mathewhe/aqua_rat huggingface dataset:
Question: Two trains are approaching each other at 60 mph each. The length of each train is 1/6 miles. When the two locomotives(engines) meet, how many seconds will it take for them to pass each other completely?
(A) 8 sec
(B) 11 sec
(C) 12 sec
(D) 10 sec
(E) 15 sec
Rationale: total distance to cover= 2*(1/6)=2/6 miles
relative speed = 60+60 = 120mph
time taken= (2/6)/120*3600 = 10 sec.
ANSWER:D
Answer: (D) 10 sec
Question: The below sequence is a bit tricky. Can you solve it to find the next number?
6, 26, 326, 4326, ?
(A) 54326
(B) 38291
(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 54326
Answer : A
Answer: (A) 54326
Question: There are some passengers riding on a bus. At the first stop, half the passengers get off and nobody gets on the bus. This pattern continues as the bus goes to the next stops. If only one passenger gets off at stop number 6, how many passengers were on the bus originally?
(A) 128
(B) 64
(C) 32
(D) 16
(E) 8
Rationale: Before stop 6, there were 2 passengers on the bus.
Before stop 5, there were 4 passengers on the bus.
etc...
Before stop x, there were 2^(7-x) passengers on the bus.
Before stop 1, there were 2^6 = 64 passengers on the bus.
The answer is B.
Answer: (B) 64
Question: If n is an integer greater than 9, which of the following must be divisible by13 ?
(A) n(n + 5)(n – 6)
(B) n(n + 4)(n – 2)
(C) n(n + 2)(n – 1)
(D) n(n + 1)(n – 4)
(E) n(n + 3)(n – 5)
Rationale: if n =10 , then n+3 is divisible by 13 ...
E
Answer: (E) n(n + 3)(n – 5)
Question: The batting average for 40 innings of a cricket player is 50 runs. His highest score exceeds his lowest score by 172 runs. If these two innings are excluded, the average of the remaining 38 innings is 48 runs. Find out the highest score of the player.
(A) 150
(B) 174
(C) 180
(D) 166
(E) 165
Rationale: Explanation:
Total runs scored by the player in 40 innings = 40 × 50
Total runs scored by the player in 38 innings after excluding two innings = 38 × 48
Sum of the scores of the excluded innings = 40 × 50 - 38 × 48 = 2000 - 1824 = 176
Given that the scores of the excluded innings differ by 172. Hence let's take
the highest score as x + 172 and lowest score as x
Now x + 172 + x = 176
=> 2x = 4
=> x =4/2= 2
Highest score = x + 172 = 2 + 172 = 174
Answer: Option B
Answer: (B) 174
Question: What will be the product of (25-1)*(25-2)*(25-3)*..............*(25-39)*(25-40)?
(A) 0
(B) 1
(C) 25
(D) less than -100,000
(E) more than 100,000
Rationale: One of the terms is (25-25) so the product is 0.
The answer is A.
Answer: (A) 0
Question: The average of 10 numbers is 23. If each number is increased by 3, what will the new average be?
(A) 36
(B) 26
(C) 72
(D) 29
(E) 22
Rationale: Sum of the 10 numbers = 230
If each number is increased by 3, the total increase =
3 * 10 = 40
The new sum = 230 + 30 = 260 The new average = 260/10
= 26.
Answer:B
Answer: (B) 26
Question: If h is a positive integer, and if the units' digit of h^2 is 4 and the units' digit of (h + 1)^2 is 1, what is the units' digit of (h + 2)^2 ?
(A) 	0
(B) 	2
(C) 	4
(D) 	6
(E) 	8
Rationale: A for me.
_1² = _1
_2² = _4
_3² = _9
_4² = _6
_5² = _5
_6² = _6
_7² = _9
_8² = _4
_9² = _1
_0² = _0
On the list, the only number that squared has the units digit = 4 preceding a number that squared has the units digit = 1 is the _8.
So, h = _8, that has square 4. The next square is 1 andnext nextsquare is 0.
Answer: (A) 	0
Question: Logx16=0.8 then what is the value of x ?
(A) 32
(B) 34
(C) 35
(D) 36
(E) 37
Rationale: x^0.8=16
x=(2^4)^(10/8)
x=2^5
x=32
ANSWER:A
Answer: (A) 32
Question: If n is a three-digit prime number and j is an integer, which of the following is NOT a possible value of k, where k is the smallest positive integer such that n – 5j = k?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: if k = 5, then n = 5j + 5 = 5(j+1)
=> n is a multiple of 5, which contradicts what is stated in the question
Also, examples for other choices :
101 - 5* 20 = 1
103 - 5*20 = 3
107 - 5 * 21 = 2
109 - 5 * 21 = 4
E is the correct answer
Answer: (E) 5
Question: A man has some hens and cows. If the number of heads be 48 and the number of feet equals 140, then the number of cows will be:
(A) 30
(B) 23
(C) 24
(D) 26
(E) 22
Rationale: Explanation:
Let the number of hens be x and the number of cows be y.
Then, x + y = 48 .... (i)
and 2x + 4y = 140 x + 2y = 70 .... (ii)
Solving (i) and (ii) we get: x = 26, y = 22.
The required answer = 22.
Answer: E
Answer: (E) 22
Question: JOHN and ANDREW can finish the work 9 days if they work together. They worked together for 6 days and then ANDREW left. JOHN finished the remaining work in another 6 days. In how many days JOHN alone can finish the work?
(A) 30 days
(B) 60 days
(C) 18 days
(D) 80 days
(E) 90 days
Rationale: Amount of work done by JOHN and ANDREW in 1 day = 1/9
Amount of work done by JOHN and ANDREW in 6 days = 6 Ã— (1/9) = 2/3
Remaining work â€“ 1 â€“ 2/3 = 1/3
JOHN completes 1/3 work in 6 days
Amount of work JOHN can do in 1 day = (1/3)/6 = 1/18
=> JOHN can complete the work in 18 days
Answer : C
Answer: (C) 18 days
Question: A man can row 7 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and back. What is the total distance traveled by the man?
(A) 6.24 km
(B) 6 km
(C) 6.79 km
(D) 5.66 km
(E) 10 km
Rationale: M = 7
S = 1.2
DS = 8.2
US = 5.8
x/8.2 + x/5.8 = 1
x = 3.40
D = 3.40 * 2 = 6.79
ANSWER:C
Answer: (C) 6.79 km
Question: A train 150 m long is running at the speed of 30 km / hr. Find the time taken by it to pass a man standing near the railway line in seconds
(A) 5 sec
(B) 6 sec
(C) 7 sec
(D) 8 sec
(E) 9 sec
Rationale: Explanation:
Speed of the train = (60 x 5/18m / sec = 50/3 m/ sec.
Distance moved in passing the standing man = 150 m.
Required time taken = 150/(50/3) = (150 Ã—(3/50)) sec =9 sec
Answer: Option E
Answer: (E) 9 sec
Question: The perimeter of a rectangle is equal to 280 meters. The ratio of its length to its width is 5:2. Find the area of the rectangle.
(A) 400 square meters
(B) 4000 square meters
(C) 20 square meters
(D) 2000 square meters
(E) 1000 square meters
Rationale: Solution
If the ratio of the length to the width is 5:2, then the measure L of the length and and the measure W of the with can be written as
L = 5x and W = 2x
We now use the perimeter to write
280 = 2(2L + 2W) = 2(5x + 2x) = 14x
Solve for x
280 = 14x
x = 280 / 14 = 20
The area A of the rectangle is given by
A = L × W = 5x × 2x = 10x^2 = 10×20^2 = 4000 square meters
ANSWER IS B
Answer: (B) 4000 square meters
Question: A sum of Rs.1440 is divided into 13 students so that each boy gets Rs.120 while each girl gets Rs.100. Find the number of boys and number of girls
(A) 8B, 5G
(B) 7B, 6G
(C) 4B, 9G
(D) 9B, 4G
(E) 9B, 5G
Rationale: 120B+100G=1460-----i
B+G=13-------ii
from i
100B+20B+100G=1440
100(B+G)+20B=1440
100(13)+20B=1440
By simplifing we get
B=7;G=6
ANSWER:B
Answer: (B) 7B, 6G
Question: Ages of two persons differ by 18 years. If 4 years ago, the elder one was 4 times as old the younger one, find their present age
(A) 6,24
(B) 9,27
(C) 10,28
(D) 18,36
(E) 19,37
Rationale: Explanation:
Let the age of younger person be x,
Then elder person's age is (x+18)
=> 4(x-4) = (x+18-4) [4 years before]
=> 4x-16 = x+14
=> x = 10.
So elder person's age is x + 18 = 28
Answer: Option C
Answer: (C) 10,28
Question: For which of the following does h(a)−h(b)=h(a−b) for all values of a and b?
(A) h(x)=x^2
(B) h(x)=x/2
(C) h(x)=x+5
(D) h(x)=2x−1
(E) h(x)=|x|
Rationale: To solve this easiest way is just put the value and see that if it equals or not.
with option 1. h(a) = a^2 and h(b) = b^2
so L.H.S = a^2 - b^2
and R.H.S = (a-b)^2 ==> a^2 + b^2 -2ab.
so L.H.S not equal to R.H.S
with option 2. h(a) = a/2 and h(b) = b/2
L.H.S = a/2 - b/2 ==> 1/2(a-b)
R.H.S = (a-b)/2
so L.H.S = R.H.S which is the correct answer.
answer:B
Answer: (B) h(x)=x/2
Question: A teacher wants to label folders with numbers using digit stickers only. If the teacher uses 501 stickers, how many folders have been numbered? (The numbers of the folders are consecutive and the number of the first folder is 1).
(A) 104
(B) 120
(C) 133
(D) 154
(E) 203
Rationale: For the first 9 folders we need 9 stickers.
For the next 90 we need 2 stickers each or 180 stickers.
For the next 900 folders we need 3 stickers each.
The first 99 folders correspond to 189 stickers.
Subtract 189 from the total number of stickers (501).
This leaves 312 stickers for folders that use 3 stickers each. So, divide 312 by 3 to get 104 folders.
Add 99 folders to 104 folders to get the total number of folders, 203.
Answer: E
Answer: (E) 203
Question: There were two candidates in an election. Winner candidate received 65% of votes and won the election by 300 votes. Find the number of votes casted to the winning candidate?
(A) 228
(B) 744
(C) 255
(D) 650
(E) 231
Rationale: W = 65% L = 35%
65% - 35% = 30%
30% -------- 300
65% -------- ? => 650
Answer:D
Answer: (D) 650
Question: If twice of a number divided by 3d gives 20 as the remainder, and five times of the same number gives 32 as the remainder. What will be the value of d?
(A) 11
(B) 12
(C) 15
(D) 14
(E) 18
Rationale: ReMainder in second case is,32. So,3d>=33.
So, minimum value of d should 11.
If number =28.
double of number=56 and take d=12 so 56/36 ReMainder=20.
Now 5times of number=140.
So 140/36 ReMainder=32.
That is,3d=36 satisfy the conditions.
So d=12.
ANSWER:B
Answer: (B) 12
Question: Of the 60 electronics components that a factory must manufacture, 80 percent would be most e¢ ciently manufactured by Machine A and the remaining 20 percent would be most efficiently manufactured by Machine B, though either machine could manufacture any of the 60 components. If 40 percent of the components were manufactured by Machine A and the remainder were manufactured by Machine B, what is thehighest possible number of components that were manufactured by the machine that would manufacture them the most efficiently?
(A)  30
(B)  32
(C)  33
(D)  35
(E)  36
Rationale: A can manufacture 80 % of 60 efficiently, which is 48.
B can manufacure 20 % of 60 efficiently, which is 12.
Now 40 % of 60 are produced by A. This means 24 parts. Since A can produce 48 efficiently, all 24 are produced efficiently. Rest (36) is produced by B, which can produce max. 12 parts efficiently.
Hence parts that were produced efficiently = 12+24 = 36. (E).
Answer: (E)  36
Question: If x represents the sum of the interior angles of a triangle and y represents the sum of the interior angles of a regular pentagon, then the difference between x and y is equal to the sum of the interior angles of what geometric shape?
(A) Circle
(B) Square
(C) Rhombus
(D) Trapezoid
(E) Pentagon
Rationale: Sum of angles of triangle = 180*(3-2) = 180 => using formula sum of interior angles of polygon = 180*(n-2) where n is the number of sides in a polygon
Sum of angles in Pentagon = 180*(5-2) =540
Difference =540 - 180= 360 => Cirlcle
hence (A).
Answer: (A) Circle
Question: If k is an integer and 121 < k^2 < 225, then k can have at most how many values?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 8
Rationale: given k is an integer
121 < k^2 < 225
11 < | k| < 15
K=-12,-13,-14,12,13,14
ANSWER:D
Answer: (D) 6
Question: If each term in the sum a1+ a2+a3+.....+an is either 7 or 77 and the sum equals 350, which of the following could be equal to n?
(A) 38
(B) 39
(C) 40
(D) 41
(E) 42
Rationale: For example: as units digit of 350 is zero then # of terms must be multiple of 10. Only answer choice which is multiple of 10 is C (40).
To illustrate consider adding:
*7
*7
...
77
77
----
=350
So, several 7's and several 77's, note that the # of rows equals to the # of terms. Now, to get 0 for the units digit of the sum the # of rows (# of terms) must be multiple of 10. Only answer choice which is multiple of 10 is C (40).
Answer: C.
Answer: (C) 40
Question: If C.P. of 23 books is equal to S.P of 30 books , then your gain or loss is ?
(A) 23 1/3 gain %
(B) 30 10/23 loss %
(C) 23 1/3 loss %
(D) 30 1/3 loss %
(E) 40 1/3 loss %
Rationale: Say the cost price of 23 books is $23 so $1 for a book.
The cost of 30 books would be $30, and the selling price of 30 books would be 23$, hence the loss = ($30 - $23)/$30 = ~23.3%.
Answer: C.
Answer: (C) 23 1/3 loss %
Question: A sales staff is composed of a sales manager and two sales people, all of whom earn commission as a percentage of sales. Each sales person earns 5% commission on sales. In a given week, the sales staff earned a total of $1,750 in commissions on $5,000 worth of sales. What commission rate did the sales manager earn during that week?
(A) 25%
(B) 30%
(C) 35%
(D) 40%
(E) 45%
Rationale: Let managers commission rate be M.
m*5000+ 2*0.05*5000=1750
5000*m=1250
m=25/100=25%
ANSWER:A
Answer: (A) 25%
Question: If a, b, c are consecutive positive integers and a<b<c, which of the following must be true?
I. b-a=1
II. abc is an even integer
III. (a+b+c)/3 is an integer
(A) I
(B) II
(C) I and II
(D) II and III
(E) I, II & III
Rationale: 1. b-a=1 --> a, b, c are consequitive positive integers and a<b<c then b=a+1 --> b-a=1. So this statement is always true;
2. abc is an even integer --> out of any 3 consecutive integers at least one must be even thus abc=even. So this statement is also always true;
3. (a+b+c)/3 is an integer --> the sum of odd number of consecutive integers is ALWAYS divisible by that odd number. So this statement is also always true. Or: (a+b+c)/3=(a+a+1+a+2)/3=(3a+3)/3=a+1=integer.
Answer: E.
Answer: (E) I, II & III
Question: A can run a kilometer race in 4 1/2 min while B can run same race in 5 min. How many meters start can A give B in a kilometer race, so that the race mat end in a dead heat?
(A) 200 m
(B) 700 m
(C) 800 m
(D) 100 m
(E) 100 m
Rationale: Explanation:
A can give B (5 min - 4 1/2 min) = 30 sec start.
The distance covered by B in 5 min = 1000 m.
Distance covered in 30 sec = (1000 * 30)/300 = 100 m.
A can give B 100m start.
Answer:D
Answer: (D) 100 m
Question: A person is saving money to purchase a car. He earns Â£4000 per month and saves Â£500 to buy the car. If he needs Â£45000 to buy his dream car. How much money he will earn, before he saves enough money to buy the car?
(A) A - 352000
(B) B - 356000
(C) C - 360000
(D) D - 348000
(E) E - 340000
Rationale: He is saving Â£500 per month. He needs Â£45000 and it takes Â£45000/Â£500 = 90 months to save the money.
In 90 months, he earns 90*Â£4000 = Â£36000.
Answer: C
Answer: (C) C - 360000
Question: The average of 7 results is 45. The average of first three results is 47 and average of last three results is 42. What is the fourth result?
(A) 48
(B) 47
(C) 44
(D) 46
(E) 49
Rationale: Explanation:
Total of results = 45 * 7 = 315
Total of first three results = 3* 47 = 141
Total of last three results = 3* 42 = 126
Fourth result = 315 - (141 + 126) = 48
Answer: Option A
Answer: (A) 48
Question: Given positive integer X, which of the following CAN NOT be evenly divisible by X?
(A) x + 4
(B) x+ 7
(C) 2x + 1
(D) x − 1
(E) x + 1⁄2
Rationale: This can be easily solved by substituting values:
Assume x to be 1
A. x + 4: 5 is evenly divisible by 1
B. x + 7: 8 is evenly divisible by 1
C. 2x + 1: 3 is evenly divisible by 1
D. x − 1: 0 is evenly divisible by 1
E. x + 1⁄2: 3/2 is not evenly divisible by 1
Option E
Answer: (E) x + 1⁄2
Question: Solve for x and check: - 12x = 72
(A) -4
(B) -2
(C) -6
(D) -12
(E) None of these
Rationale: Solution : Dividing each side by -12, we obtain
(-12x/-12)=(72/-12)
Therefore : x=-6
Check :
-12x=72
(-12*-6)=72
72=72
ANSWER : C
Answer: (C) -6
Question: A can do a work in 2 days. B can do the same work in 3days. Both A&B together will finish the work and they got $500 from that work. Find their shares?
(A) 100,200
(B) 400,100
(C) 300,150
(D) 300,200
(E) 250,250
Rationale: Ratio of their works A:B = 2:3
Ratio of their wages A:B = 3:2
A's share = (3/5)500 = 300
B's share = (2/5)500 = 200
correct option is D
Answer: (D) 300,200
Question: In an exam, W scored 60 percent, X scored 100 percent and Y 80 percent. The maximum score awarded in the exam is 1000. Find the average mark scored by all the three candidates?
(A) 700
(B) 800
(C) 900
(D) 1000
(E) 1100
Rationale: Average mark scored by all the three boys
= [60/100 (1000) + 100/100 (1000) + 80/100 (1000)] / 3
= 800
Answer: B
Answer: (B) 800
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
(A) 388
(B) 367
(C) 367
(D) 150
(E) 282
Rationale: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train
= (Speed x Time)
= (50/3 * 9) m
= 150 m.
Answer:D
Answer: (D) 150
Question: A committee has 5 men and 6 women. What are the number of ways of selecting a group of eight persons?
(A) 165 ways
(B) 166 ways
(C) 665 ways
(D) 256 ways
(E) 256 ways
Rationale: Total number of persons in the committee
= 5 + 6 = 11
Number of ways of selecting group of eight persons
= 11C8 = 11C3 = (11 * 10 * 9)/(3 * 2)
= 165 ways.
Answer: A
Answer: (A) 165 ways
Question: On Monday morning, Chris receives tickets to a baseball game that will be played at 7pm on the next evening that it does not rain. However, Chris is only in town until Wednesday morning, at which point he must fly to another city. If there is a 20% chance of rain each of the next two evenings, what is the probability that Chris will be able to attend the game?
(A)  36%
(B)  60%
(C)  96%
(D)  80%
(E)  84%
Rationale: Chris won't be able to attend the game if it be raining on Monday eveningandTuesday evening. The probability of that is 0.2*0.2 = 0.04. So, the probability that he will be able to attend is 1 - 0.04 = 0.96.
Answer: C.
Answer: (C)  96%
Question: Sum of a rational number and its reciprocal is 13/6. Find the number
(A) 2
(B) 3/2
(C) 4/2
(D) 5/2
(E) 6/2
Rationale: Explanation:
=>x+1/x=13/6
=>x2+1/x=13/6
=>6x2−13x+6=0
=>6x2−9x−4x+6=0
=>(3x−2)(2x−3)
=>x=2/3or3/2
Option B
Answer: (B) 3/2
Question: We have 4 people and 1 chairs. In how many ways chairs can be occupy?
(A) 72
(B) 86
(C) 24
(D) 14
(E) 20
Rationale: no. of ways they can be occupy = 4*3*2*1 = 24
Answer is C
Answer: (C) 24
Question: The digit in the units place of a number is equal to the digit in the tens place of half of that number and the digit in the tens place of that number is less than the digit in units place of half of the number by 1. If the sum of the digits of the number is seven, then what is the number?
(A) 52
(B) 16
(C) 34
(D) Data inadequate
(E) None of these
Rationale: Let ½ of the no. = 10x + y
and the no. = 10V + W From the given conditions,
W = x and V = y – 1
Thus the no. = 10(y – 1) + x…..(A)
∴ 2(10x + y) = 10(y – 1) + x ⇒ 8y – 19x = 10…(i)
Again, from the question,
V + W = 7 ⇒ y – 1 + x = 7
∴ x + y = 8 …(ii)
Solving equations (i) and (ii), we get x = 2 and y = 6.
∴ From equation (A), Number = 10(y – 1) + x = 52
Answer A
Answer: (A) 52
Question: A box contains one dozen donuts. Four of the donuts are chocolate, four are glazed, and four are jelly. If two donuts are randomly selected from the box, one after the other, what is the probability that both will be jelly donuts?
(A) 1/11
(B) 1/9
(C) 1/3
(D) 2/3
(E) 8/9
Rationale: Prob. of getting the first Jelly - 4/124
Since there has been no replacement, the number of donuts will decrease in second case
Prob of getting the second Jelly - 3/11
Combined Prob. - 4/12∗3/11=1/11
Ans A
Answer: (A) 1/11
Question: A bag contains five white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color?
(A) 5/5
(B) 5/9
(C) 5/8
(D) 5/1
(E) 5/2
Rationale: Two balls can be picked from nine balls in ⁹C₂ ways.
We select one white ball and one red ball from five white balls and four red balls. This can be done ⁵C₁ . ⁴C₁ ways.
The required probability
= (5 * 4)/9C2 = 20/36 = 5/9
Answer: B
Answer: (B) 5/9
Question: The National Gross Product (NGP) of Andalasia had decreased by 25 percent. Due to the ongoing war with Actasia, the NGP has decreased by an additional 10 percent. By approximately what percent would the NGP now have to be increased in order to restore it to its original amount?
(A) 32.5%
(B) 35%
(C) 48%
(D) 65%
(E) 67.5%
Rationale: Original NGP = x
NGP after 25% decrease = 0.75x
NGP after another 10% decrease = 0.675x
To restore the NGP to x the percentage increase has to be (0.325x * 100) /(0.675x) = Value slightly less than 50% = 48%
Answer: C
Answer: (C) 48%
Question: The botanic garden is planting bulbs for the spring flower show. The head gardener is trying to decide how to place three Tulips bulbs, three Daffodil bulbs, and three Crocus bulbs along the front row. How many different arrangements can he make of these bulbs in the front row?
(A) 27
(B) 108
(C) 216
(D) 512
(E) 1680
Rationale: # of ways to arrange 9 flowers out of which 3 T's are identical, 3 D's are identical and 3 C's are identical is 9!/(3!3!3!)=1,680.
Answer: E 1680
Answer: (E) 1680
Question: In a shop 40% of the articles are sold at a profit of 30% and the remaining at a loss of 15%.what is the overall profit/loss?
(A) 6% loss
(B) 2% loss
(C) 10% profit
(D) 3% profit
(E) 7% profit
Rationale: 40*1.3+60*0.85/100=1.03
ANSWER:D
Answer: (D) 3% profit
Question: If w, x, and y are consecutive even positive integers and w < x < y, which of the following could be equal to w - x - y ?
(A) -10
(B) -8
(C) -1
(D) 0
(E) 3
Rationale: Since W, X and Y are CONSECUTIVE ODD POSITIVE INTEGERS and W < X < Y, we can start with the easiest set of values that comes to mind:
W = 2
X = 4
Y = 6
The question asks for what COULD be the value of W - X - Y.
In this case, the value would be...
2 - 4 - 6 = -8
-8 IS among the answer choices, so we're done.
B
Answer: (B) -8
Question: Two numbers have a H.C.F of 12 and a product of two numbers is 2460. Find the L.C.M of the two numbers?
(A) 140
(B) 150
(C) 205
(D) 170
(E) 180
Rationale: L.C.M of two numbers is given by
(Product of the two numbers) / (H.C.F of the two numbers) = 2460/12 = 205.
ANSWER:C
Answer: (C) 205
Question: 12 men complete a work in 18 days. Six days after they had started working, 4 men joined them. How many days will all of them take to complete the remaining work ?
(A) 10 days
(B) 12 days
(C) 15 days
(D) 9 days
(E) None of these
Rationale: In 1 day, work done by 12 men = 1⁄18
In 6 days, work done by 12 men = 6⁄18 = 1⁄3
Remaining work = 2⁄3
m1 × d1 × w2 = m2 × d2 × w1
or 12 × 18 × 2⁄3 = 16 × d2 × 1
or d2 = 4×18×2/16=9days
Answer D
Answer: (D) 9 days
Question: Taps A and B can fill a bucket in 10 minutes each. If both are opened and A is closed after 3 minutes, how much further time would it take for B to fill the bucket?
(A) 2 min. 6sec.
(B) 2min. 10sec.
(C) 4min. 12sec.
(D) 2 mins
(E) 3min.
Rationale: Explanation:
Part filled in 3 minutes =
3∗(1/10+1/10)=3∗1/5=3/5
Remaining part =1−4/5=1/5
=>1/10:1/5=1:X
=>X=2
=>X=2 mins
So it will take further 2 mins to fill the bucket.
Option D
Answer: (D) 2 mins
Question: The perimeters of 2 squares are 40cm and 32cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares?
(A) 20cm
(B) 24cm
(C) 32cm
(D) 28cm
(E) 30cm
Rationale: Side of the 1st square = 40/4 = 10cm
Side of the 2nd square = 32/4 = 8cm
Area of the 3rd square = 10^2 - 8^2 = 36cm^2
Side of the 3rd square = 6cm
Required perimeter = 6*4 = 24cm
Answer is B
Answer: (B) 24cm
Question: The number of sequences in which 7 players can throw a ball, so that the youngest player may not be the last is -.
(A) 4000
(B) 2160
(C) 4320
(D) 5300
(E) 4160
Rationale: x Not younger_______ ↑
The last ball can be thrown by any of the remaining 6 players. The first 6 players can throw the ball in ⁶P₆ ways.
The required number of ways = 6(6!) = 4320
ANSWER:C
Answer: (C) 4320
Question: The length of a rectangle is 3 times its width. If the width of the rectangle is 4 inches, what is the rectangle's area, in square inches?
(A) 30 square inches
(B) 75 square inches
(C) 68 square inches
(D) 48 square inches
(E) 92 square inches
Rationale: If the width is 4 in and the length is 3 times the width, then the length is
3 * 4 = 12 in
The area is given by
4 * 12 = 48 square inches
correct answer D
Answer: (D) 48 square inches