mathewhe/aqua_rat huggingface dataset:
Question: Find out the number of ways in which 6 rings of different types can be worn in 3 fingers?
(A) 729
(B) 362
(C) 154
(D) 653
(E) 234
Rationale: The first ring can be worn in any of the 3 fingers (3 ways).
Similarly each of the remaining 5 rings also can be worn in 3 ways.
Hence total number of ways
=3×3×3×3×3×3=36=729
Ans: A
Answer: (A) 729
Question: Out of four numbers ,the average of first three is 16 and that of the last three is 15. If the last number is 22,the first number is :
(A) 22
(B) 21
(C) 77
(D) 99
(E) 25
Rationale: Explanation:
Let the numbers be a,b,c,d
Given, a + b + c = 48, b + c + d = 45
Now, d = 22
thus, b + c + 22 = 45 ⇒ b + c = 23
Putting the value of b + c in a + b + c = 48
a + 23 = 48 ⇒ a = 25
Answer: E
Answer: (E) 25
Question: 25 buses are running between two places P and Q. In how many ways can a person go from P to Q and return by a different bus?
(A) 625
(B) 600
(C) 576
(D) 676
(E) 700
Rationale: we can go in any bus out of the 25 buses.
Hence He can go in 25 ways.
Since we can not come back in the same bus that he used for travelling,
we can return in 24 ways.
Total number of ways = 25 x 24 = 600
ANSWER:B
Answer: (B) 600
Question: if m^3 has 16 factors then m^4 will have how many factors ????? and m is not a prime no.
(A) 24
(B) 25
(C) 26
(D) 27
(E) 28
Rationale: 25 m^3 = (3+1)(3+1) = 16
then m^4 = (4+1)(4+1)=25
ANSWER:B
Answer: (B) 25
Question: The area of a triangle is with base 3m and height 6m?
(A) 88 m2
(B) 9 m2
(C) 66 m2
(D) 77 m2
(E) 31 m2
Rationale: 1/2 * 3 * 6 = 9 m2
Answer: B
Answer: (B) 9 m2
Question: Find the number of zero's in the expression 1^1 * 2^2 * 3^3 * 4^4 * 5^5 * ……..10^10.
(A) 28
(B) 15
(C) 16
(D) 17
(E) 81
Rationale: To find the number of zero's we have to find the powers of 2's and 5's.
Powers of 2's = 2 + 4 + 6 + 8 + 10 = 26
But 4, 8 contains more 2's which are equal to 4 + 8 = 12
8 contains another eight 2's.
So total 2's = 46
Number of 5's = 5 + 10 = 15
So trailing zeroes = 15.
Answer:B
Answer: (B) 15
Question: If the numerator of a fraction is increased by 20% and its denominator is diminished by 25% value of the fraction is 2/15. Find the original fraction?
(A) 1/12
(B) 1/15
(C) 1/19
(D) 1/13
(E) 1/11
Rationale: X * (120/100)
---------------- = 2/15
Y * (75/100)
X/Y = 1/12
Answer: A
Answer: (A) 1/12
Question: How many words can be formed by using all the letters of the word “DAUGHTER” so that vowels always come together & vowels are never together?
(A) 5120
(B) 1240
(C) 4320
(D) 6512
(E) 1204
Rationale: Given word contains 8 different letters
When the vowels AUE are always together we may suppose
them to form an entity ,treated as one letter
then the letter to be arranged are DAHTR(AUE)
these 6 letters can be arranged in 6p6 = 6!
= 720 ways
The vowels in the group (AUE) may be arranged in 3! = 6 ways
Required number of words = 760 * 6 =4320
Ans: C
Answer: (C) 4320
Question: 5 men or 8 women do equal amount of work in a day. a job requires 3 men and 5 women to finish the job in 10 days how many woman are required to finish the job in 14 days.
(A) 10
(B) 7
(C) 6
(D) 12
(E) 13
Rationale: 1 man can do the work of 8/5 = 1.6 women
equivalent of 3*1.6 + 5 = 9.8 women take 10 days
so women needed to do the work in 14 days
= [10/14]*9.8
= 7
ANSWER:B
Answer: (B) 7
Question: A meeting has to be conducted with 6 managers. Find the number of ways in which the managers be selected from among 10 managers, if 2 managers will not attend the meeting together?
(A) 120
(B) 110
(C) 105
(D) 140
(E) 135
Rationale: we can either choose all 6 people from 8 manager who have no problems or choose 5 from the 8 and 1 from the 2 managers who have a problem sitting together
so 8C6 + (8C5 * 2C1)
this is 28 + 112=140
Answer : D
Answer: (D) 140
Question: The first three terms of a proportion are 3, 9 and 12. The fourth term is?
(A) 22
(B) 28
(C) 27
(D) 36
(E) 88
Rationale: (9*12)/3 = 36
Answer:D
Answer: (D) 36
Question: 5000 voted in an election between two candidates.14% of the votes were invalid.The winner won by a margin approximately closer to 15%.Find the number of votes secured by the person
(A) 2128
(B) 2472
(C) 2689
(D) 26707
(E) 17191
Rationale: nvalid Votes = 14 % (5000) = 700
Valid Votes = 5000 - 700 = 4300 = R (say)
Assume the looser got 'L" votes and winner got "W" votes.
W - L = 15% (R)
W + L = R
Solving we get W = 57.5% and L = 42.5%
So Winner got 57.5%(4300) = 2472
Answer:B
Answer: (B) 2472
Question: A store reduced the price of all items in the store by 10% on the first day and by another 14% on the second day. The price of items on the second day was what percent of the price before the first reduction took place?
(A) 80.0
(B) 80.9
(C) 77.4
(D) 81.1
(E) 81.9
Rationale: consider price of the all items as $100
after a initial reduction of 10% price becomes = 0.9 *100 = $ 90
after the final reduction of 14% price becomes = 0.86* 90 = $ 77.4
price of all items on second day is 77.4% of price on first day
correct answer option C
Answer: (C) 77.4
Question: A contractor undertook to do a certain piece of work in 6 days. He employed certain number of men, but 5 of them being absent from the very first day, the rest could finish the work in 10 days. The number of men originally employed were :
(A) 12
(B) 10
(C) 13
(D) 11
(E) None of these
Rationale: Explanation :
Let there be x men at the beginning. Less men, More days (Indirect Proportion)
12 : 6 :: x : (x - 5) 12 (x - 5) = 6x <=> 6x = 60 x = 10
Answer : B
Answer: (B) 10
Question: Pipe A can fill a tank in 32 minutes. Pipe B can fill the same tank 3 times faster than pipe A. If both the pipes are connected to the tank so that they fill the tank simultaneously, how long will it take for the empty tank to overflow?
(A) 4 minutes
(B) 32/7 minutes
(C) 192/7 minutes
(D) 224/7 minutes
(E) 32/5 minutes
Rationale: Pipe A can fill a tank in 32 minutes --> the rate of A = 1/32 tank/minute;
Pipe B can fill the same tank3 times fasterthan pipe A --> the rate of B = 1/32 + 3/32 = 4/32 tank/minute.
Their combined rate = 1/32 + 4/32 = 5/32tank/minute;
Therefore, A and B can fill the tank in 32/5minutes.
Answer: E
Answer: (E) 32/5 minutes
Question: The first flight out of Phoenix airport had a late departure. If the next three flights departed on-time, how many subsequent flights need to depart from Phoenix on-time, for the airport's on-time departure rate to be higher than 70%?
(A) 6
(B) 5
(C) 8
(D) 9
(E) 10
Rationale: We need on-time departure rate to be higher than 7/10, so it should be at least 8/11, which means that 8 out of 11 flights must depart on time. Since for now 3 out of 4 flights departed on time then 8-3=5 subsequent flights need to depart on-time.
Answer: B
Answer: (B) 5
Question: If 2x+y = 10, 2y+z = 20 and 2x+z = 30. Where x, y,and z are real number. What is the value of 2x ?
(A) 3/2
(B) sqrt(15)
(C) sqrt(6)/2
(D) 15
(E) 18
Rationale: Explanation :
Let, 2x = a, 2y = b and 2z = c
Then from the question:
2x+y = 2x * 2y = ab = 10
Similarly, bc = 20 , ac = 30
ab/bc = 1/2
=> a/c = 1/2
and ac = 30
(a/c)*ac = 1/2*30 = 15
a = sqrt(15)
Answer : B
Answer: (B) sqrt(15)
Question: The function F is defined for all positive integers n by the following rule: f(n) is the number of position integer each of which is less than n, and has no position factor in common with n other than 4. If p is any prime number then f(p)=
(A) p-1
(B) p-2
(C) (p+1)/2
(D) (p-1)/2
(E) 2
Rationale: The confusing moment in this question is its wording. Basically question is: how many positive integers are less than given prime number p which has no common factor with p except 1.
Well as p is a prime, all positive numbers less than p have no common factors with p (except common factor 1). So there would be p-1 such numbers (as we are looking number of integers less than p).
If we consider p=7 how many numbers are less than 7 having no common factors with 7: 1, 2, 3, 4, 5, 6 --> 7-1=6.
Answer: C.
Answer: (C) (p+1)/2
Question: A computer manufacturer produces a certain electronic component at a cost of $80 per component. Shipping costs for delivering the components are $3 per unit. Further, the manufacturer has costs of $16,500 a month related to the electronic component regardless of how many it produces. If the manufacturer produces and sells 150 components a month, what is the lowest price it can sell them for such that the costs don't exceed the revenues?
(A) $28
(B) $82
(C) $110
(D) $138
(E) $193
Rationale: by the question, the equation would be 150 p - 83*150 - 16500 = 0
p being the price we want to find and equation resulting zero means revenue and costs are equal so we can get the minimum price of the component.
solving the equation, we get p = $ 193. Answer E for me.
Answer: (E) $193
Question: At a certain paint store forest green is made by mixing 4 parts blue paint with 3 parts yellow paint.Verdant green is made by mixing 4 parts yellow paint with 3 parts blue paint.How many liters of yellow paint must be added to 42 liters of forest green to change it to Verdant green?
(A) 14
(B) 12
(C) 15
(D) 11
(E) 10
Rationale: 42 liter of Forset green have 24 liter of blue and 18 liter of yellow
Suppose we add x liter of yellow to make it a verdant green so the ratio of blue to yellow in verdant green is ¾ so the equation is
Blue/yellow =24/(18+x) = ¾
54+3x=96 => x =14
Answer : A
Answer: (A) 14
Question: Insert the missing number
1, 2, 4, 8, 16, 32, 64, ..., 256
(A) 128
(B) 148
(C) 154
(D) 164
(E) 174
Rationale: The sequence is just like multiples of 2..
i.e., 1 = 1
1 * 2 = 2
2 * 2 = 4
4 * 2 = 8
8 * 2 = 16
8 * 2 = 32
32 * 2 = 64
64 * 2 = 128
128*2 = 256
ANSWER:A
Answer: (A) 128
Question: The slant height of a conical mountian is 2.5 km and the area of its base is 1.54 km². The height of the mountain is:
(A) 2.4 km
(B) 2.6 km
(C) 4.5 km
(D) 5.4 km
(E) None
Rationale: Sol.
Let the radius of the base be r km. Then,
∏r² = 1.54 ⇒ r² = [1.54 * 7 / 22] = 0.49 ⇒ r = 0.7 km.
Now, l = 2.5 km, r = 0.7 km.
∴ h = √(2.5)² = (0.7)² km = √6.25 - 0.49 km
= √5.76 km = 2.4 km
Answer A
Answer: (A) 2.4 km
Question: Which one of the given numbers is completely divisible by 45?
(A) 202860
(B) 165642
(C) 112330
(D) 112333
(E) None of these
Rationale: We know that 45 = 9 × 5 where 9 and 5 are co-prime numbers. Also 9 and 5 are
factors of 45. Hence
if a number is divisible by 5 and 9, the number will be divisible by their product 45 also.
If a number is not divisible by 5 or 9, it is not divisible by 45
You must learn Divisibility Rules to say whether a given number is divisible by another number
Answer is A
without actually performing the division. Please go through divisibility rules before proceeding
further.
112330 is divisible by 5 but not divisible by 9 => 112330 is not divisible by 45
202860 is divisible by 5 and 9 => 202860 is divisible by 45
165642 is not divisible by 5 and 9 => 165642 is not divisible by 45
Answer: (A) 202860
Question: In a dairy farm, 16 cows eat 16 bags of husk in 16 days. In how many days one cow will eat one bag of husk?
(A) 16
(B) 40
(C) 20
(D) 26
(E) 30
Rationale: Explanation :
One bag of husk = 16 cows per day
⇒ 16 × 1 × 16 = 1 × 16 × x
For one cow = 16 days
Answer : A
Answer: (A) 16
Question: Which of the following must be equal to zero for all real numbers x ?
I. −1x−1x
II. x + (-x)
III. x^0
(A) I only
(B) II only
(C) I and III only
(D) II and III only
(E) I, II , and III
Rationale: I. -1/x will not be 0 for any real number; The value will be undefined if x is 0;
II. The value will be 0 for any real number. (ex.,) 2 + (-2) = 2-2 = 0;
III. x^0 = 1 for real numbers;
II only.
Ans is (B)
Answer: (B) II only
Question: The avg weight of A,B & C is 84 kg. If D joins the group, the avg weight of the group becomes 80 kg.If another man E who weights is 5 kg more than D Replaces A, Then the avgof B,C,D&E becomes 79 kg. What is the weight of A?
(A) 45
(B) 65
(C) 77
(D) 89
(E) 90
Rationale: A + B + C = 3 *84 = 252
A + B + C + D = 4 * 80 = 320 ---- (i)
So, D = 68& E = 68 + 5 = 73
B + C + D +E = 79 * 4 = 316 --- (ii)
From Eq. (i) & (ii)
A-E = 320 – 316 = 4
A = E +4 = 73 + 4 = 77
C
Answer: (C) 77
Question: There are four distinct pairs of brothers and sisters. In how many ways can a committee of 4 be formed and NOT have siblings in it?
(A) 4
(B) 8
(C) 12
(D) 16
(E) 20
Rationale: 4 pairs = 4*2 = 8 people total
8C4 = 8!/4!4! = 70 total outcomes
Total – unfavorable = favorable
Unfavorable outcomes
Assuming one pair of twins in the committee, we have two spaces left. Since we plugged a pair of twins in the committee, we have 8-2= 6 people to fill 2 spaces.
6C2 = 6!/2!4! = 15 ways to fill the two remaining slots
We only filled the slots with one pair, and we have to account for arrangements of the pairs. Now, we have 4 pairs. 4*15= 60 total arrangements
When we place members into the remaining slots, there may be an additional set of twins. There are 2 remaining slots to which we can fit a pair of twins. If it were one remaining slot, we cannot fit a pair of twins, so we wouldn’t have to account for duplicates.
Now we account for the number of duplicates.
# of duplicates = Total arrangements - # of unique combinations
To find the # of duplicates of twins, we need treat a pair of twins as one unit.
This means the 4 slots are really 2 slots.
Total ways of arranging four pairs of twins in two slots
4P2 = 4*3 = 12 total ways
Total # of unique combinations
Choosing two pairs out of 4 pairs
= 4C2
= 6
Therefore, # of duplicates = 12 - 6 = 6 duplicates
70 – 60 + 6 = 16
ANS:D
Answer: (D) 16
Question: A train is moving at 6/7 of its usual speed. The train is 30 minutes too late. What is the usual time for the train to complete the journey?
(A) 1 hour
(B) 30 minutes
(C) 3 hours
(D) 2 hours 30 min
(E) 2 hours
Rationale: new time = d / (6v/7) = 7/6 * usual time
30 minutes represents 1/6 of the usual time.
The usual time is 3 hours.
The answer is C.
Answer: (C) 3 hours
Question: A box has 12 shapes; 3 circles, 5 squares, and 4 triangles. How many groups of 3 shapes can be made with at least 1 triangle?
(A) 46
(B) 64
(C) 164
(D) 146
(E) 56
Rationale: The problem asks for a combination, since order doesn't matter. Now, selecting r items from a set of n gives the Combination Formula: nCr= n!/r!(n-r)!
n = 12
r = 3
So, total groups is 12C3 = 12!/(3!(12 - 3)!) = 220, and
n = 12 - 4 = 8
r = 3
for groups without a triangle is 8C3 = 8!/(3!(8 - 3)!) = 56,
so, groups with at least 1 triangle = 220 - 56 = 164
Answer: C
Answer: (C) 164
Question: Helen went to the stationers and bought things worth Euro 50, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
(A) Euro 15
(B) Euro 15.7
(C) Euro 19.7
(D) Euro 44.7
(E) None
Rationale: Explanation: Let the amount taxable purchases be Euro x.
Then, 6% of x = 30/100
x = (30/100 x 100/6) = 5.
Cost of tax free items = Euro [50 - (5 + 0.30)] = Euro 44.70
Answer: Option D
Answer: (D) Euro 44.7
Question: A student must answer 7 out of 10 questions on an examination. If at least 3 of the first 5 questions must be answered, how many possible combinations of 7 questions are available to the student?
.
(A) 50
(B) 80
(C) 110
(D) 220
(E) 360
Rationale: 1) preferred one
as there is ONLY one possiblity of choosing 7 out of 10, while choosing less than 3 in first five
choose 2 in first 5 and all 5 from later half..
ways = 5C2 = 10..
total ways = 10C3 = 120
ans = 120-10 = 110
ANSWER:C
Answer: (C) 110
Question: The cricket team of 11members is 25yrs old & the wicket keeper is 3 yrs older. If the ages ofthese 2are excluded, the average age of theremaining players is 1 year less than the average age of the whole team. What is the average age of the team ?
(A) 21
(B) 22
(C) 23
(D) 25
(E) 28
Rationale: Let the average age of the whole team be x years.
11x - (25 + 28) = 9 (x - 1)
=> 11x - 9x = 44
=> 2x = 44
=> x = 22.
So, average age of the team is 22 years.
B
Answer: (B) 22
Question: Tanks A and B are each in the shape of a right circular cylinder. The interior of tank A has a height of 6 meters and a circumference of 8 meters, and the interior of tank B has a height of 8 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B?
(A) 48%
(B) 80%
(C) 100%
(D) 120%
(E) 125%
Rationale: For A, r=8/2pi. Its capacity = (4pi)^2 * 6= 96pi
For B, r=10/pi. Its capacity = (5pi)^2 *8 = 200pi
A/B = 96pi/200pi = 0.48
A
Answer: (A) 48%
Question: What is the chance that a leap year selected at random contains 53 fridays?
(A) 1/7
(B) 2/7
(C) 3/7
(D) 4/7
(E) 5/7
Rationale: normal year =365 days
leap year = 366 days
now there are 52 weeks i.e. 364 days+2 odd days
the 2 odd may have Friday over a week has 7 days
so probability = 2/7
ANSWER:B
Answer: (B) 2/7
Question: The bus that travels from St. Louis to Chicago and back comes to St. Louis every 4 hours while the bus that travels from St. Louis to Springfield and back comes to St. Louis every 2 hours. If at 12:00 o'clock both bused arrived at St. Louis, at what time will they meet in St. Louis again?
(A) 16:00.
(B) 18:00
(C) 20:00
(D) 22:00.
(E) 24:00.
Rationale: Time taken by bus to travel from St. Louis to Chicago and back comes to St. Louis = 4 hours
Time taken by bus to travel from St. Louis to Springfield and back comes to St. Louis = 2 hours
Time taken by both buses to meet again in St. Louis will be LCM of 4 and 2 = 4
If the buses start at 12:00 o'clock from St. Louis , they will meet again in St. Louis at 16:00 hours
Answer A
Answer: (A) 16:00.
Question: If a trader sold two cars each at $ 325475 and gains 12% on the first and loses 12% on the second, then his profit or loss percent on the whole is?
(A) 3.44%
(B) 2.44%
(C) 6.44%
(D) 1.44%
(E) 7.44%
Rationale: D
1.44%
SP of each car is $ 325475, he gains 12% on first car and losses 12% on second car.
In this case, there will be loss and percentage of loss is given by = [(profit%)(loss%)]/100 = (12)(12)/100 % = 1.44%
Answer: (D) 1.44%
Question: The length of a rectangle is halved, while its breadth is tripled. Watis the % change in area?
(A) 40%
(B) 45%
(C) 50%
(D) 60%
(E) 70%
Rationale: Let original length = x and original breadth = y.
Original area = xy.
New length = x .
2
New breadth = 3y.
New area = x x 3y = 3 xy.
2 2
Increase % = 1 xy x 1 x 100 % = 50%.
2 xy
C
Answer: (C) 50%
Question: If U is an odd number and V and W are different integers, which of the following must be even?
(A) UV+UW
(B) U+VW
(C) UVW
(D) U+V+W
(E) None of these
Rationale: Let U = 3.
a. UV + UW
If V = 1 and W = 2 -> UV + UW = 3*1 + 3*2 = 9 (Odd)
b. U + VW
If V = 1 and W = 2 -> U+VW = 3 + 1*2 = 5 (Odd)
c. UVW
If V = 1 and W = 5 -> UVW = 1*3*5 = 15 (Odd)
d. U + V + W
If V = 1 and W = 5 -> U + V + W = 1 + 3 + 5 = 9 (Odd)
Answer is E.
Answer: (E) None of these
Question: What is the probability that the sum of two dice will yield a 5, and then when both are thrown again, their sum will again yield a 5? assume that each die has 4 sides with faces numbered 1 to 4.
(A) 1/144
(B) 1/36
(C) 1/12
(D) 1/16
(E) 1/3
Rationale: Solution -
Rolling dices is an independent event.
The combinations to get 5 are (1,4), (4,1), (2,3), (3,2), and total combinations of both dices is 16.
The probability of getting 5 in first attempt is 4/16=1/4.
Probability of getting 5 again in second attempt = (1/4)*(1/4) = 1/16. ANS D
Answer: (D) 1/16
Question: Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
(A) 16 sec
(B) 12 sec
(C) 17 sec
(D) 21 sec
(E) 23 sec
Rationale: Speed of the first train = 120/10 = 12 m/sec.
Speed of the second train = 120/5 = 8 m/sec.
Relative speed = 12 + 8 = 20 m/sec.
Required time = (120 + 120)/20 = 12 sec.
Answer: B
Answer: (B) 12 sec
Question: A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is:
(A) 18
(B) 24
(C) 42
(D) 81
(E) 28
Rationale: Let the ten's and unit's digit be x and 8/x respectively.
Then,
(10x + 8/x) + 18 = 10 * 8/x + x
9x2 + 18x - 72 = 0
x2 + 2x - 8 = 0
(x + 4)(x - 2) = 0
x = 2
So, ten's digit = 2 and unit's digit = 4.
Hence, required number = 24.
ANSWER:B
Answer: (B) 24
Question: Two persons A and B can complete a piece of work in 30 days and 45 days respectively. If they work together, what part of the work will be completed in 3 days?
(A) 1/5
(B) 1/1
(C) 1/6
(D) 1/3
(E) 1/7
Rationale: A's one day's work = 1/30
B's one day's work = 1/45
(A + B)'s one day's work = 1/30 + 1/45 = 1/18
The part of the work completed in 3 days = 3 (1/18) = 1/6.
Answer: C
Answer: (C) 1/6
Question: In the first week of the Year, Pancy saved $1. In each of the next 51 weeks, she saved $1 more than she had saved in the previous week. What was the total amount that Pancy saved during the 52 weeks?
(A) $1,326
(B) $1,352
(C) $1,378
(D) $2,652
(E) $2,756
Rationale: In the first week of the Year, Pancy saved $1.If you don't recall the formula, there is one method:
1 + 2 + 3 + 4 + 5 ........ + 26 + 27 + ............ + 48 + 50 + 51 + 52
Sum of 1stlast digit = 1 + 52 = 53
Sum of 2nd2nd last digit = 2 + 51 = 53
Sum of 3rd3rd last digit = 3 + 50 = 53
.
.
.
.
This is repeated 26 times
So, 26 * 53 = 1378
Answer = C
Answer: (C) $1,378
Question: In a games hour 4 different types of players came to the ground? cricket 11, hockey 15, football 21, softball 15. In these 4 people play both cricket and hockey, 3people play both softball and football. 5 people play both cricket and football. How many people play only cricket?
(A) 11
(B) 2
(C) 5
(D) 3
(E) 9
Rationale: people play only cricket = total players in cricket- both cricket and football- both cricket and hockey.
people play only cricket = 11-4-5 = 2
Answer is B
Answer: (B) 2
Question: Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 14 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
(A) 477
(B) 420
(C) 279
(D) 276
(E) 291
Rationale: 1h ----- 5
? ------ 60
12 h
RS = 14 + 21 = 35
T = 12
D = 35 * 12 = 420.Answer: B
Answer: (B) 420
Question: A certain tank is filled to one quarter of its capacity with a mixture consisting of water and sodium chloride. The proportion of sodium chloride in the tank is 40% by volume and the capacity of the tank is 24 gallons. If the water evaporates from the tank at the rate of 0.5 gallons per hour, and the amount of sodium chloride stays the same, what will be the concentration of water in the mixture in 2 hours?
(A) 43%
(B) 50%
(C) 52%
(D) 54%
(E) 56%
Rationale: The tank of 24 gallons is filled to a quarter so it had 6 gallons of water with 40% sodium chloride. In 2 hrs, .5*2 = 1 gallon of pure water (0% sodium chloride) will evaporate.
In essence, the initial mix of 6 gallons (40% sodium chloride) was a mix of 5 gallons of x% sodium chloride and 1 gallon of pure water.
Working with sodium chloride concentrations:
w1/w2 = (A2 - Avg)/(Avg - A1)
5/1 = (0 - 40)/(40 - x)
x = 48
So concentration of water is 100 - 48 = 52%
ANSWER:C
Answer: (C) 52%
Question: Find the roots of the quadratic equation: x2 + 2x - 15 = 0?
(A) -5,3
(B) 6,5
(C) 8,9
(D) 7,6
(E) 3,5
Rationale: Explanation:
x2 + 5x - 3x - 15 = 0
x(x + 5) - 3(x + 5) = 0
(x - 3)(x + 5) = 0
=> x = 3 or x = -5.
Answer A
Answer: (A) -5,3
Question: Pipe A can fill a tank in 24 minutes. Pipe B can fill the same tank 6 times faster than pipe A. If both the pipes are connected to the tank so that they fill the tank simultaneously, how long will it take for the empty tank to overflow?
(A) 4 minutes
(B) 32/7 minutes
(C) 192/7 minutes
(D) 3 minutes
(E) 28 minutes
Rationale: Pipe A can fill a tank in 24 minutes --> the rate of A = 1/24 tank/minute;
Pipe B can fill the same tank6 times fasterthan pipe A --> the rate of B = 1/24 + 6/24 = 7/24 tank/minute.
Their combined rate = 1/24 + 7/24 = 1/3tank/minute;
Therefore, A and B can fill the tank in 3 minutes.
Answer: D
Answer: (D) 3 minutes
Question: A and B start a business jointly. A invests Rs.16000 for 8 months and B remains in the business for 4 months. Out of the total profit B claims 2/7th share. How much money is contributed by B?
(A) 12899
(B) 12800
(C) 27891
(D) 18992
(E) 78812
Rationale: 16*8: x*4 = 5:2
x = 12.8
=> Rs.12800
Answer: B
Answer: (B) 12800