mathewhe/aqua_rat huggingface dataset:
Question: In a particular 100 meter race, 8 athletes are participating that are numbered 1-8. In how many ways can athlete #4 finish ahead of #2 provided there's no tie among the athletes?
(A) 14,540
(B) 16,580
(C) 18,920
(D) 20,160
(E) 24,320
Rationale: The total number of ways for the athletes to finish is 8! = 40,320.
#4 will be ahead of #2 in exactly half of these possibilities.
40,320/2 = 20,160
The answer is D.
Answer: (D) 20,160
Question: The chance of rain on any given day in Tel-Aviv is 50%. What is the probability that it rained in Tel-Aviv on exactly 4 out of 6 randomly chosen days?
A.
B.
C.
D.
E.
(A) 15/64
(B) 30/64
(C) 1/2
(D) 1/4
(E) 52/64
Rationale: chances of rain on exactly 4 days and not rain on 2 days = (1/2)^4* (1/2)^2 = 1/64
Chosing 4 days out of 6 = 6!/(4!*2!) = 15
chances of rain on exactly 4 days out of 6 days = 15/64
Ans A
Answer: (A) 15/64
Question: The profit earned by selling an article for 892 is equal to the loss incurred when the same article is sold for 448. What should be the sale price of the article for making 50 per cent profit?
(A) 960
(B) 1005
(C) 1,200
(D) 920
(E) None of these
Rationale: Let the profit or loss be x
and 892 – x = 448 + x or, x = 444⁄2 = 222
\ Cost price of the article = 892 – x = 448 + x = 670
\ SP of the article = 670 × 150⁄100 = 1005
Answer B
Answer: (B) 1005
Question: For any integer n greater than 1, n* denotes the product of all the integers from 1 to n, inclusive. How many prime numbers E are there between 6* + 2 and 6* + 6, inclusive?
(A) None
(B) One
(C) Two
(D) Three
(E) Four
Rationale: Given that n* denotes the product of all the integers from 1 to n, inclusive so, 6*+2=6!+2 and 6*+6=6!+6.
Now, notice that we can factor out 2 our of 6!+2 so it cannot be a prime number, we can factor out 3 our of 6!+3 so it cannot be a prime number, we can factor out 4 our of 6!+4 so it cannot be a prime number, ... The same way for all numbers between 6*+2=6!+2 and 6*+6=6!+6, inclusive. Which means that there are no primes E in this range.
Answer: A.
Answer: (A) None
Question: Seven people enter a race. There are 4 types of medals. Winner - platinum, runner up - gold, next two racers - silver and the last 3 - bronze. Ways to do it?
(A) 7!/3!
(B) 7!/2!3!
(C) 1*1*2!*3!
(D) 7*6*2!*3!
(E) 7*6*5*4
Rationale: let me take the approach adopted by you..
platinum-7 different people..
gold- remaining 6 different people..
silver- 2 out of remaining 5=5C2= 5!/2!3!...
bronze - 1 as all the three remaining are getting it..
total ways= 7*6*5!/2!3!=7!/2!3!.
ANS:B
Answer: (B) 7!/2!3!
Question: A dishonest person wants to make a profit on the selling of milk. He would like to mix water (costing nothing) with milk costing 33 $ per litre so as to make a profit of 60% on cost when he sells the resulting milk and water mixture for 36$. In what ratio should he mix the water and milk?
(A) 7:15
(B) 7:10
(C) 7:8
(D) 7:4
(E) 7:2
Rationale: First of all, let's consider 1 liter of the stuff he is going to sell --- naive customers think it's pure milk, but we know it's some milk-water mixture. He is going to sell this liter of milk-water for $36.
This $36 should be a 60% increase over cost. Here, we need to think about percentage increases as multipliers.
Using multipliers
(cost)*1.60 = $36
cost = 36/1.6 = $22.5
If he wants a 60% increase over cost on the sale of one liter of his milk-water, the cost has to be $22.5
Well, a liter of milk costs $33, so if he is going to use just $30 of milk in his mixture, that's 22.5/33 = 15/22 of a liter. If milk is 15/22 of the liter, then water is 7/22 of the liter, and the ratio of water to milk is 7:15. Answer choice(A)
Answer: (A) 7:15
Question: The ratio between the number of sheep and the number of horses at the Stewart farm is 2 to 7, If each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day, what is the number of sheep in the farm?
(A) 18
(B) 16
(C) 32
(D) 56
(E) 60
Rationale: Let the number of sheeps and horses be 4x and 7x.
Now total number of horses = total consumption of horse food/consumption per horse = 12880/230 = 56, which is equal to 7x. => x = 8
Sheeps = 2x = 2*8 = 16. Hence B
Answer: (B) 16
Question: In a group of 90 people, 55 have visited Iceland and 33 have visited Norway. If 51 people have visited both Iceland and Norway, how many people have visited neither country?
(A) 50
(B) 51
(C) 52
(D) 53
(E) 54
Rationale: This is an example of a standard Overlapping Sets question. It has no 'twists' to it, so you'll likely find using the Overlapping Sets Formula to be a fairly easy approach. If you're not familiar with it, then here is the Formula:
90= 55 + 33 - 51 + (# in Neither Group)
=53
The prompt gives you all of the numbers you need to get to the correct answer. Just plug in and solve.
D
Answer: (D) 53
Question: What is the smallest positive integer x such that 280-x is the cube of a positive integer
(A) 5
(B) 64
(C) 62
(D) 60
(E) 12
Rationale: Given 280-x is a perfect cube
so we will take 216= 6*6*6
280-x = 216
x =280-216 = 64
correct option is B
Answer: (B) 64
Question: If a farmer sells 15 of his chickens, his stock of feed will last for 4 more days than planned, but if he buys 10 more chickens, he will run out of feed 6 days earlier than planned. If no chickens are sold or bought, the farmer will be exactly on schedule. How many chickens does the farmer have?
(A) 20
(B) 50
(C) 40
(D) 30
(E) 60
Rationale: Let x = total feed required for the planned period
n= number of chicken
t = total time of the planned feed
x = nt
1) x = (n-15) * (t+4)
2) x = (n+10) * (t-6)
equating 1&2
(n-15) * (t+4) = (n+10) * (t-6) or nt+4n-15t-60 =nt-6n+10t-60
10n = 25t
n =5/2 *t or t = 2n/5
x= n *2n/5
substituting this value in 1
n * 2n/5 = (n-15) * (2n/5+4)
2n = 60
n =30
D
Answer: (D) 30
Question: If p + | p | = 0, which of the following must be true?
(A) p > 0
(B) p≥0
(C) p < 0
(D) p≤0
(E) p = 0
Rationale: Manipulate the equations:
p + | p | = 0
|p| = -p
-p > 0 OR -p = 0
This means p could be 0 or p is less than 0.
D. p≤0
E. p=0
Answer: D
Answer: (D) p≤0
Question: A positive whole number has factors of 5 and 10. The number MUST be divisible by:
I. 10
II. 30
III. 60
(A) I
(B) II
(C) I & II
(D) III
(E) I & III
Rationale: 10 , 30 is not divisible by 60.But 60 is divisible by 5,10,30,60.
So answer is III
Answer : D
Answer: (D) III
Question: One-third of Rahul's savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,25,000 as total savings, how much has he saved in Public Provident Fund ?
(A) 80000
(B) 60000
(C) 50000
(D) 75000
(E) 90000
Rationale: Let savings in N.S.C and P.P.F. be Rs. x and Rs. (125000 - x) respectively. Then,
=1/3 x = 1/2 (125000 - x)
=x/3 + x/2 = 62500
=5x/6 = 62500
=x = 62500 x 6 /5	= 75000
Savings in Public Provident Fund = Rs. (125000 - 75000) = Rs. 50000
Answer is C.
Answer: (C) 50000
Question: Of 70 players on a football team, 31 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total?
(A) 57
(B) 59
(C) 63
(D) 71
(E) 92
Rationale: Total = 70
Thrower = 31
Rest = 70 - 31 = 39
Left Handed = 39/3 = 13
Right handed = 26
If all Thrower are right handed then total right handed is 31 + 26 = 57
so A. 57 is the right answer
Answer: (A) 57
Question: There are 2 vessels A & B containing 25 liters each of pure milk and pure water respectively. 5 liters of milk from A is taken and poured into B , then 6 liters of mixture from B is taken and poured in A. What is ratio of water A and B respectively.
(A) 1:3
(B) 1:4
(C) 1:5
(D) 1:6
(E) 1:7
Rationale: At first
A cotain Milk = 25 Water = 0
B cotain Milk = 00 Water = 25
5 litres of milk taken from A and poured in B then
A cotain Milk = 20 Water = 0
B cotain Milk = 5 Water = 25
6 litres(1 lit Milk & 5 lit Water) of mixture from B and poured in A.
So, Finally
A cotain Milk = 21 Water = 5
B cotain Milk = 4 Water = 20
Ratio of water in A & B is 5:20 = 1:4
ANSWER:B
Answer: (B) 1:4
Question: A certain number of men can finish a piece of work in 10 days. However, if there were 10 less men it will take 10 days more for the work to be finished. How many men were there originally?
(A) 10 men
(B) 30 men
(C) 40 men
(D) 20 men
(E) none of these
Rationale: Let x be the number of men originally
Thus, 10x=(10+10)(x-10)
10x=20(x-10)
x=2(x-10)
x = 20
ANSWER:D
Answer: (D) 20 men
Question: A letter lock consists of two rings each marked with four different letters. The number of distinct unsuccessful attempts to open the lock is at the most ?
(A) 17
(B) 19
(C) 15
(D) 168
(E) 167
Rationale: Since each ring consists of four different letters, the total number of attempts possible with the two rings is
= 4*4 = 16. Of these attempts, one of them is a successful attempt.
Maximum number of unsuccessful attempts
= 16 - 1
= 15.
Answer: C
Answer: (C) 15
Question: how many prime no. are there from 0 to 50?
(A) 14
(B) 15
(C) 16
(D) 17
(E) 19
Rationale: we calculate it manually.we know the definition of prime no.prime no. should only have two distinctâ€‹ natural no. divisor 1 and itself.
note:1 is not a prime no.
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47
total no.=15
answer B
Answer: (B) 15
Question: Boston is 4 hr ahead of Frankfurt and 2 hr behind India. X leaves Frankfurt at 6 p.m. on Friday and reaches Boston the next day. After waiting there for 2 hr, he leaves exactly at noon and reaches India at 1 a.m. On his return journey, he takes the same route as before, but halts at Boston for 1hr less than his previous halt there. He then proceeds to Frankfurt.
What is X's average speed for the entire journey (to and fro)?
(A) 176 mph
(B) 180 mph
(C) 165 mph
(D) Data insufficient
(E) None of these
Rationale: Explanation :
X reaches Boston at 10 AM. At the same moment, time in Frankfurt is 6 AM. Hence, the journey time was 12 hours.
X reaches India at 1 AM. At the same moment, time in Boston is 11 PM. Hence, the journey time was 11 hours.
Waiting time = 2 hours.
So, total time = 12 + 2 + 11 = 25 hours.
Avg speed = 180 mph .
Answer : B
Answer: (B) 180 mph
Question: The height of a triangle is decreased by 5% and its base increased by 50%. Its area will
(A) decrease by 12.5%
(B) increase by 12.5%
(C) decrease by 25%
(D) Increase by 25%
(E) Increase by 42.5%
Rationale: Explanation :
Let the initial height be 100 and the base be 200 units.
âˆ´ Area = 1/2 x 100 x 200 = 10000sq units
Now, height = 95 units and base = 300 units
âˆ´ New area = 1/2 x 95 x 300 = 14250
âˆ´ Area is increased by (14250 - 10000)/10000 x 100
= 42.5%
Answer : Option E
Answer: (E) Increase by 42.5%
Question: If P's height is 40% less than that of Q, how much percent Q's height is more than that of P?
(A) 75.56%
(B) 66.66%
(C) 70.05%
(D) 80%
(E) 85%
Rationale: Excess of Q's height over P =(40/(100-40))*100
= => 66.66%
ANSWER B
Answer: (B) 66.66%
Question: Car A runs at the speed of 35 km/hr & reaches its destination in 10hr. Car B runs at the speed of 25 km/h & reaches its destination in 6h. What is the respective ratio of distances covered by Car A & Car B?
(A) 7 : 3
(B) 5 : 7
(C) 9 : 7
(D) 3 : 5
(E) 11 : 6
Rationale: Sol. Distance travelled by Car A = 36 × 10 = 350 km
Distance travelled by Car B = 25 × 6 = 150 km
Ratio = 350/150 = 7 : 3
A
Answer: (A) 7 : 3
Question: If a certain sample of data has a mean of 10.0 and a standard deviation of 2.0, which of the following pairs contain two values that are each at least 2.5 standard deviations from the mean?
(A) (5.0; 16.5)
(B) (8.5; 21.0)
(C) (14.0; 26.5)
(D) (16.5; 26.0)
(E) (21.0; 26.5)
Rationale: 2.5 standard deviation equals to 2.5*2=5;
2.5 standard deviations from the mean, so5 points, from the mean is the range from {mean-5} to {mean+5}, so from 5 to 15:
The correct answer choice must cover all this range: only answer choice A does this.
Answer:A.
Answer: (A) (5.0; 16.5)
Question: A sum of money is distributed among w,x,y,z in the proportion of 4:2:5:3. If y gets $500 more than z, what is the x's share?
(A) $4000
(B) $500
(C) $2500
(D) $2800
(E) $1400
Rationale: Let the shares of w,x,y,z are 4a,2a,5a,3a
5a-3a = 500
2a = 500,a=250
x's share = 2a = $500
Answer is B
Answer: (B) $500
Question: In a group of 80 children and 30 youngsters, each child got sweets that are 15% of the total number of children and each youngster got sweets that are 25% of the total number of children. How many sweets were there?
(A) 1140
(B) 1160
(C) 1180
(D) 1560
(E) 1210
Rationale: Number of sweets each child got = 15% of 80 = 15/100 * 80 = 12.
Number of sweets 80 children got = 80 * 12 = 960.
Number of sweets each youngster got = 25% of 80 = 25/100 * 80 = 20.
Number of sweets 10 youngsters got = 30 * 20 = 600.
Total number of sweets = 960 + 200 = 1560.
D)
Answer: (D) 1560
Question: How many diagonals does a 63-sided convex polygon have?
(A) 1890
(B) 1953
(C) 3780
(D) 3843
(E) 3906
Rationale: A 63-sided convex polygon has 63 vertices.
If we examine a single vertex, we can see that we can connect it with 60 other vertices to create a diagonal. NOTE: there are 60 options because we can't connect the vertex to ITSELF, and we can't connect it to its ADJACENT vertices, since this would not create a diagonal.
If each of the 63 vertices can be connected with 60 vertices to create a diagonal then...
...the total number of diagonals = (63)(60) = 3780
HOWEVER, before we select answer choice C, we must recognize that we have counted every diagonal TWICE.
For example, we might connect vertex A with vertex F and count that as 1 diagonal, and at the same time we connect vertex F with vertex A and count that as 1 diagonal. Of course these diagonals are the SAME.
To account for counting each diagonal twice, we must divide 3780 by 2 to get: 1890
ANSWER:A
Answer: (A) 1890
Question: Which of the following is(are) true for a@b=b@a?
I. a@b=b+ba
II. a@b=(a+b)(a-b)
III. a@b=(a/b)+(b/a)
(A) only Ⅰ
(B) only Ⅱ
(C) only Ⅲ
(D) only ⅠⅢ
(E) only ⅡⅢ
Rationale: -> If I. a@b=ab+ba, a@b=ab+ba=ba+ab=b@a (X).
If II. a@b=(a+b)(a-b), a@b=(a+b)(a-b)≠(b+a)/(b-a)=b@a (O).
If III.a@b=(a/b)+(b/a), a@b=(a/b)+(b/a)=(b/a)+(a/b)=b@a (O).
Thus, ⅠⅢ are the answers. Therefore, A is the answer.
Answer: (A) only Ⅰ
Question: ♠n denotes the number obtained when n is rounded to the nearest tenth. For example ♠4.31 = 4.3
♠0.089 - ♠2.135 =
(A) 1.05
(B) 1.04
(C) -1.05
(D) -2
(E) -0.1
Rationale: ♠0.089 - ♠2.135 =
0.1 - 2.1 = -2
Answer : D
Answer: (D) -2
Question: The simplified value of 1.2 + (1.2)2 + (1.2)3 is:
(A) 4.248
(B) 4.368
(C) 3.248
(D) 3.368
(E) 4.368
Rationale: The expression is in geometric progression with a common ratio of 1.2. Formula to sum a geometric sequence is a(1-r^n)/1-r where a=r=1.2.Solving it we get the ans as 4.368
ANSWER:B
Answer: (B) 4.368
Question: Martin buys a pencil and a notebook for 80 cents. At the same store, Gloria buys a notebook and an eraser for $1.15 cents, and Zachary buys a pencil and an eraser for 75 cents. How many cents would it cost to buy three pencils, three notebooks, and three erasers? (Assume that there is no volume discount.)
(A) 325
(B) 345
(C) 365
(D) 385
(E) 405
Rationale: pencil + notebook = 80
notebook + eraser = 115
pencil + eraser = 75
Let's add all three equations.
2 pencils + 2 notebooks + 2 erasers = 270 cents
The cost to buy 3 of each would be (3/2)(270) = 405
The answer is E.
Answer: (E) 405
Question: A person jogged 10 times along the perimeter of a rectangular field at the rate of 12 kilometers per hour for 30 minutes. If field has a length that is twice its width, find the area of the field in square meters.
(A) 70,000 square meters
(B) 60,000 square meters
(C) 50,000 square meters
(D) 20,000 square meters
(E) 30,000 square meters
Rationale: Let us first find the distance d jogged
distance = rate* time = (12 km / hr) ? 30 minutes
= (12 km/hr) * 0.5 hr = 6 km
The distance of 6 km corresponds to 10 perimeters and therefore 1 perimeter is equal to
6 km / 10 = 0.6 km = 0.6 * 1000 meters = 600 meters
Let L and W be the length and width of the field. The length is twice the width. Hence
L = 2 W
The perimeter is 600 meters and is given by
2 (L + W) = 600
Substitute L by 2 W
2 (2 W + W) = 600
Simplify and solve for W
4 W + 2 W = 600
6 W = 600
W = 100
Find L
L = 2 W = 200
Find the area A of the rectangle
A = L * W = 200 * 100 = 20,000 square meters
correct answer D
Answer: (D) 20,000 square meters
Question: How many times are the hands of a clock at right angles in a day?
(A) 22
(B) 44
(C) 55
(D) 888
(E) 11
Rationale: In 12 hours, they are at right angles 22 times.
==> In 24 hours, they are at right angles 44 times.
Answer: Option 'B'
Answer: (B) 44
Question: A car gets 20 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 190 kilometers?
(A) 3.5 gallons
(B) 9.5 gallons
(C) 8.7 gallons
(D) 4.5 gallons
(E) 9.2 gallons
Rationale: Each 40 kilometers, 1 gallon is needed. We need to know how many 40 kilometers are there in 180 kilometers?
180 Ã· 40 = 9.5 Ã— 1 gallon = 9.5 gallons
correct answer is B) 9.5 gallons
Answer: (B) 9.5 gallons
Question: Two trains are moving in opposite directions with speed of 60 km/hr and 90 km/hr respectively. Their lengths are 1.10 km and 0.9 km respectively. the slower train cross the faster train in --- seconds
(A) 56
(B) 48
(C) 47
(D) 26
(E) 25
Rationale: Explanation:
Relative speed = 60+90 = 150 km/hr (Since both trains are moving in opposite directions)
Total distance = 1.1+.9 = 2km
Time = 2/150 hr = 1//75 hr = 3600/75 seconds = 1200/25 = 240/5 = 48 seconds
Answer: Option B
Answer: (B) 48
Question: How many of the following numbers are divisible by 132 ?
264, 396, 462, 792, 968, 2178, 5184, 6336
(A) 3
(B) 4
(C) 6
(D) 7
(E) 8
Rationale: 132 = 4 x 3 x 11
So, if the number divisible by all the three number 4, 3 and 11, then the number is divisible by 132 also.
264 11,3,4 (/)
396 11,3,4 (/)
462 11,3 (X)
792 11,3,4 (/)
968 11,4 (X)
2178 11,3 (X)
5184 3,4 (X)
6336 11,3,4 (/)
Therefore the following numbers are divisible by 132 : 264, 396, 792 and 6336.
Required number of number = 4.
B)
Answer: (B) 4
Question: If x and y are unique prime integers, which of the following must be even?
(A) x−y
(B) x−2y
(C) 2x−2y
(D) 2x−y
(E) xy^2
Rationale: Any number multiplied by 2 has to be an even number
Answer C
Answer: (C) 2x−2y
Question: A motorcyclist goes from Bombay to Pune, a distance of 192 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 ½ hours after the first, and reaches Pune ½ hour earlier. What is the ratio of the speed of the motorcycle and the car?
(A) 1:2
(B) 1:6
(C) 1:9
(D) 1:3
(E) 1:1
Rationale: T = 192/32 = 6 h
T = 6 - 3 = 3
Time Ratio = 6:3 = 2:1
Speed Ratio = 1:2.Answer: A
Answer: (A) 1:2
Question: What is the % change in the area of a rectangle when its length increases by 60% and its width decreases by 60%?
(A) 0%
(B) 20% increase
(C) 36% decrease
(D) 1% decrease
(E) Insufficient data
Rationale: (16/10)*(4/10) = 64/100 of original area
64/100 is a 36% decrease from 100/100 ->C
Answer: (C) 36% decrease
Question: Which of the following could be the sides of an obtuse angled triangle? all values are in degree only
I. 51, 29, 100
II. 10,110, 60
III. 20, 30, 50
(A) I and III only
(B) II only
(C) I and II only
(D) I
(E) I, II and III
Rationale: obtuse angled triangle means one angle more than 90 deg and total 180 deg.. I and II only
HENCE, (C)
Answer: (C) I and II only
Question: When positive integer N is divided by positive integer J, the remainder is 14. If N/J = 213.28, what is value of J?
(A) 30
(B) 35
(C) 40
(D) 50
(E) 60
Rationale: When a number is divided by another number, we can represent it as : Dividend = Quotient * Divisor + Remainder
So, Dividend/Divisor = Quotient + Remainder/Divisor
Given that N/J = 213.28
Here 213 is the quotient.
Given that Remainder = 14
So, 213.28 = 213 + 14/J
So, J = 50
Answer: (D) 50
Question: Rs.160 contained in a box consists of one rupee, 50 paisa and 25 paisa coins in the ratio 4:5:6. What is the number of 25 paisa coins?
(A) 120
(B) 125
(C) 115
(D) 110
(E) 111
Rationale: 4x 5x 6x
100 50 25
400x + 350x + 150x = 16000
x = 20
6x = 120
ANSWER A
Answer: (A) 120
Question: 5 men and 12 boys finish a piece of work in 4 days, 7 men and 6 boys do it in 5 days. The ratio between the efficiencies of a man and boy is?
(A) 1:5
(B) 6:5
(C) 4:5
(D) 9:5
(E) 8:5
Rationale: B
6:5
5M + 12B ----- 4 days
7M + 6B ------- 5 days
20M + 48B = 35M + 30B
18B = 15M => 5M = 6B
M: B = 6:5
Answer: (B) 6:5
Question: Ramu and Shamu invested in a shop. The profits were divided in the ratio of 4 : 4 respectively. If Ramu invested Rs. 35,500, the amount invested by Shamu is:
(A) 35000
(B) 40000
(C) 45000
(D) 35500
(E) None
Rationale: Suppose Shamu invested Rs. y. Then, 35500/y =4/4 or y = [35500 x 4 / 4] = 35500.
Answer D
Answer: (D) 35500
Question: The principal that amounts to Rs. 4913 in 3 years at 6 1/4 % per annum C.I. compounded annually, is?
(A) Rs. 3096
(B) Rs. 4076
(C) Rs. 4085
(D) Rs. 4096
(E) Rs. 5023
Rationale: Explanation:
Principal = [4913 / (1 + 25/(4 * 100))3]
= 4913 * 16/17 * 16/17 * 16/17 = Rs. 4096.
ANSWER IS D
Answer: (D) Rs. 4096
Question: If Nancy's income is Rs 17000, calculate his savings given that his income and expenditure are in the ratio 5:3.?
(A) Rs.3800
(B) Rs.1800
(C) Rs.6800
(D) Rs.7800
(E) Rs.2800
Rationale: Let the income and the expenditure of the person be Rs.5x and Rs.3x respectively.
Income, 5x = 17000 => x = 3400
Savings = Income - expenditure = 5x - 3x =2x
So, savings = Rs.6800
Answer: C
Answer: (C) Rs.6800
Question: Kate wanted to buy 2kgs of apples. The vendor kept the 2kg weight on the right side and weighed 4 apples for that. She doubted on the correctness of the balance and placed 2 kg weight on the left side and she could weight 14 apples for 2 kgs. If the balance was correct how many apples she would have got?
(A) 6
(B) 9
(C) 8
(D) 4
(E) 3
Rationale: As she got less apples when the weight put on the right side, the left pan has more weight say w kgs.
Now w + 4a = 2
and w+ 2 = 14a
Solving we get a = 2/9 Kgs.
So she gets, 2/(2/9) = 9 apples
Answer:B
Answer: (B) 9
Question: How many seconds will a 900 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 63 km/hr?
(A) 22
(B) 54
(C) 99
(D) 77
(E) 12
Rationale: Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 900 * 3/50 = 54 sec.
Answer: B
Answer: (B) 54
Question: The ratio between the present ages of P and Q is 5:7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years?
(A) A)3:4
(B) B)8:9
(C) C)4:3
(D) inadequate
(E) of these
Rationale: Let P's age and Q's age be 5x and 7x years respectively.
Then, 7x - 5x = 4 => x = 2
Required ratio = (6x + 4) : (7x + 4)
16 : 18= 8:9
ANSWER:B
Answer: (B) B)8:9
Question: If a rectangle length and width are both doubled,by what percent is the rectangle area increase?
(A) 100
(B) 150
(C) 300
(D) 200
(E) 250
Rationale: let length and width are l and b
so area = lb
now after doubling both we will get area = 2l*2b = 4lb
so % increase = 400-100 =300
ANSWER:C
Answer: (C) 300
Question: Traders A and B buy two goods for Rs. 1000 and Rs. 2000 respectively. Trader A marks his goods up by x%, while trader B marks his goods up by 2x% and offers a discount of x%. If both make the same non-zero profit, find x.
(A) 25%
(B) 12.5%
(C) 37.5%
(D) 40%
(E) 50%
Rationale: DETAILED SOLUTION
SP of trader A = 1000 (1 + x).
Profit of trader A = 1000 (1 + x) – 1000.
MP of trader B = 2000 (1 + 2x).
SP of trader B = 2000 (1 + 2x) (1 – x).
Profit of trader B = 2000(1 + 2x) (1 – x) – 2000.
Both make the same profit => 1000(1 + x) – 1000 = 2000(1 + 2x) (1 – x) – 2000
1000x = 2000 – 4000x2 + 4000x – 2000x – 2000
4000x2 -1000x = 0
1000x (4x – 1) = 0
=> x = 25%.
Answer choice (A)
Answer: (A) 25%
Question: The ratio of the present age of Viju to that of Aju is 7:2. Four years from now, the ratio of the ages of Viju to Aju will be 5:2. What was Viju age 2 years ago ? (RBI Assistant 2015)
(A) 24
(B) 19
(C) 12
(D) 15
(E) 13
Rationale: Let the present age of Viju be 7x years and that of Aju be 2x years.
Then, 4 years from now
7x + 4 / 2x + 4 = 5 / 2
or 4x = 12
or x = 3
Viju present age = 7 * 3 = 21 years
Viju age 2 years ago = 21 - 2 = 19 years
answer :B
Answer: (B) 19