mathewhe/aqua_rat huggingface dataset:
Question: The greatest number which can divide 1356,1868 and 2764 leaving the same remainder 12 in each case, is :
(A) 64
(B) 124
(C) 156
(D) 260
(E) None of these
Rationale: Solution
Required number = H.C.F. of (1356-12), (1868-12) and (2764-12)
= H.C.F of 1344,1856 and 2752 = 64. Answer A
Answer: (A) 64
Question: If X+Y = 2X-2Z, X+2Y = 4Z and X+Y+Z = 21, what is the value of Y/Z?
(A) -4.5.
(B) 0.667.
(C) 1.7.
(D) 3.
(E) 2.5.
Rationale: X+Y = 2X-2Z
Y= X-2Z---------- 1
X+2Y = 4Z
-X+4Z= 2Y--------- 2
Adding equation 1 from equation 2
2Z = 3Y
Y/Z = 0.667
B is the answer
Answer: (B) 0.667.
Question: Two children want to walk together to visit their aunt, who lives exactly 6 blocks north and 5 blocks east of their current location. If they travel only along streets and do not travel diagonally, the shortest possible route connecting the two points is exactly 11 blocks. How many different 11-block routes may they take to travel the shortest possible distance to their aunt’s house?
(A) 11!/(6!*5!)
(B) 11!/(6*5)
(C) 11!*6!*5!
(D) 6!*5!
(E) 11*6*5
Rationale: If they need to walk 6 blocks north and 5 blocks east, we can express this route as NNNNNNEEEEE. The question thus asks us how many ways we can arrange those letters.
The number of arrangements of 11 things is 11!
We then divide by the repetitions of N's and E's, which are 6! and 5! respectively.
The number of walking routes is 11!/(6!*5!).
The answer is A.
Answer: (A) 11!/(6!*5!)
Question: 65% of x = 20% of 487.50. Find the value of x?
(A) 100
(B) 150
(C) 160
(D) 180
(E) 199
Rationale: 65% of x = 20% of 487.50
Then, 65/100 * x = 20/100 * 4875/10
x= 150
Answer is B
Answer: (B) 150
Question: On seven consecutive flips of a coin, what is the probability that all seven produce the same result?
(A) 1/64
(B) 1/8
(C) 1/4
(D) 3/8
(E) 1/2
Rationale: TTTTTTT case --> P = (1/2)^7 = 1/128
HHHHHHH case --> P = (1/2)^7 = 1/128
P(TTTTTTT or HHHHHHH) = 1/8 + 1/8 = 1/64
Answer: A
Answer: (A) 1/64
Question: find The last digit in the product 287 x 287 + 269 x 269 - 2 x 287 x 269?
(A) 5
(B) 6
(C) 8
(D) 9
(E) 4
Rationale: Explanation:
Given Exp.	= a2 + b2 - 2ab, where a = 287 and b = 269
= (a - b)2 = (287 - 269)2
= (182)
= 324
Answer is E
Answer: (E) 4
Question: A marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each. There can be no less than 8 musicians per row and no more than 30 musicians per row. How many different rectangular formations G are possible?
(A) 3
(B) 4
(C) 5
(D) 6
(E) G=8
Rationale: The combinations could be {(1,240),(2,120),(3,80),(4,60),(5,48),(6,40),(8,30),(10,24),(12,20),)15,16),(16,15),(20,12),(24,10),(30,8),(40,6),(48,5),(60,4),(80,3),(120,2),(240,1)}
Of these we are told 8<=t<=30 So we can remove these pairs, and we are left only with.
{(8,30,(10 ,24),(12,20),(15,16),(16,15),(20,12),(24,10),(30,8)}
Hence 8..E
Answer: (E) G=8
Question: An arithemetic sequence of numbers begins p, 2p + 3, 4p + 4... What is the 13th member of this sequence?
(A) A)37
(B) B)40
(C) + 13
(D) D)62
(E) + 13
Rationale: Common difference of an arithmetic series is constant.
2p+3-p=4p+4-2p-3
p=2
1, 7, 12, 17, 22, 27, 32, 37, 42, 47, 52, 57, 62
Ans:D
Answer: (D) D)62
Question: Given that a is the average (arithmetic mean) of the first nine positive multiples of six and b is the median of the first seven positive multiples of six, what is the ratio of a to b?
(A) 5:4
(B) 10:13
(C) 5:6
(D) 13:10
(E) 4:3
Rationale: The first nine positive multiples of six are {6, 12, 18, 24,30, 36, 42, 48, 54}
The first twelve positive multiples of six are {6, 12, 18, 24, 30,36,42 }
Both sets are evenly spaced, thus their median=mean:
a=30 and b=24 --> a/b=30/24=5/4.
Answer: A.
Answer: (A) 5:4
Question: In how many W ways can 5 people from a group of 6 people be seated around a circular table
(A) 56
(B) 80
(C) 100
(D) 120
(E) 144
Rationale: W=6C5 * (5-1)! (Select 5 out of 6 and arrange them in circular manner)
= 6 * 4!
= 6 * 24
= 144
Answer - E
Answer: (E) 144
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 5 boys when a boy gets any no. of prizes?
(A) 125
(B) 150
(C) 130
(D) 167
(E) 190
Rationale: Ans.(A)
Sol. In this case, repetitions are allowed, so all the three prizes can be given in 5 ways, i.e. (5 x 5 x 5) ways = 53 ways = 125 ways Or nr ways = 43 ways = 125 ways
Answer: (A) 125
Question: A family consists of grandparents, parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family ?
(A) 31( 5/7
(B) 31( 5/9
(C) 31( 5/6
(D) 31( 5/3
(E) 31( 5/1
Rationale: Explanation:
Required average = (67 * 2 + 35 * 2 + 6 * 3) / (2 + 2 + 3)
= (134 + 70 + 18) / 7 = 222 / 7 = 31(5/7) years.
Answer: A) 31( 5/7)
Answer: (A) 31( 5/7
Question: When the positive integer x is divided by 5 and 7, the remainder is 3 and 4, respectively. When the positive integer y is divided by 5 and 7, the remainder is 3 and 4, respectively. Which of the following is a factor of x-y?
(A)  12
(B)  24
(C)  35
(D)  16
(E)  30
Rationale: If I have a number n which when divided by 5 gives a remainder 3 and when divided by 7 gives a remainder 4, the number is of the form:
n = 5x + 3
n = 7y + 4
I will need to check for the smallest such number.
I put y= 1. n = 11. Is it of the form 5x + 3? No.
Put y= 2. n = 18. Is it of the form 5x + 3? Yes.
When 18 is divided by 5, it gives a remainder of 3. When it is divided by 7, it gives a remainder if 4.
Next such number will be 35 + 18 because 35 will be divisible by 5 as well as 7 and whatever is the remainder from 18, will still be the remainder
Next will be 35*2 + 18
and so on...
Difference between such numbers will be a multiple of 35 so your answer is 35.
your answer is C
Answer: (C)  35
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
(A) 140
(B) 156
(C) 175
(D) 214
(E) 216
Rationale: Given that the area of the square = 1225 sq.units
=> Side of square = √1225 = 35 units
The radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35 = 14 units
Given that breadth = 10 units
Area of the rectangle = lb = 14 * 10 = 140 sq.units
ANSWER:A
Answer: (A) 140
Question: How many odd integers V between 200 and 600 are there such that their tens digit is even?
(A) 20
(B) 25
(C) 100
(D) 150
(E) 200
Rationale: The hundreds digit can take 4 values: 2, 3, 4 and 5;
The tens digit can take 5 values: 0, 2, 4, 6 and 8;
The units digit can take 5 values: 1, 3, 5, 7 and 9;
Total V: 4*5*5=100.
Answer: C.
Answer: (C) 100
Question: Machines A and B produce bottles at their respective constant rates. Machine A produces k bottles in 2 hours and machine B produces k bottles in 5 hours. How many hours does it take machines A and B, working simultaneously, to produce 14k bottles?
(A) 14
(B) 16
(C) 18
(D) 20
(E) 22
Rationale: A's rate = k/2
B's rate = k/5
k/2 + k/5 = 7k/10
14k / (7k/10) = 20 hours
The answer is D.
Answer: (D) 20
Question: Saturn travels around the sun at a speed of approximately 6.1 miles per second. The approximate speed is how many miles per hour?
(A) 17,430
(B) 18,560
(C) 19,720
(D) 20,840
(E) 21,960
Rationale: 6.1 * 3600 = 29,160
The answer is E.
Answer: (E) 21,960
Question: A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of A?
(A) 240
(B) 278
(C) 209
(D) 267
(E) 262
Rationale: (3*8 + 2*4):(4*8 + 5*4)
8:13
8/21 * 630 = 240
Answer: A
Answer: (A) 240
Question: For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum of odd all the integers between 10 and 100?
(A) 1345
(B) 1576
(C) 2475
(D) 2578
(E) 1895
Rationale: numbers are 11,13,15-------,97,99
Average of the set: (largest+smallest)/2=(99+11)/2=55;
# of terms: (largest-smallest)/2+1=(99-11)/2+1=45
The sum = 45*55= 2475
Answer: C
Answer: (C) 2475
Question: Prove that there exists infinitely many positive integers n such that 4n^2 + 1 is divisible both by 5 and 13.
(A) 5
(B) 6
(C) 5|4n^2+ 1 and 13|4n^2+ 1
(D) 3|4n^2+ 1 and 10|4n^2+ 1
(E) 2|4n^2+ 1 and 1|4n^2+ 1
Rationale: For instance, all numbers n in the arithmetic progression 65k+56 (k = 0, 1, 2, ... ) have the desired property. Indeed, if n = 65k+56 with an integer k>=0, then n == 1 (mod 5) and n == 4 (mod 13), hence 4n^2+ 1 == o (mod 5) and 4n^2+ 1== 0 (mod 13). Thus, 5|4n^2+ 1 and 13|4n^2+ 1
Answer is C 5|4n^2+ 1 and 13|4n^2+ 1
Answer: (C) 5|4n^2+ 1 and 13|4n^2+ 1
Question: If |x – 9/2| = 5/2, and if y is the median of a set of u consecutive integers, where u is odd, which of the following must be true?
I. xyu is odd
II. xy(u^2 + u) is even
III. x^2y^2u^2 is even
(A) II only is true
(B) III only is true
(C) I and III
(D) II and III
(E) I, II, and III
Rationale: given:
u is Odd
y is the median of odd numbers, hence y is Odd
x = solving the modulus you get 7 and 2. Hence x is Even or Odd
Therefore: u = O, y = O and x = O or E
Statement I = x*y*u = y*u*x = O x O x O/E = O x O/E = Odd or even. So False
Statement II = xy(u^2 + u) = O/E x O (O + O) = O/E x O(E) = O/E x E = Always Even. So true
Statement III. x^2y^2u^2 is even. E/O x O x O = Odd or even. Hence False.
Answer = A.
Answer: (A) II only is true
Question: If the simple interest on a certain sum of money for 7 years is one–fifth of the sum, then the rate of interest per annum is
(A) 4%
(B) 2.50%
(C) 6.20%
(D) 5%
(E) 2.85%
Rationale: Explanation:
Let the Principal(P) be x
Then, Simple Interest(SI) = x/5
Time(T) = 7 years
Rate of interest per annum(R) = (100×SI)/PT
= (100 × (x/5)/(x × 7) = 20/7 = 2.85%
Answer: Option E
Answer: (E) 2.85%
Question: By selling a watch for Rs.560/-, a man loses 20% what is that watch cost price
(A) s. 700/-
(B) s. 800/-
(C) s. 880/-
(D) s. 900/-
(E) s. 990/-
Rationale: 80 % ------> 560 (80 * 7 = 560)
100 % ------>700 (100 * 7 = 700)
Cost price = Rs. 700/-
A
Answer: (A) s. 700/-
Question: In a rare coin collection, all coins are either pure gold or pure silver, and there is initially one gold coin for every three silver coins. With the addition of 12 more gold coins to the collection, the ratio of gold coins to silver coins is 1 to 2. Based on this information, how many total coins are there now in this collection (after the acquisition)?
(A) 72
(B) 84
(C) 96
(D) 108
(E) 120
Rationale: Initially the number of gold coins and silver coins is 2k and 6k.
After adding gold coins, the number of coins is 3k and 6k.
Thus k = 12 and the total number of coins is 9k = 108.
The answer is D.
Answer: (D) 108
Question: In how many ways can 6 boys and 3 girls be arranged at a table if 3 girls are never together?
(A) 47520
(B) 45620
(C) 47888
(D) 42156
(E) 43210
Rationale: Total ways of arranging 10 person in a circle = 9! = 51840 ways
If we consider three women as one, then we have 6+1=7 persons. Arranging these seven persons in circle will take = 6! = 720 ways
And three women can arrange themselves in 3! ways
Total ways in which three women sit together in circle = 6!*3! = 4320 ways
Total ways in which three women doesn’t sit together in circle = 9! - 6!*3! = 51840 - 4320 = 47520 ways
A
Answer: (A) 47520
Question: A textile manufacturing firm employees 80 looms. It makes fabrics for a branded company. The aggregate sales value of the output of the 80 looms is Rs 5,00,000 and the monthly manufacturing expenses is Rs 1,50,000. Assume that each loom contributes equally to the sales and manufacturing expenses are evenly spread over the number of looms. Monthly establishment charges are Rs 75000. If one loom breaks down and remains idle for one month, the decrease in profit is:
(A) 13000
(B) 7000
(C) 10000
(D) 4375
(E) None of these
Rationale: Explanation :
Profit = 5,00,000âˆ’(1,50,000+75,000) =Rs. 2,75,000.
Since, such loom contributes equally to sales and manufacturing expenses.
But the monthly charges are fixed at Rs 75,000.
If one loan breaks down sales and expenses will decrease.
New profit :-
=>500000Ã—(79/80)âˆ’150000Ã—(79/80)âˆ’75000.
=>Rs 2,70,625.
Decrease in profit
=>2,75,000âˆ’2,70,625
=>Rs. 4,375
Answer : D
Answer: (D) 4375
Question: In a apartment, 30% of the people speak English, 20% speak Hindi and 10% speak both. If a people is selected at random, what is the probability that he has speak English or Hindi?
(A) 2/3
(B) 1/3
(C) 2/5
(D) 2/7
(E) 3/8
Rationale: P (E) = 30 / 100 = 3 / 10 , P (H) = 20 / 100 = 1 / 5 and P (E ∩ H) = 10 / 100 = 1 / 10
P (E or H) = P (E U H)
= P (E) + P (H) - P (E ∩ H)
= (3 / 10) + (1 / 5) - (1 / 10) = 4 / 10 = 2/5
C
Answer: (C) 2/5
Question: A 45° -45° - 90° right triangle has hypotenuse of length h. What is the area of the triangle W in terms of h?
(A) h/ √2
(B) h/2
(C) h/4
(D) (h)^2
(E) (h)^2/4
Rationale: IF...each of the two shorter sides = 3, then the hypotenuse = H = 3(root2).
The AREA W= (1/2)(Base)(Height) = (1/2)(3)(3) = 9/2.
So we're looking for an answer that = 9/2 when H = 3(root2). There's only one answer that matches...
E
Answer: (E) (h)^2/4
Question: In a stack of boards at a lumber yard, the 20th board counting from the top of the stack is immediately below the 15th board counting from the bottom of the stack. How many boards are in the stack?
(A) 38
(B) 36
(C) 35
(D) 34
(E) 33
Rationale: Counting from the top, after the 20th board, there are 13 boards left to count.
The answer is E.
Answer: (E) 33
Question: The size of a flat-screen television is given as the length of the screen’s diagonal. How many square inches greater is the screen of a square 34-inch flat-screen television than a square 27-inch flat-screen television?
(A) 106.75
(B) 213.5
(C) 427
(D) 729
(E) 1,156
Rationale: Diagonal of a square =√2*side of square
=> side =Diagonal/(√2)
Area of square =s*s
=(diagonal^2)/2
Difference of both tv's =(34^2-27^2)/2
=427
ANSWER:C
Answer: (C) 427
Question: Equal amount of water were poured into two empty jars of different capacities, which made one jar 1/3 full and other jar 1/2 full. If the water in the jar with lesser capacity is then poured into the jar with greater capacity, what fraction of the larger jar will be filled with water?
(A) 2/3
(B) 2/7
(C) 1/2
(D) 7/12
(E) 1/7
Rationale: Same amount of water made bigger jar 1/3 full, thenthe same amount of water(stored for a while in smaller jar) were added to bigger jar, so bigger jar is 1/3+1/3=2/3 full.
Answer: A.
Answer: (A) 2/3
Question: A can do a job in 20 days and B can do it in 30 days. A and B working together will finish twice the amount of work in ------- days?
(A) 14 days
(B) 16 days
(C) 24 days
(D) 11 days
(E) 19 days
Rationale: C
1/20 + 1/30 = 1/12
12 *2 = 24 days
Answer: (C) 24 days
Question: A man travels from A to B at a speed of 30 kmph and returns with a speed of 60 kmph. What is the average speed of the man?
(A) 47.5
(B) 50
(C) 45
(D) 40
(E) 30
Rationale: Explanation:
The average speed ‘v’, when a man travels two same distance with different speeds ‘v1’ and ‘v2’ is:
v = (2*v1*v2) / (v1 + v2)
In the above problem, v1 = 30 and v2 = 60
Therefore, v = (2*30*60)/(30 + 60) = 3600/90
v = 40
ANSWER D
Answer: (D) 40
Question: Ram and Raj start a business with investments of Rs. 2500 and Rs. 2250 respectively. After 2 months, Ram takes out Rs.1250 from his capital. After 1 more month, Raj takes out Rs.750 of his capital while Rakesh joins them with a capital of Rs. 3500. At the end of 6 months, they earn a profit of Rs. 2540. Which of the following is the share of each member in the profit ?
(A) Ram - Rs. 800, Raj - Rs. 900, Rakesh - Rs. 840
(B) Ram - Rs. 800, Raj - Rs. 900, Rakesh - Rs. 821
(C) Ram - Rs. 800, Raj - Rs. 200, Rakesh - Rs. 840
(D) Ram - Rs. 800, Raj - Rs. 900, Rakesh - Rs. 811
(E) Ram - Rs. 800, Raj - Rs. 100, Rakesh - Rs. 840
Rationale: Initial investment of Ram = Rs.2500.
After 2 months he withdraw Rs.1250 from his capital.
Therefore, we have, Ram invested Rs.2500 for 2 months and Rs.(2500-1250=) 1250 for 4 months.
Raj invested Rs. 2250 for 3 months and Rs.(2250-750=) 1500 for 3 months.
And, Rakesh invested Rs.3500 for 3 months;
Their investing ratio:
Ram:Raj:Rakesh = (2500x2 + 1250x4):(2250x3 + 1500x3):(3500x3)
= (10,000):(11,250):(10,500) = 1000:1125:1050 = 40:45:42
Total profit for 6 months = Rs.2540
Therefore, Ram's share = Rs.(2540 x 40/(40+45+42)) = Rs.(2540 x 40/127) = Rs.800
Raj's share = Rs.(2540 x 45/127) = Rs.900
Rakesh's share = Rs.(2540 x 42/127) = Rs.840
Answer: A
Answer: (A) Ram - Rs. 800, Raj - Rs. 900, Rakesh - Rs. 840
Question: In a bag there are coins of 50 paisa, 25 paisa and one rupee in the proportion 5:6:2. If there are in all Rs.42, the number of 25 paisa coins is?
(A) 76
(B) 42
(C) 17
(D) 14
(E) 44
Rationale: 5x 6x 2x
50 25 100
250x + 150x + 200x = 4200
600x = 4200
x = 7 => 6x = 42
Answer:B
Answer: (B) 42
Question: The difference between the compound interest compounded annually and simple interest for 2 years at 20% per annum is Rs.216. Find the principal?
(A) 2277
(B) 2667
(C) 5400
(D) 2766
(E) 1811
Rationale: P = 216(100/5)^2 => P = 5400
Answer: C
Answer: (C) 5400
Question: The shopkeeper increased the price of a product by 25% so that customer finds difficult to purchase the required amount. But Somehow the customer managed to purchase only 70% of the required amount. What is the net difference in the expenditure on that product ?
(A) 55 more
(B) 10% more
(C) 12.5% less
(D) 17.5% less
(E) None of these
Rationale: Solution: Let initially the quantity and rate be 100 each.
Quantity*rate = Expenditure
100*100 = 10000
Now, Increase in price is 25% and new quantity is 70% of original.
Quantity*rate = Expenditure
70*125 = 8750
Decreased expenditure,
= 10000-8750 = 1250
% decrease,
= (1250*100)/10000
= 12.5%.
Answer: Option C
Answer: (C) 12.5% less
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are drawn what is the probability that one is yellow and two are red?
(A) 12/455
(B) 24/455
(C) 3/91
(D) 15/91
(E) 15/111
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
When three marbles are drawn, the probability that one is yellow and two are red
= (²C₁)(⁴C₂)/¹⁵C₃
= (2 * 4 * 3 * 3 * 2)/(1 * 2 * 15 * 14 * 13) = 12/455
A)
Answer: (A) 12/455
Question: Audrey 4 hours to complete a certain job. Ferris can do the same job in 3hours. Audrey and Ferris decided to collaborate on the job, working at their respective rates. While Audrey worked continuously, Ferris took 6 breaks of equal length. If the two completed the job together in 2 hours, how many minutes long was each of Ferris’ breaks ?
(A) 2
(B) 5
(C) 15
(D) 20
(E) 25
Rationale: Audery and Ferris collective Work rate:
1/4 + 1/3 = 7/12
Collective work Time = 12/7 = 1.7 Hrs
Job Was actually done in = 2 (Includes breaks)
Breaks = Actual time taken - Collective work time
= 2 - 1.7
= .3 Hrs = 1/2
so ferrais took 6 breaks
=.3/6=.06 hrs = 5 m
so Answer is B) 10 mins
Answer: (B) 5
Question: There are eight leopards and one sheep.
Leopard can eat sheep but since as the land is magical, the leopards who eats the sheep , turns into sheep and then can be eaten by the remaining leopard(s).
If we leave them for some time then how many sheep and leopard will be there , when we come back ?
(A) 7 leopard and 1 sheep
(B) 4 leopard and 7 sheep
(C) 6 leopard and 4 sheep
(D) 5 leopard and 1 sheep
(E) 2 leopard and 5 sheep
Rationale: A
7 leopard and 1 sheep
since all animal are rational , once 1st leopard eats the sheep all the rest of leopard would know about this.
Answer: (A) 7 leopard and 1 sheep
Question: X starts a business with Rs.52000. Y joins in the business after 6 months with Rs.26000. What will be the ratio in which they should share the profit at the end of the year?
(A) 1:2
(B) 2:3
(C) 1:3
(D) 4:1
(E) None of these
Rationale: Explanation :
Ratio in which they should share the profit
= Ratio of the investments multiplied by the time period
= 52000 * 12: 26000 * 6
= 52 * 12: 26 * 6
= 24:6
= 4:1. Answer : Option D
Answer: (D) 4:1
Question: Positive integer n leaves a remainder of 2 after division by 6 and a remainder of 3 after division by 5. If n is greater than 30, what is the remainder that n leaves after division by 30?
(A) 3
(B) 12
(C) 18
(D) 22
(E) 28
Rationale: The theory says:
if a # x is devided by y and leave the positive # r as the remainder then it can also leave negative # (r-y) as the remainder.
e.g:
9 when devided by 5 leves the remainder 4 : 9=5*1+4
it can also leave the remainder 4-5 = -1 : 9=5*2 -1
back to the original qtn:
n leaves a remainder of 4 after division by 6 and a remainder of 3 after division by 5
==> n leaves a remainder of -2 (i.e. 4-6) after division by 6 and a remainder of -2 (i.e. 3-5) after division by 5
==> n when devided by 5 and 6 leaves the same remainder -2.
what is n?
LCM (5,6)-2 = 30-2 = 28
CHECK: 28 when devided by 6 leaves the remainder 4 and when devided by 5 leaves the remainder 3
However, the qtn says n > 30
so what is the nex #, > 28, that can give the said remainders when devided by 6 and 5
nothing but 28 + (some multiple of 6 and 5) as thissome multiple of 6 and 5will not give any remainder when devided by 5 or 6 but 28 will give the required remainders.
hence n could be anything that is in the form 28 + (some multiple of 6 and 5)
observe thatsome multiple of 6 and 5is always a multiple of 30 as LCM (5,6) = 30.
hence when n (i.e. 28 + some multiple of 6 and 5) is devided by 30 gives the remainder 12.
B
Answer: (B) 12
Question: Out of 40 consecutive integers, two are chosen at random. Find the probability that their sum is odd?
(A) 21/40
(B) 19/39
(C) 21/39
(D) 20/39
(E) 23/39
Rationale: Explanation :
Forty consecutive integers will have 20 even and 20 odd integers. The sum of 2 chosen integers will be odd, only if:
First is even and second is odd
First is odd and second is even
Mathematically the probability will be given by:
P(First is even) * P(Second is odd) + P(First is odd) * P(Second is even)
= (20/40) * (20/39) + (20/40) * (20/39)
= 20/39
Answer : D
Answer: (D) 20/39
Question: At what price must an article costing Rs.47.50 be marked in order that after deducting 9% from the list price. It may be sold at a profit of 25% on the cost price?
(A) 65.25
(B) 62.6
(C) 62.1
(D) 62.7
(E) 62.2
Rationale: CP = 47.50
SP = 47.50*(125/100) = 59.375
MP*(91/100) = 59.375
MP = 65.25
Answer: A
Answer: (A) 65.25
Question: A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?
(A) 2.91 m
(B) 3 m
(C) 5.82 m
(D) 6.72 m
(E) None of these
Rationale: Explanation:
Area of the park = (60 x 40) m2 = 2400 m2.
Area of the lawn = 2109 m2.
Area of the crossroads = (2400 - 2109) m2 = 291 m2.
Let the width of the road be x metres. Then,
60x + 40x - x2 = 291
x2 - 100x + 291 = 0
(x - 97)(x - 3) = 0
x = 3.
Answer: B
Answer: (B) 3 m
Question: Two trains of equal lengths take 8 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) 10.4
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: Speed of the first train = 120/8 = 15 m/sec.
Speed of the second train = 120/15 = 8 m/sec.
Relative speed = 15 + 8 = 23 m/sec.
Required time = (120 + 120)/23 = 10.4 sec.
Answer: Option A
Answer: (A) 10.4
Question: The square root of 25=5. What does the square root of a multiple of 25 has to end in for it to be a correct square root?
(A) 1 or 0
(B) 5 or 3
(C) 5 or 0
(D) 4 or 0
(E) 2 or 6
Rationale: Any multiple of 5 has to end in a 5 or a 0
Ex) 10 is a multiple of 5 because it ends in a 5
Ex2) 5*8=40, which means that 40 is a multiple of 5 because it ends in a 0
Correct answer is (C)
Answer: (C) 5 or 0