) None of these
Rationale: Explanation:
A+B 1 day work = 1/8
B+C 1 day work = 1/12
A+B+C 1 day work = 1/6
We can get A work by (A+B+C)-(B+C)
And C by (A+B+C)-(A+B)
So A 1 day work =
1/6−1/12=1/12
Similarly C 1 day work =
1/6−1/8 = 4−3/24=1/24
So A and C 1 day work =
1/12+1/24=3/24=1/8
So A and C can together do this work in 8 days
Option D
Answer: (D) 8 days
Question: Barbata invests $1400 in the National Bank at 5%. How much additional money must she invest at 8% so that the total annual income will be equal to 6% of her entire investment?
(A) 700
(B) 300
(C) 1000
(D) 360
(E) 2400
Rationale: Let the additional invested amount for 8% interest be x;
Equation will be;
1400+0.05*2400+x+0.08x = 1400+x+0.06(2400+x)
0.05*1400+0.08x = 0.06x+0.06*1400
0.02x = 1400(0.06-0.05)
x = 1400*0.01/0.02 = 700
Ans:A
Answer: (A) 700
Question: The ratio of the length and the width of a rectangle is 4 : 3 and the area of the rectangle is 6348 sq cm. What is the ratio of the width and the area of the rectangle?
(A) 1: 96
(B) 1: 99
(C) 1: 94
(D) 1: 92
(E) 1: 91
Rationale: Let the length and the width be 4x and 3x respectively.
Area = (4x)(3x) = 6348
12x^2 = 6348
x^2 = 529
x = 23
The ratio of the width and the area is 3x : 12x^2 = 1 : 4x = 1: 92
The answer is D.
Answer: (D) 1: 92
Question: What is the place value of 3 in the numeral 3259
(A) 2500
(B) 3400
(C) 3500
(D) 3000
(E) 4000
Rationale: Option 'D'
3 * 1000 = 3000
Answer: (D) 3000
Question: The radius of a cylindrical vessel is 7cm and height is 3cm. Find the whole surface of the cylinder?
(A) 308 sq cm
(B) 220 sq cm
(C) 440 sq cm
(D) 132 sq cm
(E) 138 sq cm
Rationale: r = 7 h = 3
2πr(h + r) = 2 * 22/7 * 7(10) = 440
ANSWER:C
Answer: (C) 440 sq cm
Question: If 175*s is a perfect square then s can be which of the following numbers?
(A) 21
(B) 35
(C) 54
(D) 105
(E) 150
Rationale: My solution:
For a number to be a perfect square all the prime factors must be in pairs. So,
Prime factors of 175 are 5 *5 * 7
1) 21 = 3 * 7
2) 35 = 5 * 7
3) 54 = 2 * 3 * 3 * 3
4) 105 = 3 * 5 * 7
5) 150 = 2 * 3 * 5 * 5
So only answer choice D completes the pairing of 5 and 7. It adds a3, a5, and a7to the prime factors of 175 (5*5*7) and makes it a perfect square. B
Answer: (B) 35
Question: Sales price is $54, gross profit is 125% of cost, what is the value of gross profit?
(A) 32
(B) 30
(C) 39
(D) 40
(E) 42
Rationale: Cost + Profit = Sales
Cost + (125/100)Cost = 54
Cost = 24
Profit = 54 - 24 = 30
Answer (B)
Answer: (B) 30
Question: 10 books are placed at random in a shelf. The probability that a pair of books will always be together is -.
(A) 1/10
(B) 9/10
(C) 1/5
(D) 3/10
(E) 1/2
Rationale: Explanation:
10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!
Required probability = 1/5
ANSWER IS C
Answer: (C) 1/5
Question: A,B and C are brothers . D is A's father while G is B's son. Which of the following statements is definitely true ?
(A) D is G's grandparent
(B) B is D's uncle
(C) C is G's brother
(D) D is B's brother
(E) A is G's nephew
Rationale: Explanation:
A,B and C are children of same parents. So. G who is B's son is a grandchild to D.
Answer: A)
Answer: (A) D is G's grandparent
Question: A positive number when decreased by 4 is equal to 21 times the reciprocal of the number. The number is
(A) 3
(B) 5
(C) 7
(D) 9
(E) 12
Rationale: Sol.
Let the numbers be x.
Then, x - 4 = 21/x
⇔ x2 - 4x - 21 = 0
⇔ (x-7)(x+3) = 0
⇔ x = 7.
Answer C
Answer: (C) 7
Question: The average wages of a worker during a fortnight comprising 15 consecutive working days was $90 per day. During the first 7 days, his average wages was $87 per day and the average wages during the last 7 days was $93 per day. What was his wage on the 8th day?
(A) $83
(B) $90
(C) $92
(D) $97
(E) $104
Rationale: Average daily wage of a worker for 15 consecutive working days = 90$
During the first 7 days , the daily average daily wage = 87$
During the last 7 days , the daily average daily wage = 93$
Wage on 8th day = 90*15 -( 87*7 + 93 *7)
= 1350 - (609 + 651)
=1350 - 1260
= 90
Answer B
Answer: (B) $90
Question: Solve the equation for x : 8x - 40 + 2x = 5 + 10 - x
(A) 4
(B) 10
(C) 7
(D) 5
(E) 3
Rationale: D
5
10 x + x = 15 + 40
11 x = 55 => x = 5
Answer: (D) 5
Question: 1!+2!+3!+4!+5!+..100! is divided by 24. Find the remainder?
(A) 3
(B) 6
(C) 9
(D) 11
(E) 13
Rationale: By applying rule 2, we divide the terms of the above expression individually, and add them to get the final remainder. But from 4! onwards all the terms leave a remainder 0 when divided by 24.
So the remainder = 1 + 2 + 6 + 0 + 0....... = 9
C
Answer: (C) 9
Question: Three clocks were set to true time and starts to run together, makes a beep sound at intervals of 8,10 and 12 minutes respectively. In 2 days, how many times do they will make the sound together ?
(A) 12
(B) 15
(C) 25
(D) 30
(E) 35
Rationale: Explanation :
The clocks make sound at intervals of 8, 10 and 12 minutes respectively.
The LCM of 8,10 and 12 is 120.
So, the clocks will make sound together after every 120 minutes. i.e., after every 2 hours.
In 2 days(48 hours), they will make the sound together (48/2) = 24 times.
At the end of 2nd day, they will make one more beep together.
Therefore, totally (24+1) 25 times beep sound is made together.
Hence the answer is 25 times.
Answer : C
Answer: (C) 25
Question: Suganya and Suriya are partners in a business. Suganya invests Rs. 35,000 for 8 months and Suriya invests Rs.42,000 for 10 months. Out of a profit of Rs.30,570. Suganya's share is
(A) Rs.9471
(B) Rs.12,628
(C) Rs.262.8
(D) Rs.241.7
(E) None
Rationale: Solution
Ratio of their shares	=(35000Ã—8):(42000Ã—10)
= 128 : 125
Suganya's share	= Rs.(30570 Ã—2/253)
= Rs.241.7.
Answer D
Answer: (D) Rs.241.7
Question: There are three vessels of equal capacity .Vessel A contains Milk and water in the ratio 12:10 ;Vessel B contains Milk and water in the ratio 2:1 and Vessel C contains Milk and water in the ratio 3:2 .If the mixture in all the three vessels is mixed up.What will be the ratio of milk and water ?
(A) 921:630
(B) 598:392
(C) 118:126
(D) 193:122
(E) 201:132
Rationale: 12:10=>12x+10x=22x
2:1=>2y+1y=3y
3:2=>3z+2z=5z
22x=3y=5z
Take LCM of 22,3,5=330
Or simply;
x=15
y=110
z=66
So,
Ratio of Milk:Water= (12x+2y+3z)/(10x+y+2z)=598/392
Ans:B
Answer: (B) 598:392
Question: How many multiples of 5 are there between 5 to 95?
(A) 9
(B) 18
(C) 17
(D) 16
(E) 15
Rationale: As you know, multiples of 5 are integers having 0 or 5 in the digit to the extreme right (i.e. the unit’s place). So the numbers are 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90.
Answer C
Answer: (C) 17
Question: 2^x +2* 2^-x = 4 What is the value of x?
(A) -1
(B) -1/2
(C) 1
(D) 1/2
(E) 0
Rationale: let 2^x = t
t+1/t =2
t^2 -4t +4 =0
(t-2)^2=0
t-2=0
t=2
2^x=2
x=1
Ans: C
Answer: (C) 1
Question: A sum of Rs.3800 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.
(A) A)282
(B) B)2470
(C) C)8383
(D) D)8383
(E) E)3284
Rationale: Let A be the amount received at the end of the three years.
A = 3800[1 + 10/100][1 + 20/100][1 + 25/100]
A = 3800 * 1.65
A = Rs.6270
So the interest = 6270 - 3800 = Rs.2470
Answer: B
Answer: (B) B)2470
Question: Rs. 6000 is lent out in two parts. One part is lent at 6% p.a simple interest and the other is lent at 10% p.a simple interest. The total interest at the end of one year was Rs. 450. Find the ratio of the amounts lent at the lower rate and higher rate of interest?
(A) 3750:2250
(B) 3751:2250
(C) 3752:2250
(D) 3760:2250
(E) 3762:2250
Rationale: Let the amount lent at 6% be Rs. x
Amount lent at 10% is Rs. (6000 - x)
Total interest for one year on the two sums lent
= 6/100 x + 10/100 (6000 - x) = 600 - 3x/100
=> 600 - 3/100 x = 450 => x = 3750
Amount lent at 10% = 2750
Required ratio = 3750:2750
Answer:A
Answer: (A) 3750:2250
Question: Two mechanics were working on your car. One can complete the given job in six hours, but the new guy takes 9 hours. They worked together for the first two hours, but then the first guy left to help another mechanic on a different job. How long will it take the new guy to finish your car?
(A) 7/4
(B) 32/9
(C) 15/4
(D) 10/3
(E) 17/5
Rationale: Rate(1)=1/6
Rate(2)=1/9
Combined = 5/18
Work done in 2 days=5/9
Work left = 4/9
Rate * Time = Work left
1/8 * Time = 4/9
Time=32/9
B
Answer: (B) 32/9
Question: P is four times as old as Q, and Q is five years older than R. If R is z years old, what is P’s age in terms of z?
(A) 4z + 5
(B) 4z + 20
(C) 4z - 20
(D) (z + 5)/4
(E) (z − 5)/4
Rationale: P = 4Q
Q = R+5 = z+5
P = 4(z+5) = 4z + 20
The answer is B.
Answer: (B) 4z + 20
Question: From among the 31 students in a class, one leader and one class representative are to be appointed. In how many ways can this be done?
(A) 1360
(B) 1260
(C) 1060
(D) 1160
(E) 930
Rationale: There are 31 students and every one has equal chance of being selected as a leader. Hence, the leader can be appointed in 31 ways. When one person is appointed as leader, we are left with 35 students. Out of these 30 teachers, we can select one class representative. So, a class representative can be selected in 30 ways. Hence, the number of ways in which a leader and class representative can be selected = 31 x 30 = 930
ANSWER:E
Answer: (E) 930
Question: A person is traveling at 20 km/hr and reached his destiny in 8 hr then find the distance?
(A) 180 km
(B) 200 km
(C) 160 km
(D) 220 km
(E) 240 km
Rationale: T = 8 hrs
D= T*S = 20*8 = 160 km
Answer is C
Answer: (C) 160 km
Question: In how many ways can 6 apples (identical) be distributed among 5 children? (Some children may get no apples.)
(A) 124
(B) 210
(C) 128
(D) 130
(E) 132
Rationale: Generalised form for n = number of identical objects, and r = number of children is n+r-1Cr-1.
n=6 r= 5
10C4 =210
Answer : B
Answer: (B) 210
Question: If Teena is driving at 55 miles per hour and is currently 7.5 miles behind Joe, who is driving at 40 miles per hour in the same direction then in how many minutes will Teena be 52.5 miles ahead of Joe?
(A) 15
(B) 240
(C) 75
(D) 90
(E) 105
Rationale: This type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30-40 seconds for a difficult one.
Teena covers 55 miles in 60 mins.
Joe covers 40 miles in 60 mins
So teena gains 15 miles every 60 mins
Teena need to cover 7.5 +52.5 miles.
Teena can cover 7.5 miles in 30 mins
Teena will cover 52.5 miles in 210 mins
So answer 30+210= 240 mins. (ANSWER B)
Answer: (B) 240
Question: What is the rational number for recurring decimal 0.890890890.... ?
(A) 890890/1000
(B) 67/421
(C) 890/999
(D) None of these
(E) Cannot be determined
Rationale: Explanation :
0.890890890.... = 0.890¯=890/999. Answer : Option C
Answer: (C) 890/999
Question: If each side of a rectangle is increased by 100%, by what % the area increases?
(A) 100%
(B) 200%
(C) 250%
(D) 300%
(E) 400%
Rationale: if length is l and width is b then area=l*b
now new l and b is 2l and 2b respectively.
so new area is=4*l*b
% increase= 300%
ANSWER:D
Answer: (D) 300%
Question: A man saves Rs 250 at the end of each year and lends the money at 5% compound interest. How
much will it become at the end of 3 years.
(A) Rs 662
(B) Rs 862.01
(C) Rs 827.53
(D) Rs 686.53
(E) None of these
Rationale: Explanation:
=[250(21/20×21/20×21/20)+250(21/20×21/20)+250(21/20)]=827.53
Answer: C
Answer: (C) Rs 827.53
Question: If Bill can buy 3 pairs of jeans and 2 shirts for $69 or 2 pairs of jeans and 3 shirts for $86, how much does one shirt cost?
(A) $10
(B) $12
(C) $13.20
(D) $15
(E) $24
Rationale: 3J + 2S = 69
2J + 3S = 86
----------------
5J + 5S = 155 ----(divide by 5)---> J + S = 31
3J + 2S = J + 2(J + S) = J + 62 = 69 ---> J = 7
3*7 + 2S = 69
21 + 2S = 69
2S = 48
S = 24
Answer: E
Answer: (E) $24
Question: If x/y = 2/z, then 5x^2 =
(A) y/z
(B) 20y²/z²
(C) y²z²
(D) 5y²/z²
(E) yz
Rationale: This question is most easily solved by isolating y in the equation and substituting into the expression 5x²:
x/y = 2/z
x = 2y/z
If we substitute 2y/z into the expression for x, we get:
5(2y/z)² = 5(4y²/z²) = 20y²/z².
The correct answer is choice (B)
Answer: (B) 20y²/z²
Question: P, Q and R can do a work in 20, 30 and 60 days respectively. How many days does it need to complete the work if P does the work and he is assisted by Q and R on every third day?
(A) 10 days
(B) 14 days
(C) 15 days
(D) 9 days
(E) 19 days
Rationale: Explanation :
Amount of work P can do in 1 day = 1/20
Amount of work Q can do in 1 day = 1/30
Amount of work R can do in 1 day = 1/60
P is working alone and every third day Q and R is helping him
Work completed in every three days = 2 × (1/20) + (1/20 + 1/30 + 1/60) = 1/5
So work completed in 15 days = 5 × 1/5 = 1
Ie, the work will be done in 15 days
Answer : Option C
Answer: (C) 15 days
Question: If the LCM of two integers P, Q (where Q> P and P>1) is P*Q, then which of the following can not be true?
(A) Both P and Q can be consecutive integers.
(B) Both P and Q can be Prime Numbers.
(C) P and Q do not have a common factor.
(D) P and Q do not share any Prime factors.
(E) All Prime factors of P must be Prime factors of Q.
Rationale: If LCM of two numbers P and Q is the product PQ then both numbers are Co- prime.
(Co-prime numbers are any two numbers which have an HCF of 1 i.e. when two numbers have no common prime factor apart from the number 1).
Numbers that can be Co-Prime are :
1) Two consecutive natural numbers.
2) Two consecutive odd numbers.
3) Two prime numbers.
4) One prime number and the other a composite number such that the composite number is not a multiple of the prime number.
With above four statements it can be concluded that Options A, B, C and D are all true.
Only Option E cannot be true.
Hence answer is E
Answer: (E) All Prime factors of P must be Prime factors of Q.
Question: A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?
(A) 10/21
(B) 11/21
(C) 2/7
(D) 5/7
(E) 3/7
Rationale: Total number of balls = (2 + 3 + 2) = 7.
Let S be the sample space.
Then, n(S)	= Number of ways of drawing 2 balls out of 7
= 7C2 `
=(7 x 6)/(2 x 1)
= 21.
Let E = Event of drawing 2 balls, none of which is blue.
n(E)	= Number of ways of drawing 2 balls out of (2 + 3) balls.
= 5C2
=(5 x 4)/(2 x 1)
= 10.
P(E) =n(E)/n(S)=10/21
Answer :A
Answer: (A) 10/21
Question: In the biology lab of "Jefferson" High School there are 6.48*10^6 germs, equally divided among 10,800 Petri dishes. How many germs live happily in a single dish?
(A) 100
(B) 200
(C) 500
(D) 600
(E) 5000
Rationale: 6.48*10^6/ 10800==> 64.8*10^3/108==> 64800/108= 600
ANSWER:D
Answer: (D) 600
Question: Of the science books in a certain supply room, 41 are on botany, 65 are on zoology, 90 are on physics. 50 are on geology, and 100 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science?
(A) 81
(B) 159
(C) 166
(D) 315
(E) 324
Rationale: First, you can take all 41 Botany books, all 65 zoology books and all 50 geology books because you're sure to never pick 80 of them.
There are still 90 on physics and 100 on chemistry
The worst case could be that we pick 79 physics and 79 chemistry. So that the next book picked will necessary complete 80 books picked, either in physics or chemistry.
Minimum number of books picked to reach 80 in the same science should be : 41 + 65 + 50 + 79 +79 + 1 = 315
D
Answer: (D) 315
Question: Tom read a book containing 480 pages by reading the same number of pages each day. If he would have finished the book 2 days earlier by reading 16 pages a day more, how many days did Tom spend reading the book?
(A) 12
(B) 15
(C) 10
(D) 20
(E) 14
Rationale: Actually u can set up 2 equation
P--stands for the pages
D--stands for the days
1) P*D=480 (we want to find the Days, soP=480/D)
2) (P+16)(D-2)=480 => PD-2P+16D-32=480
as the 1) stated u can put 1) into 2)
=> 480-2P+16D-32=480 => 16D-2P=32
put the bold one into it => 16D-2(480/D)=80
the we get the final equation 16D^2-960=80D (divide 16)
=> D^2-5D-60=0
(D-12)(D+5)=0 so D=12 days Ans: A
Answer: (A) 12
Question: If 625(5^x) = 1 then x=
(A) –2
(B) -4
(C) 0
(D) -1
(E) 2
Rationale: 5^x = 1/625
5^x = 1/5^4
5^x= 5^-4
x = -4
B
Answer: (B) -4
Question: Ten years ago, P was half of Q's age. If the ratio of their present ages is 3:4, what will be the total of their present ages?
(A) 35
(B) 38
(C) 37
(D) 36
(E) 30
Rationale: Let present age of P and Q be 3x and 4x respectively.
Ten years ago, P was half of Q's age
⇒(3x−10)=12(4x−10)⇒6x−20=4x−10⇒2x=10⇒x=5
Total of their present ages
=3x+4x=7x=7×5=35
Answer is A.
Answer: (A) 35
Question: (2^2+4^2+6^2+.....+40^2)=?
(A) 11480
(B) 76868
(C) 57898
(D) 68886
(E) 75865
Rationale: =(1x2)^2+(2x2)^2,+(2x3)^3+......(2x20)^2
=2^2 x (1^2+2^2+3^2+.......+20^2)
formula is =1/6 n(n+1)(2n+1)
=(4x1/6x20x21x41)
=(4x2870)=11480
Answer is A
Answer: (A) 11480
Question: Using all the letters of the word "THURSDAY", how many different words can be formed?
(A) 8
(B) 8!
(C) 7!
(D) 7
(E) 6!
Rationale: Explanation:
Total number of letters = 8
Using these letters the number of 8 letters words formed is â¸Pâ‚ˆ = 8!.
ANSWER IS B
Answer: (B) 8!
Question: A box contains 3 red chips and 2 blue chips. If two chips are selected at random without replacement, what is the probability that the chips are different colors?
(A) 1/2
(B) 3/5
(C) 7/12
(D) 2/3
(E) 7/10
Rationale: Total selection ways: 5C2=5!/2!3!=10
Selecting one blue chip out of two: 2C1=2!/1!1!=2
Selecting one red chip out of four: 3C1=3!/2!1!=3
Thus, (2C1*3C1)/5C2=(2*3)/10=6/10=3/5=B
Answer: (B) 3/5
Question: Two integers are in the ratio of 1 to 4. If 6 is added to the smaller number, the ratio becomes 1 to 2. Find the larger integer.
(A) 4
(B) 6
(C) 12
(D) 24
(E) 30
Rationale: Assume the integers to be x and y, where x < y
Given x/y = 1/4 - (i) or y = 4x
and x+6 / y = 1/2 - (ii) or y = 2x + 12
Substituting the value of y from (i), 4x = 2x + 12
x = 6
Hence y = 4*6 = 24
ANSWER D
Answer: (D) 24
Question: In the x-y plane, point (x, y) is a lattice point if both x and y are integers. Circle C has a center at (-2, -2) and a diameter of 8. Some points, such as the center (-2, -2), are inside the circle, but a point such as (-2, 2) is on the circle but not in the circle. How many lattice points are in circle C?
(A) 40
(B) 10
(C) 73
(D) 60
(E) 63
Rationale: The lattice points that are in the circle that lie on the perspective axes is as follows: since the diameter is 8, 9 points lie on the horizontal axis (8 + center), but the end points are not in the circle, so 9 - 2 (the same for the vertical axis, but don't count center again), 7 - 1. The lattice points in the circle and not on the horizontal and vertical axes is as follows: lattice points can be found at 45, 45/2 and 30 degrees of axes (30 and 45/2 degrees from horizontal and vertical axes), so same numbers as before, but don't count center again. So, 13 + 5 * 12 = 73
There are a total of 73 lattice points in the circle.
Answer: C
Answer: (C) 73
Question: A and B enter into partnership with capitals in the ratio 3 : 4. At the end of 10 months A withdraws,and the profits now are divided in the ratio of 5 : 6. Find how long B remained in the business?
(A) 9 months
(B) 8 months
(C) 6 months
(D) 7 months
(E) None of these
Rationale: Initially A’s investment = 3x and B’s investment = 4x
Let B remain in the business for ‘n’ months.
⇒ 3x × 10 : 4x × n = 5 : 6
∴ 3x × 10 × 6 = 4x × n × 5
⇒ n = 9
Answer A
Answer: (A) 9 months
Question: 8103/x is a non-terminating decimal. Which of the following could be a value of x?
(A) 2
(B) 5
(C) 9
(D) 12
(E) 1
Rationale: Then:
c. 9=3*3
d. 12=3*2*2
e. 15=3*5
The sum of digits in 8103 is 12, it means that 8103 is divisible by 3 (i.e. 3 is one of the factors of 8103), which will eliminate one "3" from x, leaving us with only 2's or 5's in options d. and e. Only c is left.
ANSWER:C
Answer: (C) 9
Question: (208% of 1265) ÷ 6 = ?
(A) A)125
(B) B)439
(C) C)225
(D) D)375
(E) E)524
Rationale: Explanation :
? = (208 x 1265/100) ÷ 6 = 263120/600 = 439
Answer : Option B
Answer: (B) B)439
Question: Bill downloads the movieRevenge of the Avengersto his computer in 2.5 hours, using a download manager that downloads from 3 sources marked A, B and C. Each source provides download at a constant rate, but the rates of different sources are not necessarily identical. If the movie was downloaded from sources A and C alone, it would take 4 hours to complete the download. The next day, source B is available, but the other sources are inactive. How long will it take to download the trailer of the movie, a file that is 50 times smaller, from source B alone?
(A) 6 hours and 40 minutes
(B) 8 minutes
(C) 12 minutes
(D) 10 minutes
(E) 3 minutes
Rationale: Let the movie size be 400 u.
Given,A+C=4 hrs.
A+C=100 u/hr
And A+B+C=2.5 hrs or 400/2.5=160 u/hr
B alone=160-100=60 u/hr
Trailer=40 times smaller or400/50=8 u
B will take 8/60 hrs or 8 minutes.
Ans B
Answer: (B) 8 minutes
Question: Find the L.C.M of 22, 25, 44 and 20.
(A) 1240
(B) 1600
(C) 1320
(D) 1150
(E) 1100
Rationale: Explanation:
2 x 2 x 11 x 5 x 5 = 1100
Answer: Option E
Answer: (E) 1100