mathewhe/aqua_rat huggingface dataset:
Question: Out of first 26 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is -.
(A) 1/2
(B) 16/19
(C) 4/5
(D) 21/26
(E) 3/5
Rationale: n(S) = 26
n(Even no) = 13 = n(E)
n(Prime no) = 9 = n(P)
P(EᴜP) = 13/26 + 9/26 - 1/26 = 21/26
ANSWER:D
Answer: (D) 21/26
Question: f1(x)f1(x) = 2x - 1 and fn(x)=f1(fn−1(x))fn(x)=f1(fn−1(x)) for n ≥≥ 2. Find f5(2)
(A) 7
(B) 6
(C) 78
(D) 9
(E) 1
Rationale: Answer:A
Answer: (A) 7
Question: If f(x) = 5x − √x and g(x) = x^2, what is f(g(6))?
(A) -4
(B) 8
(C) 16
(D) 32
(E) 174
Rationale: g(x) = x²
g(6) = 6² = 36
So, f(g(6)) = f(36)
f(x) = 5x − √x
So, f(36) = 5(36) − √36
= 180 - 6
= 174
= E
Answer: (E) 174
Question: How much interest can a person get on Rs. 8000 at 17.5% p.a. simple interest for a period of two years and six months?
(A) 3587.58
(B) 3500
(C) 3587.5
(D) 3587.52
(E) 3587.56
Rationale: I = (8000 * 2.5 * 17.5)/100 = (8000 * 5 * 35)/(100 * 2 * 2) = Rs. 3500.Answer: B
Answer: (B) 3500
Question: Choose the missing terms out of the given alternatives.
AZ, CX, FU, ?
(A) IR
(B) IV
(C) JQ
(D) KP
(E) QC
Rationale: C
JQ
The first letter moves 2, 3, 4 ... steps forward. The second letter moves 2, 3, 4 ... steps backward.
Answer: (C) JQ
Question: A bag contains 12 red marbles. If someone were to remove 2 marbles from the bag, one at a time, and replace the first marble after it was removed, the probability that neither marble would be red is 25/36. How many marbles are in the bag?
(A) 24
(B) 48
(C) 60
(D) 72
(E) 84
Rationale: ok let me see if i can explain what went on in the previous post
lets say i have x marbles in the bag in total --> out of them 12 are red
so the probability of pulling a non-red marble is (x -12) / x
now the marble is placed back in the bag and we have x marbles again, of which again 12 are red. so the probability of pulling a non-red marble out is (x-12) / x
probability theorm states that if the probability of event A occuring is m and the probability of event B occuring is n then the probability of both A and B occuring is m*n
so therefore the probability of 2 non-red marbles getting pulled out is [(x-12)/x ] * [(x-12)/x]
this is given as 25/36
-->(x-12)^2= 25/36
x^2
square rooting u have x-12/x = 5/6 or 6x-72 =5x therefore x = 72
B
Answer: (B) 48
Question: An oil cylinder was 3/4th full. When FOUR bottles of oil is poured into it, it is 4/5th full. How many bottles of oil
can the full cylinder hold?
(A) 90
(B) 75
(C) 70
(D) 80
(E) 85
Rationale: (4/5 -3/4) cylinder is filled by 4 bottles
0.8 -0.75 = 0.05 cylinder is filled by 4 bottles
1 cylinder is filled by 4/0.05 = 80 bottles
ANSWER:D
Answer: (D) 80
Question: If v is a positive integer, then 3^v + 3^(v +1) =
(A) 4^a
(B) 3^a − 1
(C) 3^(2a) + 1
(D) 3^a*(a − 1)
(E) 4(3^v)
Rationale: 3^v + 3^(v +1)
= 3^v + (3^v * 3^1)
= 3^v (1 + 3)
= 3^v(4)
Ans. E) 4(3^v)
Answer: (E) 4(3^v)
Question: In a certain neighborhood, there are half as many beige houses as white houses, and four times as many white houses as brown houses. What is the ratio of the number of brown houses to the number of beige houses?
(A) 1:4
(B) 1:2
(C) 1:8
(D) 3:2
(E) 5:1
Rationale: The ratio of beige:white:brown = 2:4:1
The answer is B.
Answer: (B) 1:2
Question: The below sequence is a bit tricky. Can you solve it to find the next number?
9, 29, 329, 4329, ?
(A) 29816
(B) 54329
(C) 54325
(D) 38290
(E) 55291
Rationale: See the pattern. With every digit, the previous numbers are added after that digit
So the next number in the series is 54329
Answer : B
Answer: (B) 54329
Question: Two trains of length 100 m and 200 m are 150 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. After how much time will the trains meet?
(A) 21/9 sec
(B) 32/3 sec
(C) 20/7 sec
(D) 32/3 sec
(E) 30/7 sec
Rationale: They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (54 + 72)*5/18 = 7*5 = 35 mps.
The time required = d/s = 150/35 = 30/7 sec.
Answer:E
Answer: (E) 30/7 sec
Question: A boat can travel with a speed of 13 km/hr in still water.If the speed of the stream is 4 km/hr,find the time taken by the boat to go 68 km downstream.
(A) 2 hours
(B) 3 hours
(C) 4 hours
(D) 5 hours
(E) None of these
Rationale: Solution
Speed downstream = km/hr = 17 km/hr.
Time taken to travel 68 km downstream =(68/17) hrs = 4 hrs. Answer C
Answer: (C) 4 hours
Question: A wire in the form of a circle of radius 3.5 m is bent in the form of a rectangule, whose length and breadth are in the ratio of 6 : 5. What is the area of the rectangle?
(A) 11
(B) 30
(C) 88
(D) 66
(E) 41
Rationale: The circumference of the circle is equal to the permeter of the rectangle.
Let l = 6x and b = 5x 2(6x + 5x) = 2 * 22/7 * 3.5
=> x = 1
Therefore l = 6 cm and b = 5 cm Area of the rectangle = 6 * 5 = 30 cm2
Answer:B
Answer: (B) 30
Question: A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 720sq. feet, how many feet of fencing will be required?
(A) 34
(B) 92
(C) 68
(D) 88
(E) None
Rationale: EXPLANATION
We have: l = 20 ft and lb = 720 sq. ft.
So, b = 36 ft.
Length of fencing = (l + 2b) = (20 + 72) ft = 92 ft.
Answer B
Answer: (B) 92
Question: A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in metres) is :
(A) 130
(B) 360
(C) 500
(D) 540
(E) 650
Rationale: Explanation:
Speed = (78 *5/18)m/sec =65/3m/sec
Time = 1 minute = 60 sec.
Let the length of the tunnel be x metres.
Then,800+X/60=65/3
=> 3 (800 + x) = 3900 =>X=500.
ANSWER IS C
Answer: (C) 500
Question: P and Q had the same number of candies. P gave Q 18 candies so that now Q has five times as many candies as P has. How many candies does Q have now?
(A) 35
(B) 40
(C) 45
(D) 50
(E) 55
Rationale: Let P and Q be the number of candies they had at the start.
P = Q
5(P-18) = Q+18
5(Q-18) = Q+18
4Q = 108
Q = 27
Now person Q has 27+18 candies which is 45 candies.
The answer is C.
Answer: (C) 45
Question: If a < 0 and b > 5, which of the following is true?
I. a * b > 0
II. a * b < 0
III. a^2 * b > 0
(A) I only
(B) II only
(C) III only
(D) I and III only
(E) II and III only
Rationale: I. Not true, example: a = -1, b = 6, so a * b = -6
II. True, since a is negative and b is positive, a * b is negative and the a * b < 0
III. True, a^2 is positive and so is b so the product is positive
E
Answer: (E) II and III only
Question: For any positive integer n, n>1, thelengthof n is the number of positive primes (not necessary distinct) whose product is n. For ex, the length of 30 is 3, since 50=2x5x5. What is the greatest possible length of a positive integer less than 1000.
(A) 10
(B) 9
(C) 8
(D) 7
(E) 6
Rationale: you are missing something in your post:
For any positive integer n , n > 1, thelengthof n is the number of positive primes (not distinct) whose product is n. For example, the length of 50 is 3 since 50 = (2)(5)(5)
the lenght of 1000 = (2)(5)(2)(5)(2)(5) = 6
but we need n < 1000
using 2 as the base = (2)(2)(2)(2)(2)(2)(2)(2)(2) = 6 the length of 512.
the answer is (E)
Answer: (E) 6
Question: In a camp, food was was sufficient for 2000 people for 54 days. After 15 days, more people came and the food last only for 20 more days. How many people came?
(A) 1900
(B) 1800
(C) 1940
(D) 2000
(E) None of these
Rationale: Explanation :
Given that food was sufficient for 2000 people for 54 days
Hence, after 15 days, the remaining food was sufficient for 2000 people for 39 days (∵ 54 - 15 = 39)
Let x number of people came after 15 days.
Then, total number of people after 15 days = (2000 + x)
Then, the remaining food was sufficient for (2000 + x) people for 20 days
More men, Less days (Indirect Proportion)
⇒Men 2000:(2000+x)}:: 20 : 39
⇒2000 × 39 = (2000 + x)20
⇒ 100 × 39 = (2000 + x)
⇒ 3900 = 2000 + x
x = 3900 − 2000 = 1900. Answer : Option A
Answer: (A) 1900
Question: If 1 > 1 - ab > 0, which of the following must be true?
I. a/b > 1
II. a/b > 0
III. ab < 1
(A) I only
(B) II only
(C) III only
(D) II and III only
(E) I and III only
Rationale: MANHATTAN GMATOFFICIAL SOLUTION:
You can manipulate the original compound inequality as follows, making sure to perform each manipulation on every term:
1 > 1 - ab > 0
0 > -a b > -1 Subtract 1 from all three terms.
0 < ab < 1 Multiply all three terms by -1 and flip the inequality signs.
Therefore you know that 0 < ab < 1. This tells you that ab is positive, so a/b must be positive (a and b have the same sign). Therefore, I must be true. However, you do not know whether a/b < 1, so II is not necessarily true. But you do know that ab must be less than 1, so III must be true.
Therefore, the correct answer is (D).
Answer: (D) II and III only
Question: There are 990 male and female participants in a meeting. Half the female participants and one-quarter of the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female?
(A) 75
(B) 100
(C) 125
(D) 175
(E) 165
Rationale: female = x
Male = 990-x
x/2 + 990-x/4 = 1/3* (990)= 330
x= 330
x/2 = 165 is supposed to be the answer
M is missing something
Correct Option E
Answer: (E) 165
Question: In one alloy there is 10% chromium while in another alloy it is 8%. 15 kg of the first alloy was melted together with 35 kg of the second one to form a third alloy. Find the percentage of chromium in the new alloy.
(A) 9.0%
(B) 9.4%
(C) 9.2%
(D) 8.8%
(E) 8.6%
Rationale: The amount of chromium in the new 15+35=50 kg alloy is 0.10*15+0.08*35=4.3 kg, so the percentage is 4.3/50*100=8.6%.
Answer: E.
Answer: (E) 8.6%
Question: A train passes a platform in 30 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is
(A) 150 meter
(B) 240 meter
(C) 200 meter
(D) 260 meter
(E) None of these
Rationale: Explanation:
Speed of the train = 54 km/hr = (54×10)/30 m/s = 15 m/s
Length of the train = speed × time taken to cross the man = 15×20 = 300 m
Let the length of the platform = L
Time taken to cross the platform = (300+L)/15
=> (300+L)/15 = 30
=> 300+L = 15×30 = 450
=> L = 450-300 = 150 meter
Answer: Option A
Answer: (A) 150 meter
Question: I bought two books; for Rs.500. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?
(A) 337
(B) 280
(C) 299.67
(D) 266.67
(E) 291.67
Rationale: x*(85/100) = (500 - x)119/100
x = 291.67
Answer: E
Answer: (E) 291.67
Question: If 1 + x^4 + x^3 + x^2 + x = 80, then the average (arithmetic mean)Y of x, x^2, x^3, x^4 and x^5 is equal to which of the following?
(A) 12x
(B) 13x
(C) 14x
(D) 16x
(E) 20x
Rationale: 1 + x^4 + x^3 + x^2 + x = 81
i.e. 1 +x+ x^2+ x^3+ x^4 = 81
x+ x^2+ x^3+ x^4 = 80
x(1 +x+ x^2+ x^3) = 80
x(81-x^4) = 80
81x - x^5 = 80
x^5 = 81x -80
Now x+ x^2+ x^3+ x^4+ x^5 = 80 + 81x -80 = 81x
Average of Y{x, x^2, x^3, x^4, x^5} = 81x/5 ~ 16x
AnswerD
Answer: (D) 16x
Question: Two numbers N and 14 have LCM = 56 and GCF = 12. Find N.
(A) 48
(B) 34
(C) 44
(D) 54
(E) 64
Rationale: The product of two integers is equal to the product of their LCM and GCF. Hence.
14 × N = 56 × 12
N = 56 × 12 / 14 = 48
correct answer A
Answer: (A) 48
Question: The membership of a committee consists of 3 science teachers, 4 Mathematics teachers, and 2 Social Studies teachers. If 2 committee members are to be selected at random to write the committee’s report, what is the probability that the two members selected will both be science teachers?
(A) 1/12
(B) 1/3
(C) 2/9
(D) 1/14
(E) 1/24
Rationale: Probability of first member an science teacher = 3/9
Probability of second member an science teacher = 2/8
Probability of both being english teacher = 3/9 x 2/8 =1/12 (A)
Answer: (A) 1/12
Question: A shopkeeper fixes the marked price of an item 30% above its cost price. The percentage of discount allowed to gain 8% is
(A) 15.92%
(B) 16.92%
(C) 17.92%
(D) 18.92%
(E) None of these
Rationale: Explanation:
Let the cost price = Rs 100
then, Marked price = Rs 130
Required gain = 8%,
So Selling price = Rs 108
Discount = 130 - 108 = 22
Discount% = (22/130)*100 = 16.92%
Option B
Answer: (B) 16.92%
Question: If the dimensions of a certain rectangular box are 5 inches by 2 inches by 3 inches, then the face of greatest area is of what area?
(A) 225 square inches
(B) 45 square inches
(C) 25 square inches
(D) 15 square inches
(E) 10 square inches
Rationale: Definitely (D) 5*3 = 15 sq Inches
The question asks to find the greatest area of the faces of a cuboid
The Possible area of the faces are -
Length*Breadth , Breadth*Height & Height*Length
The possible areas are - 6 , 10 & 15
Thus 15 is the greatest possible area....
ANSWER:D
Answer: (D) 15 square inches
Question: If the number 24*32 is completely divided by 6. what is the smallest whole number in the place of * ?
(A) 4
(B) 3
(C) 1
(D) 2
(E) 5
Rationale: Solution
The number is divisible by 6 means it must be divisible by 2 and 3. Since the number has 2 as its end digit it is divisible by 2. Now, 2+4+x+3+2=11+x which must be divisible by 3. Thus x=1
Answer C
Answer: (C) 1
Question: Maxwell leaves his home and walks toward Brad's house at the same time that Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 20 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 6 km/h, what is the distance traveled by Brad?
(A)  12
(B)  18
(C)  20
(D)  24
(E)  30
Rationale: Time taken = Total Distance / Relative Speed
Total Distance = 20 kms
Relative Speed (Opposite side) (As they are moving towards each other speed would be added ) = 6+ 4 = 10 kms/hr
Time taken = 20 / 10 = 2 hrs
Distance traveled by Brad = Brad's speed * time taken = 6 * 2 = 12 kms... Answer - A
Answer: (A)  12
Question: An inspector rejects 0.00008% of the meters as defective. How many will be examine to project ?
(A) 2000
(B) 2300000
(C) 2700
(D) 2500000
(E) 250
Rationale: Let the number of meters to be examined be x.
Then, 0.00008% of x =2
[(8/100000)*(1/100)*x] = 2
x = [(2*100000*100)/8] = 2500000
Answer is D.
Answer: (D) 2500000
Question: Perimeter of front wheel =30, back wheel = 20. If front wheel revolves 240 times. How many revolutions will the back wheel take?
(A) 120
(B) 180
(C) 240
(D) 360
(E) 480
Rationale: sice the distance covered by both the wheels should be same
so
let x be the no. of revolutions by the back wheel
so 240*2*pie*30=x*2*pie*20
so x=360.
ANSWER:D
Answer: (D) 360
Question: The sum of the smallest six digit number and the greatest five digit number is
(A) 201110
(B) 199999
(C) 211110
(D) 1099999
(E) None
Rationale: Solution
Requires sum	=(100000 + 99999)
=199999.
Answer B
Answer: (B) 199999
Question: if a * b = 2a – 3b + ab, then 3 * 5 + 5 * 3 is equal to :
(A) 22
(B) 24
(C) 26
(D) 28
(E) 29
Rationale: Solution
3 × 5 + 5 ×3 = (2 ×3 - 3 × 5 + 3 × 5) + 2 (2 × 5 - 3 × 3 +5 × 3)
= (6 + 10 - 9 + 15) = 22.
Answer A
Answer: (A) 22
Question: There is a soccer tournament that is single elimination meaning that after one loss the team is out. There are 15 teams in this tournament. How many games are played?
(A) 15
(B) 7
(C) 8
(D) 14
(E) 10
Rationale: D
The number of games always adds up to one less than the number of teams in a single elimination tournament. You may calculate it any way. Therefore, 14 games were played.
Answer: (D) 14
Question: The sum of the present ages of a father and his son is 60 years. five years ago, father's age was four times the age of the son. so now the son's age will be:
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25
Rationale: Explanation:
Let the present ages of son and father be x and (60 -x) years respectively.
Then, (60 - x) - 5= 4(x - 5)
55 - x = 4x - 20
5x = 75 x = 15. Answer: C
Answer: (C) 15
Question: In how many seconds will a train 100 meters long pass an oak tree, if the speed of the train is 36 km/hr?
(A) 6
(B) 8
(C) 10
(D) 12
(E) 14
Rationale: speed = 36 * 5/18 = 10 m/s
time = 100/10 = 10 seconds
The answer is C.
Answer: (C) 10
Question: What positive number, when squared, is equal to the cube of the positive square root of 15?
(A) 64
(B) 32
(C) 8
(D) 6
(E) 2
Rationale: Let the positive number be x
x^2 = ((15)^(1/2))^3
=>x^2 = 4^3 = 36
=> x = 6
Answer D
Answer: (D) 6
Question: Find the amount on Rs.8000 in 2 years, the rate of interest being 4% per first year and 5% for the second year?
(A) 5568
(B) 6369
(C) 8736
(D) 5635
(E) 6734
Rationale: 8000 * 104/100 * 105/100
=> 8736
Answer:C
Answer: (C) 8736
Question: If 16 toys cost 240, then what do 40 toys cost ?
(A) Rs. 600
(B) Rs. 620
(C) Rs. 640
(D) Rs. 660
(E) None of these
Rationale: Explanation:
Although we can first calculate the cost of one toy and then can multiply it with 40 to get the result.
but we will solve it with chain rule so that we can prepare ourself for other complex problems which we can solve easily by applying this rule.
Let the required cost be Rs. x
More toys means More Cost. (Direct Proportion)
15:40::240:x=>x=240∗40/15=>x=640
So 40 toys will cost Rs 640
Option C
Answer: (C) Rs. 640
Question: Of the three numbers, the sum of the first two is 45; the sum of the second and the third is 55 and the sum of the third and thrice the first is 90. The third number is
(A) 15
(B) 20
(C) 25
(D) 30
(E) 35
Rationale: Sol.
Let the numbers be x,y and z.
Then, x + y = 45
y+z = 55 and
3x+z = 90
⇒ y = 45 - x, z = 55 - y = 55 - (45 - x) = 10 + x.
∴ 3x + 10 + x = 90 or x = 20.
y = (45 - 20) = 25 and z = (10 + 20) = 30.
∴ Third number = 30.
Answer D
Answer: (D) 30
Question: A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?
(A) 35 hours
(B) 25 hours
(C) 20 hours
(D) Cannot be determined
(E) None of these
Rationale: Suppose the efficiencies of pipes C, B and A are 4K, 2K and K.
Since, the tank is filled in 5 hours by the three pipes having combined efficiency equal to 7K, the time required to fill the tank by A alone = 7K×5 /K=35hours
Answer A
Answer: (A) 35 hours
Question: If X = 2 + 1/(1+1/(1-1/2))then the value of 4x+7/3?
(A) 9 2/3
(B) 10 1/3
(C) 11
(D) 11 2/3
(E) 12
Rationale: X = 2 + 1/(1+1/(1-1/2))
= 2 + 1/(1+2)
= 2 + 1/3
X = 7/3 ==> 4X + 7/3 => 4(7/3) + 7/3
==> 28/3 + 7/3
==> 35/3
==> 11 2/3.
D)
Answer: (D) 11 2/3
Question: Tammy climbed a mountain in two days. She spent a total of 14 hours climbing the mountain. On the second day, she walked at an average speed that was half a kilometer per hour faster, but 2 hours less than what she walked on the first day. If the total distance she climbed during the two days is 52 kilometers, how many Q kilometers per hour did Tammy walk on the second day?
(A) 3
(B) 3.5
(C) 4
(D) 4.5
(E) 6
Rationale: Ans: C
Total time = 14 hrs
Let time traveled during 1st day = x
Let time traveled during 2nd day = x-2
Total time =14
x+x-2 = 14
x=8
speed * time = distance
s*8 + (s+0.5)(8-2) = 52
solving s = 4.5
now speed for 2nd day is 0.5 less than the 1st day which is 4.5
Thus speed for 2nd day = 4
Its simple algebra for s*8 + (s+0.5)(8-2) = 52 but for some reason Im getting 3.5 and not 4.5.
8s+6s+3=52
14s=49
s=3.5
Answer: (C) 4
Question: 500 students took the test on English and Maths. 35% students failed in english and 45% failed in maths. 40% of those who passed in maths also passed in english, then how many students failed in both ?
(A) 162
(B) 138
(C) 60
(D) 10
(E) 12
Rationale: Passed in english = 65%
Passed in maths = 55%
Passed in both = 40% of 55% = 2/5 * (55%) = 22%
Passed in (English + Maths - Both + Neither) = 100%
65 + 55 - 22 + Neither = 100
Neither = 100 - 98 = 2% = 0.02 * 500 = 10
Answer: D
Answer: (D) 10
Question: How many multiples of 4 are less than 3200, and also multiples of 16?
(A) 104
(B) 200
(C) 625
(D) 832
(E) 833
Rationale: The LCM of 4 and 16 is 16. Divide 3200/16 = 200.xxx. So B is your answer.
Answer: (B) 200
Question: A man has a pool. This full pool can be drained using four different drainage, if he uses A it takes 10 hours to drain pool, if he uses B it takes 50 hour to drain and if he uses C it takes 5 hours to drain the pool. He first runs the water by A for 5 hours, then turning that off, he continues with B for 10 hours. Then turning that off as well he uses C for 1 hours and lastly using D for 1 hour the pool is empty. How long does it take to empty the pool only using the drainage D?
(A) 2 hours
(B) 4 hours
(C) 6 hours
(D) 8 hours
(E) 10 hours
Rationale: 1 - (5/10 +10/50 +2/5 + 1/x) = 0 x = 10 hours ANSWER = E
Answer: (E) 10 hours
Question: At Children's General Hospital, 10 out of every 13 babies are crying. If 1 out of every 4 crying babies are hungry, and there are 50 hungry babies crying, how many babies total are there in the hospital?
(A) 140
(B) 240
(C) 50
(D) 130
(E) 150
Rationale: Proportions: Let B = babies, and Bc = babies crying, and Bch = hungry babies crying.
50Bch/xBc = 1Bch/4Bc
xBc = 100Bc
100Bc/yB = 10Bc/13B
yB = 130B
Answer: D
Answer: (D) 130
Question: 7 people average age is 30. youngest person age is 6. find average of the people when youngest was born.
(A) 23
(B) 24
(C) 25
(D) 26
(E) 27
Rationale: average age of people =30
so have total age =210
before 7 years we have to deduct each person age by seven years 210-42=161
so average age would be 161/7=24
ANSWER:B
Answer: (B) 24
Question: Rs.1010/- distributed among A,B and C such that on decreasing their shares by RS.25,RS.10 and RS.15 respectively, The balance money would be divided among them in the ratio 3:2:5. Then, A’s share is:?
(A) Rs.255/-
(B) Rs.313/-
(C) Rs.365/-
(D) Rs.355/-
(E) Rs.345/-
Rationale: A:B:C = 3:2:5
Total parts = 10
A's share is = 3 parts
10 -----> Rs.960/-
3 -----> Rs.288/-
A's total =288 + 25 = Rs.313/-
B)
Answer: (B) Rs.313/-
Question: In 50 l can, milk and water in the ratio of 3:1. if the ratio has made 1:3 then the quantity of water that has to be added further is?
(A) 100
(B) 120
(C) 90
(D) 80
(E) 70
Rationale: 100 litre water is to be added.
let 'x' liter water is to be added more.
Then 1/3 = 37.5 /(12.5 + x)
x= 100
ANSWER:A
Answer: (A) 100
Question: A truck owner will refuel his vehicle at a rate of 2 gallons of diesel fuel every 5 seconds. If diesel fuel costs $ 1.0 per gallon, how long will it take for the truck owner to refuel his vehicle with $ 40 worth of diesel fuel?
(A) 20 seconds
(B) 1 minute
(C) 1 minute 40 seconds
(D) 20 minutes
(E) 1 hour 20 minutes
Rationale: 2 gal / 5 sec
$1.25 / gal
$40/$1.25 = 40 gal
2 gal / 5 sec with 40 gal = 100 sec
C. 1 minute 40 seconds
Answer: (C) 1 minute 40 seconds
Question: The avg age of class of 20 students in 20 years. If the lecturer’s age is added to the avg, increases by one. What is the age of the lecturer?
(A) 37
(B) 38
(C) 47
(D) 51
(E) 41
Rationale: E
41
Average x Number = Total Years
20 x 20 = 400 …(1)
21 x 21 = 441 …(2)
Lecturer’s age =Eqn (2) -Eqn (1)
= 441 – 400
= 41 years.
Answer: (E) 41
Question: Mane can make a handcrafted drum in 4 weeks. Zane can make a similar handcrafted drum in 6 weeks. If they both work together, how many weeks will it take for them to produce 15 handcrafted drums?
(A) 30
(B) 36
(C) 70
(D) 80
(E) 150
Rationale: Method I: the rates solution
“Mane can make a handcrafted drum in 4 weeks. Zane can make a similar handcrafted drum in 6 weeks.” Mane’s rate is (1 drum)/(4 weeks) = 1/4. Zane’s rate is (1 drum)/(6 weeks) = 1/6. The combined rate of Mane + Zane is
R = 1/4 + 1/6 = 3/12 + 2/12 = 5/12
That’s the combined rate. We need to make 15 drums — we have a rate and we have an amount, so use the “art” equation to solve for time:
T = A/R = 15/(5/12) = 15*(12/5) = (15/5)*12 = 3*12 = 36
BTW, notice in the penultimate step, the universal fraction strategy: cancelbeforeyou multiply (Tip #3:http://magoosh.com/gmat/2012/can-i-use- ... -the-gmat/. Mane and Zane need 36 weeks to make 15 drums.
Answer = B.
Answer: (B) 36
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 328
(B) 279
(C) 240
(D) 288
(E) 231
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 36 = 15
x + 300 = 540
x = 240 m. Answer:C
Answer: (C) 240