RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: There is a set consisting of 5 numbers--{1,2,3,4,5}. If all possible subsets including null set are created and one subset is picked up, what is the probability that the subset does not have 5 as its largest number?
A.1/5
B.1/4
C.1/3
D.1/2
Answer: D.1/2
Explanation: Total Number of possible subsets [ including Null Subset ] : 2525 -- (A number can occur or not occur in a subset -- 2 ways)
Possible subsets where 5 is not present [will include null subset] : 24∗124∗1.
P = 2424 / 2525 = 1 / 2.
ANSWER:D
Question: The number of positive integers valued pairs (x, y) ssatisfying 4x -17y = 1 and x <= 1000 (x is less than or equal to 1000) is
A.fifty nine
B.57
C.55
D.58
Answer: A.fifty nine
Explanation: 4x-17y=1
y=(4x-1)/17
x has to be a positive integer such that 1<=x<=1000(4x-1) is a factor of 17 so that y is also a positive integer
So we need to know how many numbers in the set {3,7,11,15,....,3999} are divisible by 17
Lets try to observe the pattern
1. 3 mod 17 = 3
2. 7 mod 17 = 7
3. 11 mod 17 = 11
4. 15 mod 17 = 15
5. 19 mod 17 = 2
6. 23 mod 17 = 6
7. 27 mod 17 = 10
8. 31 mod 17 = 14
9. 35 mod 17 = 1
10. 39 mod 17 = 5
11. 43 mod 17 = 9
12. 47 mod 17 = 13
13.51 mod 17 = 0
14. 55 mod 17 = 4
15. 59 mod 17 = 8
16. 63 mod 17 = 12
17. 67 mod 17 = 16
... and after this the remainders will repeat (this is no co-incidence that the cyclicity is also 17)
So the right choices are x=13,13+17,13+17+17,.....
The number of such numbers is 59 (highest one being 999) A
Question: A man spends on an average Rs 269.47 for the first 7 months and Rs 281.05 for the next 5 months. Find his monthly salary if he saves Rs 308.46 during the whole year.
A.Rs 300
B.Rs 500
C.Rs 840
D.Rs 400
Answer: A.Rs 300
Explanation: Total spending in 12 months = Rs [269.47 x 7 - 281.05 × 5] = Rs 3,291.54
Total income = Spending + Saving
= Rs 3,291.54 + Rs 308.46
= Rs 3,600.00
Monthly salary = Rs 3600/12 = Rs 300
ANSWER:A
Question: At the library, 50 books were checked out that day from the display. 5 copies of Sandry's Book were checked out and 15 copies of Howl's Moving Castle. If only two other books were checked out (Harry Potter and the Lightning Thief) and they were both checked out in equal quantities, how many copies of the Lightning Thief were checked out?
A.5
B.10
C.15
D.20
Answer: C.15
Explanation: First, subtract the number of other books that were checked out from the total: 50-5-15=30. As the remaining two books were checked out in equal quantities, simply divide 30 by 2: 30/2=15. The answer is C, 15.
Question: Twenty percent of the skiers that tried out for the ski patrol were selected. Of those that were not selected, 7 skiers were CPR certified and 17 were not. How many skiers tried out for the ski patrol?
A.30
B.50
C.60
D.70
Answer: A.30
Explanation: Not Selected = 80%
If total is x.
Then 0.8x=7+17=24
x=30
Hence answer is A.
Question: A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.4 per sq m?
A.675, Rs.1350
B.575, Rs.1350
C.1350, Rs.675
D.675, Rs.2700
Answer: D.675, Rs.2700
Explanation: Area = (l + b +2d) 2d
= (75 + 55 +2.5 * 2) 2*2.5 => 675
675 * 4 = Rs.2700
ANSWER:D
Question: In 60 litres mixture milk and water are in the ratio 3:1. After adding how many liters of water its ratio will become 3:2
A.1
B.15
C.7
D.5
Answer: B.15
Explanation: Milk quantity = 3/4 * 60 = 45
water quantity = 60-45 = 15
new ratio of M:W = 45:15+x = 3:2
45+3x = 90
x = 15
Answer is B
Question: A shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 3 a rupee. Find his net profit or loss percent?
A.33 1/6 %
B.33 8/3 %
C.33 1/3 %
D.73 1/3 %
Answer: C.33 1/3 %
Explanation: The total number of mangoes bought by the shopkeeper be 12.
If he buys 4 a rupee, his CP = 3
He selling at 3 a rupee, his SP = 4
Profit = SP - CP = 4 - 3 = 1
Profit Percent = 1/3 * 100 = 33 1/3 %
Answer: C
Question: From a group of 4 boys and 4 girls, 2 children are to be randomly selected. What is the probability that 1 boy and 1 girl will be selected?
A.1/2
B.2/3
C.3/5
D.4/7
Answer: D.4/7
Explanation: The total number of ways to choose 2 children from 8 is 8C2 = 28
The number of ways to choose 1 boy and 1 girl is 4*4 = 16
P(1 boy and 1 girl) = 16/28 = 4/7
The answer is D.
Question: 9 men can do a work in 12 days working 4 hours a day. In how many days can 6 men do the same work, working 8 hours a day?
A.18
B.9
C.10
D.8
Answer: B.9
Explanation: We have, M1D1H1 = M2D2H2
So, 9*12*4= 6*D2*8
D2 = 9*12*4/6*8 = 9
ANSWER:B
Question: Find the cost of fencing around a circular field of diameter 18 m at the rate of Rs.2.50 a meter?
A.138
B.132
C.150
D.140
Answer: D.140
Explanation: 2 * 22/7 * 9 = 56
56 * 2 1/2
= Rs.140
Answer: D
Question: With out any halt a train travels a certain distance with an average speed of 49 km ph , and with halts it covers the same distance at an average speed of 28 kmph. When it is traveling with halts, how many minutes/per hour does the train halt on an average ?
A.48 min.
B.45min.
C.15min.
D.18min.
Answer: B.45min.
Explanation: With halt in 1 hour the train travels 60km
With out halt for traveling same distance it take 49/28 = 7/4 = 105 minutes
:. 45 minutes is the halting time per hour
ANSWER:B
Question: Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?
A.3/4
B.3/8
C.3/1
D.3/2
Answer: A.3/4
Explanation: Explanation:
In a simultaneous throw of two dice, we have n(S) = (6 x 6) = 36.
Then, E= {(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3,4),(3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (5, 6), (6, 1),6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
n(E) = 27.
P(E) = n(E)/n(S) = 27/36 = 3/4.
Answer: A) 3/4
Question: In traveling from a dormitory to a certain city, a student went 1/2 of the way by foot, 3/5 of the way by bus, and the remaining 4 kilometers by car. What is the distance, in kilometers, from the dormitory to the city?
A.20
B.15
C.40
D.10
Answer: A.20
Explanation: Whole trip = distance by foot + distance by bus + distance by car
x = 1/2x + 3/5x + 4
x - 1/2x - 3/5x = 4
x=20km
Option: A
Question: When positive integer A is divided by positive integer B, the result is 5.15. Which of the following could be the integer A is ?
A.107
B.117
C.103
D.123
Answer: C.103
Explanation: the remainder will be obtained from the decimal part when A is divided by B i.e. 0.15
0.15 = 15/100 = 3/20 so possible remainders are 3,6,12,9,15.
let remainder is 3
Now when we divide option C i.e 103/20 = 5 is quotient and remainder is 3
therefore ans - C
Question: Three positive integers a, b, and c are such that their average is 80 and a ≤ b ≤ c. If the median is (a + 20), what is the least possible value of c?
A.88
B.89
C.90
D.92
Answer: A.88
Explanation: Solution
Given Data
3 positive integers
Average of a, b, and c = 80
So, a+b+c3a+b+c3 = 240 or a + b + c = 240
a ≤ b ≤ c
Median = (a + 20)
Median of these 3 numbers a, b, and c is ‘b’ because a ≤ b ≤ c
Therefore, b = a + 20
Objective To find the least value of 'c'
Theoretically, the least value of c is when c = b.
Therefore, a + (a + 20) + (a + 20) = 240 (b and c are equal and b, the median, is a + 20)
Or 3a = 200 or a = 66.66
So, b = c = 66.66+ 20 = 86.66
However, we know that these numbers are all integers.
Therefore, a, b, and c cannot take these values.
So, the least value for c with this constraint is NOT likely to be when c = b
Let us increment c by 1. Let c = (b + 1)
In this scenario, a + (a + 20) + (a + 21) = 240
Or 3a = 199. The value of the numbers is not an integer in this scenario as well.
Let us increment c again by 1. i.e., c = b + 2
Now, a + (a + 20) + (a + 22) = 240
Or 3a = 198 or a = 66
If a = 66, b = 86 and c = 88.
The least value for c that satisfies all these conditions is 88.
Correct answer is choice A.
Question: A certain store sells all maps at one price and all books at another price. On Monday the store sold 12 maps and 8 books for a total of $38.00, and on Tuesday the store sold 20 maps and 12 books for a total of $60.00. At this store, how much less does a map sell for than a book?
A. $0.25
B. $0.50
C. $0.75
D. $1.00
Answer: D. $1.00
Explanation: 12x+8y=38
20x+12y=60
multiply eq 1 by 5 and eq 2 by 3
60x+40y=38*5
60x+36y=60*3
subtracting 1 from 2
4y=190-180
y=2.5
therefore
x=1.5
difference in price =1
D
Question: David buys an old scooter for Rs. 2400 and spends Rs. 600 on its repairs. If he sells the scooter for Rs. 3600, his gain percent is :
A.20%
B.12%
C.10%
D.5%
Answer: A.20%
Explanation: Explanation :
Solution: C.P. =Rs. (2400+600) =Rs. 3000; S.P. = Rs. 3600.
Gain% = (600*100/3000) = 20%.
Answer : A
Question: A gold purification process cycle, is able to remove 1/16 of impurities in gold. If we have a 10 grams of gold ore dust containing 16/24 pure gold. How much impurities would have been removed from that old after 4 cycles of purification using that method?
A.0.72
B.0.74
C.0.76
D.0.78
Answer: C.0.76
Explanation: X is the initial quantity of impurities in that gold.
After a cycle of purification the quantity of impurities left would be X1=X-1/16X i.e. X1=15/16X
Same thing for X2, X3, X4, respectively representing the quantity of impurities left after 2, 3, 4 cycles of purification.
So we have:
X1=15/16 X
X2=15/16 X1
X3=15/16 X2
X4=15/16 X3
By multiplying both ends of the equations we get:
X1*X2*X3*X4 = (15/16)^4 X*X1*X2*X3
Simplification leaves us with:
X4 = (15/16)^4 X
X4 is the quantity of impurities left after four cycles. So the cumulative quantity of impurities (Q4) which has been removed after 4 cycles is: Q4= X-X4=X-(15/16)^4X i.e. Q4 = X (1-(15/16)^4)
In this case, given X was: X=(1-16/24) * 10 g = 3.33 g (Remember we had 16/24 pure gold)
So we have Q4 = 3.33 * (1-(15/16)^4) = 3.33 * (1-(50625/65536)) = 3.33 * (14911/65536) = 0.757 rounded gives Q4=0.76
Answer: C
Question: One ball will drop from a certain height. The height it will reach after rebounding from the floor is 50 percent of the previous height. The total travel is 150cm when it touches the floor on third time. What is the value of the original height?
A.60cm
B.90cm
C.100cm
D.120cm
Answer: A.60cm
Explanation: when Ball comes down, Then i have indicated the distance covered in green
when Ball goes up, Then i have indicated the distance covered in red
Distance travelled uptil the ball touches the floor 3rd time:h+0.5h+0.5 h+0.5*0.5 h+0.5*0.5 h
h + 2 * 0.5 * h + 2 * 0.25 * h = h (1+2*0.5+2* 0.25) = h (1+1+0.5) = 150
2.5 h = 150
h = 60.
A is the answer.
Question: Let f(x) = x^2 + bx + c. If f(1) = 0 and f(-9) = 0, then f(x) crosses the y-axis at what y-coordinate?
A.-9
B.-1
C.0
D.1
Answer: A.-9
Explanation: When x = 1 and when x = -9, the expression f(x) = x² + bx + c equals 0.
Then f(x) = (x-1)(x+9)
f(0) = -9
The answer is A.
Question: In triangle PQR, the angle Q = 90 degree, PQ = 2 cm, QR = 8 cm. X is a variable point on PQ. The line through X parallel to QR, intersects PR at Y and the line through Y, parallel to PQ, intersects QR at Z. Find the least possible length of XZ
A.1.6 cm
B.2.4 cm
C.4.8 cm
D.2.16 cm
Answer: A.1.6 cm
Explanation: Look at the diagram below:
Now, in case when QY is perpendicular to PR, two right triangles PQR and PQY are similar: QY:QP=QR:PR --> QY:2=8:10 --> QY=1.6.
Answer: A.
Question: A boat having a length 5 m and breadth 2 m is floating on a lake. The boat sinks by 1cm when a man gets on it. The mass of the man is:
A.100 kg
B.60 kg
C.72 kg
D.96 kg
Answer: A.100 kg
Explanation: Explanation:
Volume of water displaced = (5 x 2 x 0.01) m3
= 0.10 m3.
∴ Mass of man = Volume of Water displaced x Density of water
= (0.10 x 1000)kg
= 100 kg.
Answer: A
Question: The price of a coat in a certain store is $500. If the price of the coat is to be reduced by $250, by what percent is the price to be reduced?
A.10%
B.15%
C.50%
D.25%
Answer: C.50%
Explanation: price of a coat in a certain store = $500
the price of the coat is to be reduced by $250
% change = (Final Value - Initial Value)*100 / Initial Value
% Reduction= (Reduction in Price)*100 / Initial Value
i.e. % Reduction= (250)*100 / 500 = 50%
Answer: Option C
Question: The triplicate ratio of 1:4 is?
A.1:64
B.1:8
C.1:7
D.1:2
Answer: A.1:64
Explanation: 13: 43 = 1:64
Answer: A
Question: The respective ages of father and his son are 51 and 16 years. In how many years will the father be twice as old as his son ?
A.19 years
B.9 years
C.10 years
D.15 years
Answer: A.19 years
Explanation: Suppose x years later the father will be twice as old as his son.
x + 51 = 2 (x + 16)
x = 51 - 32 = 19 years
answer : A
Question: What inequality represents the condition 1<x<13?
A.|x|<3
B.|x+5|<4
C.|x-7|<6
D.|-5+x|<4
Answer: C.|x-7|<6
Explanation: 1<x<13 represents segment with
length: 13-1 = 12
center: (13+1)/2 = 7
For any |x-a|<b a is a center and b is a half of length. So, |x-7|<12/2 represents our inequality (answer C)
Question: It takes one machine 4 hours to complete a production order and another machine 9 hours to complete the same order. How many hours would it take both amhcines working simultaneously at their respective rates to complete the order?
A.a) 7/12
B.b) 2 10/13
C.c) 1 5/7
D.d) 3 1/2
Answer: B.b) 2 10/13
Explanation: RT = W
Given:
R = 1/9 + 1/4 = 13/36
T = ?
W = 1
T = 1 / (13/36) = 36/13 = 2 10/13
Answer: B
Question: A sells a Cricket Bat to B at a profit of 20%. B sells it to C at a profit of 25%. If C pays $231 for it, the cost price of the Cricket Bat for A is:
A.150
B.120
C.154
D.160
Answer: C.154
Explanation: 125% of 120% of A = 231
125/100 * 120/100 * A = 231
A = 231 * 2/3 = 154.
ANSWER C
Question: 1/[(1/0.03) + (1/0.37)] = ?
A.0.004
B.0.02775
C.2.775
D.3.6036
Answer: B.0.02775
Explanation: Approximate.
1/.03 = 100/3 = 33
1/.37 = 100/37 = 3
Denominator becomes 33 + 3 = 36
1/36 = .02 something
Answer (B)
Question: A basket has 5 apples and 7 oranges. Three fruits are picked at random. What is the probability that at least 2 apples are picked?
A.2/7
B.4/11
C.5/11
D.7/22
Answer: D.7/22
Explanation: The total possible choices are 12C3 = 220
The ways to choose 3 apples: 5C3 = 10
The ways to choose 2 apples: 5C2 * 6C1 = 60
P(at least 2 apples) = 70/220 = 7/22
The answer is D.
Question: Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes are open,in how many hours will the tank be filled ?
A.2
B.2.5
C.3
D.3.5
Answer: C.3
Explanation: 1/5+1/10+1/30=10/30=1/3. soo 3 hrs
ANSWER:C
Question: A seven-digit phone number is divisible by 5. After adding the two digits of the area code the number is not divisible by 3, which of the following cannot be the area code?
A.05.
B.06.
C.03.
D.04.
Answer: A.05.
Explanation: Given that 7 digit number is divisible by 5
we know any number will not be divisible by 5 if the sum of all digits of the number is not the multiple of5.
Hence looking at the option we can say that the number that should be added to the seven digit number must be 06 as adding it will make it divisible by 5... hence answer is A
Question: Carmen made a sculpture from small pieces of wood. The sculpture is 2 feet 10 inches tall.Carmen places her sculpture on a base that is 2 inches tall. How tall are the sculpture andbase together?
A.3.1 feet
B.3.2 feet
C.3.3 feet
D.3.0 feet
Answer: D.3.0 feet
Explanation: we know 1 feet =12 inch then
2 feet =24 inch
24+10=34 then
34+2=36
36/12=3.0 feet
ANSWER:D
Question: When Q is divided by W, the quotient is R and the remainder is r. Which of the following expressions is equal to r?
A.RW + Q
B.Q - RW
C.RW - Q
D.QW - R
Answer: B.Q - RW
Explanation: Q/W = R + r/W
Q -RW = r
Amswer: B
Question: If a coin is tossed twice what is the probability that it will land either heads both times or tails both times?
A.1/8
B.1/6
C.1/4
D.1/2
Answer: D.1/2
Explanation: Prob to get 2 heads = 1/2*1/2 = 1/4
Prob to get 2 tails = 1/2*1/2 = 1/4
So, Prob to get either 2 heads or 2 tails = 1/4+1/4 = 1/2
Answer will be D.
Question: What is the least value of x. So that 4x569 is divisible by 3?
A.2
B.5
C.1
D.0
Answer: D.0
Explanation: The sum of the digits of the number is divisible by 3, then the number is divisible by3.
4 + x +5 + 6 + 9 =24 + x
Least value of x may be 0
Therefore 24+0 = 24 is divisible by 3.
D
Question: A shipment of 1500 heads of cabbage, each of which was approximately the same size, was purchased for $600. The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head. The following day the rest were sold at a price equal to 20% less than the price each head sold for on the day before. What was the total gross profit on this shipment.
A.$100
B.b $115
C.c $125
D.d $130
Answer: A.$100
Explanation: Purchase cost = 600/1500= $ 0.4
25% above the cost per head = (125/100)*0.4= $ 0.5
2/3 of the heads were sold means 2/3*1500 =1000 ,Selling amount for 1000 cabbage = 1000 * 0.5 = $ 500
Remaining were sold at a price equal to 20% less than the price each head sold for on the day before i.e , (80/100)*0.5 = $ 0.4
Hence selling cost for the remaining cabbage = 500 * 0.4 = $ 200
Total selling cost = 500 + 200 = $ 700
Gross profit = $ 700 - $ 600 = $ 100
Hence Answer is A.
Question: The ratio of a to b to c is 2 to 3 to 4, and a, b, c are positive integers. If the average (arithmetic mean) of the three numbers is 42, what is the value of a?
A.24
B.25
C.28
D.30
Answer: C.28
Explanation: Let a=2k, b=3k, and c=4k.
a+b+c = 2k+3k+4k = 9k
Since the average is 42:
9k/3 = 42
3k = 42
k=14
Then a=28.
The answer is C.
Question: What is the remainder when 9^1 + 9^2 + 9^3 +...+ 9^9 is divided by 3?
A.0
B.3
C.2
D.5
Answer: A.0
Explanation: Notice that in the brackets we have the sum of 8 odd multiples of 3, which yields remainder of 0 upon division by 3.
Answer : A
Question: A number is doubled and 5 is added. If the resultant is trebled, it becomes 117. What is that number?
A.12
B.29
C.27
D.17
Answer: D.17
Explanation: Explanation:
Let the number be x.
Therefore,
3(2x + 5) = 117
6x + 15 = 117
6x = 102
x = 17
ANSWER:D
Question: What will the value replace by x if 210x0 is divisible by 5?
A.4
B.3
C.2
D.All the Above
Answer: D.All the Above
Explanation: Divisibility of 5 is Last of the digit is 0 or 5.
In 210x0 has 0.So the Number must divisible by 5.
That is any number can be replaced in the place of x
Answer is D
Question: A certain rectangular window is four times as long as it is wide. If its perimeter is 50 feet, what are its dimensions in terms of length by width?
A.12 by 2
B.11 by 3
C.20 by 5
D.10 by 4
Answer: C.20 by 5
Explanation: 2x+2y=50
x+y=25
x+4x=25
5x=25
x=5
Answer C
Question: A motorcyclist goes from Bombay to Nagpur, a distance of 600 kms at an average of 120 kmph speed. Another man starts from Bombay by car 1 Â½ hours after the first, and reaches Nagpur Â½ hour earlier. What is the ratio of the speed of the motorcycle and the car?
A.1:2
B.1:7
C.1:9
D.3:5
Answer: D.3:5
Explanation: T = 600/120 = 5 h
T = 5 - 2 = 3
Time Ratio = 5:3
Speed Ratio = 3:5
Answer: D
Question: Three picked up 30 mangoes .In how many ways can they divide them if all mangoes be identical?
A.A)4^30
B.B)2^30
C.C)1^30
D.D)3^30
Answer: D.D)3^30
Explanation: Each Mango can be given to any one of the Three people or in other words..1 mango can be divided into 3 ways...so all 30 can be divided in 3^30 ways
ANS:D
Question: 45% of 750 - 25% of 480 = ?
A.216
B.217.5
C.236.5
D.245
Answer: B.217.5
Explanation: Explanation:
Given expression = (45/100 * 750) - (25/100 * 480) = (337.50 - 120) = 217.50
Answer IS B
Question: It is the New Year and Mandy has made a resolution to lose weight this year. She plans to exercise and do yoga. For exercise she plans to workout at the gym and ride her bicycle in the ratio of 2:3 everyday. She will also do yoga in the ratio, yoga:exercise = 2:3. If she rides her bike for 20 minutes, how much time will she spend doing yoga? (rounded to minutes)
A.10 min.
B.33 min.
C.17 min.
D.23 min.
Answer: B.33 min.
Explanation: The ratio is 2:3 = gym:ride, so (20)(3/2) = 30 minutes at the gym, and 30 + 20 = 50 minutes exercise, so (2/3)(50) = 33 minutes yoga.
Answer: B
Question: 53 x 22 = 1276 then (4221)n=()10?
A.3896
B.3897
C.3898
D.3899
Answer: B.3897
Explanation: Sol:
As we don't know the base system here we take the base as n. So 53 in base n can be written as 5n+3, and 22 as 2n+2 and 1276 as n3+2n2+7n+6
⇒⇒ (5n + 3)(2n + 2) = n3+2n2+7n+6
⇒⇒ 10n2+16n+6=n3+2n2+7n+6
⇒⇒ n3−8n2−9n=0
⇒⇒ n(n2−8n−9)=0
⇒⇒ (n + 1)(n - 9) = 0
So n = 9
(4221)9=4×93+2×92+2×9+1
= 3716 + 162 + 18 + 1 = 3897
Answer B
Question: Four friends, Thomas, Mike, Brian, and John, went on a fishing trip. If Mike caught 4 more than Brian did, John caught 12 less than Thomas did, and Thomas caught 4 more than Mike did, how many more fish did Brian catch than John did?
A.6
B.4
C.8
D.1
Answer: B.4
Explanation: In this word problem, the first key is to turn the story into equations:
Mike caught 4 more than Brian did: M = 4 + B
John caught 12 less than Thomas did: J = T - 12
Thomas caught 4 more than Mike did: T = 4 + M
Then, in classic GMAT style, the problem doesn't ask you to solve for a single variable, but instead to solve for the difference between B and J (how many more fish did Brian catch than John did?). This means that your goal is to get the equations in terms of B and J so that you can solve for the expression B - J.
Taking the first equation and solving for B, you have B = M - 4.
Taking the second equation and solving for J you have J = T - 12, and then with the third equation you can replace T with 4 + M so that both B and J are in terms of M: J = (4 + M) - 12.
So if B = M - 4 and J = M - 8, then:
B - J = (M - 4) - (M - 8)
B - J = M - 4 - M + 8 (remove the parentheses by distributing the multiplication)
B - J = 4, so the answer is B.
Question: Ram's age and Shyam's age are in the ratio 3 : 4. Seven years ago the ratio of their ages was 2: 3. Find the ratio of their ages five years hence?
A.33:21
B.44:44
C.33:45
D.26:33
Answer: D.26:33
Explanation: Let ages of Ramu and Shyamu be x and y respectively.
x/y = 3/4 => x = 3/4 y
Also (x - 7) / (y - 7) = 2/3
=> 3x - 21 = 2y - 14
3x = 2y + 7
But x = 3/4 y
3 * 3/4 y = 2y + 7
9y = 8y + 28 => y = 28 years
Ratio of their ages five years hence
= (21 + 5) / (28 + 5) = 26/33.
Answer:D
Question: Dick and Jane each saved $4,000 in 1989. In 1990 Dick saved 10 percent more than in 1989, and together he and Jane saved a total of $6,500. Approximately what percent less did Jane save in 1990 than in 1989?
A.20%
B.70%
C.50%
D.30%
Answer: B.70%
Explanation: 1990
Dick saved = $ 4400
Jane saved = $ 2100 (jane saved $2800 less than she did the prior year)
Jane saved approximately $2800/4000$ (70%) less in 1990
Answer: B
Question: 2/5 of the fish in an aquarium are red and 1/4 of the fish are brown. 3/4 of the red fish and 3/5 of the brown fish are male. If the rest of the fish in the aquarium are female, what is the probability that a fish randomly picked from the aquarium is male?
A.2/5
B.3/10
C.7/10
D.9/20
Answer: D.9/20
Explanation: 3/4*2/5 + 3/5*1/4 = 9/20
The answer is D.
Question: A young girl counted in the following way on the fingers of her left hand. She started collang the thumb 1, the index finger 2, the middle finger 3, the ring finger 4, the little finger 5, then reversed direction calling the ring finger 6, the the middle finger 7, the index finger 8, the thumb 9 then back to the index finger for 10, the middel finger for 11, and so on. She counted up to 1994. She ended on her
A.thumb
B.the index finger
C.the middle finger
D.the ring finger
Answer: B.the index finger
Explanation: Notice the pattern. The thumb lands up at numbers 1,9,17,25,33,... so every 8th number
By this patter the thumb is also at number 1993 (multiple of 8 + 1)
Hence 1994 has to be the index finger
Answer is B
Question: How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 66 km/hr?
A.11
B.30
C.29
D.88
Answer: C.29
Explanation: Speed of train relative to man = 66 - 3 = 63 km/hr.
= 63 * 5/18 = 35/2 m/sec.
Time taken to pass the man = 500 * 2/35 = 28.57 sec.
approx. 29 sec
Answer: C