mathewhe/aqua_rat huggingface dataset:
Question: The marks obtained by Vijay and Amith are in the ratio 4:5 and those obtained by Amith and Abhishek in the ratio of 3:2. The marks obtained by Vijay and Abhishek are in the ratio of?
(A) 6:8
(B) 6:9
(C) 6:5
(D) 6:2
(E) 6:3
Rationale: 4:5
3:2
-------
12:15:10
12:10
6:5
Answer:C
Answer: (C) 6:5
Question: Ramesh start a bike at 1pm. and rides it at 50kmph. Mahesh started at 2pm with his car at 70kmph. When will Mahesh overtake Ramesh?
(A) 4:30
(B) 5:10
(C) 3:00
(D) 6:10
(E) 5:30
Rationale: Suppose bike is overtaken by car xhrs after 1pm
Distance covered by the bike in x hrs = distance covered by the car in x-1 hr
50x = 70(x-1)
20x = 70
x = 7/2 hrs
Required time = 1+3.5 = 4:30pm
Answer is A
Answer: (A) 4:30
Question: When the integer k is divided by 7, the remainder is 3. Which of the following expressions below when divided by 7, will have a remainder of 5?
I. 4k + 7
II. 6k + 1
III. 8k + 5
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II and III
Rationale: k = 7j + 3
4k + 7 = 28j + 12 + 7 = 28j + 14 + 5
6k + 1 = 42j + 18 + 1 = 42j + 14 + 5
8k + 5 = 56j + 24 + 5 = 56j + 28 + 1
The answer is D.
Answer: (D) I and II only
Question: Company X sells a selection of products at various price points. Listed below are unit sales made for one particular day. How many unit sales on that day were greater than the mean sale price but less than the median sale price?
$50, $50, $97, $97, $97, $120, $125, $155, $199, $199, $229
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: Taking the prices of products in ascending order(already arranged)
$50, $50, $97, $97, $97, $120, $125, $155, $199, $199, $229
we see that median value is the 6th value as there in total 11 values given
Arithmetic mean = total/number of entries = 1418/11 =128.9090
We are asked to find how many unit sales on that day were greater than the mean sale price but less than the median sale price
as we can clearly see that there is one value between $120 and $128.90, answer is 1 unit
Correct Answer - B
Answer: (B) 1
Question: A boy divided the numbers 7654, 8506 and 9997 by a certain largest number and he gets same remainder in each case. What is the common remainder?
(A) 199
(B) 200
(C) 28
(D) 12
(E) 25
Rationale: If the remainder is same in each case and remainder is not given, HCF of the differences of the numbers is the required largest number
9997 - 7654 = 2343
9997 - 8506 = 1491
8506 - 7654 = 852
Hence, the greatest number which divides 7654, 8506 and 9997 and leaves same remainder
= HCF of 2343, 1491, 852
= 213
Now we need to find out the common remainder.
Take any of the given numbers from 7654, 8506 and 9997, say 7654
7654 ÷ 213 = 35, remainder = 199
Answer is A
Answer: (A) 199
Question: The population of a small beach town on Australia's east coast grows by 50% from May 1 to June 1 and then grows by another 50% from June 1 to July 1. The population then decreases by 11.11% from July 1 to August 1. By approximately what percentage has the population grown from May 1 to August 1?
(A) 50%
(B) 90%
(C) 100%
(D) 200%
(E) 225%
Rationale: Pop Aug1 = Pop May1 * (3/2) * (3/2) * (8/9) = Pop May1 * 2
Population of August is twice the population of May. So it has grown by 100%.
Answer (C)
Answer: (C) 100%
Question: If 5a + 7b = m, where a and b are positive integers, what is the largest possible value of m for which exactly one pair of integers (a, b) makes the equation true?
(A) 35
(B) 48
(C) 69
(D) 70
(E) 74
Rationale: 5*a1 + 7*b1 = m
5*a2 + 7*b2 = m
5*(a1 - a2) = 7*(b2 - b1)
since we are dealing with integers we can assume that a1 - a2 = 7*q and b2 - b1 = 5*q where q is integer, so whenever we get a pair for (a;b) we can find another one by simply adding 7 to a and subtracting 5 from b or vice versa, subtracting 7 from a and adding 5 to b.
Lets check how it works for our numbers, starting from the largest:
E)74 = 5*12 + 7*2 (a1 = 12, b1 = 2), subtract 7 from a and add 5 to b respectively, so a2 = 5 and b2 = 7, second pair - bad
D)70 = 5*7 + 7*5 (a1 = 7, b1 = 5), if we add 7 toawe will have to subtract 5 from b but b can't be 0, so - no pair, if we subtract 7 froma, we'll get a = 0 which also isn't allowed - no pair, thus this is the only pair for (a;b) that works,good!, thus
D is the answer
Answer: (D) 70
Question: The average of six numbers is x and the average of three of these is y. If the average of the remaining three is z, then
(A) x = y + z
(B) 2x = y + z
(C) 3x = 2y - 2z
(D) 3x = 9y - 2z
(E) 3x = 2y - 1z
Rationale: Explanation:
Clearly, we have : x = (3y + 3z ) / 6 or 2x = y + z
Answer: B
Answer: (B) 2x = y + z
Question: n the given series, you can find a set of numbers. Of course, there is a particular pattern that has been followed here with every progressing set.
Find the pattern and complete the series.
(2 + 6), (21 + 6), (58 + 6), (119 + 6), ___
(A) 215
(B) 216
(C) 217
(D) 218
(E) none
Rationale: Solution:
(210 + 6)
Explanation:
If you add the numbers, you will find that they add up to be 8, 27, 64 and 125.
8 = 2^3
27 = 3^3
64 = 4^3
125 = 5^3
Thus the next sum should be 6^3 = 216.
Since 6 has been added in each set, the first number will be (216 - 6) = 210.
Hence, the missing set will be (210 + 6).
Answer B
Answer: (B) 216
Question: How many different positive integers exist between 10^6 and 10^7, the sum of whose digits is equal to 2?
(A) 6
(B) 7
(C) 5
(D) 8
(E) 18
Rationale: So, the numbers should be from 1,000,000 to 10,000,000
The following two cases are possible for the sum of the digits to be 2:
1. Two 1's and the rest are 0's:
1,000,001
1,000,010
1,000,100
1,001,000
1,010,000
1,100,000
6 numbers.
2. One 2 and the rest are 0's:
2,000,000
1 number.
Total = 7 numbers.
Answer: B.
Answer: (B) 7
Question: A tailor trims 7 feet from opposite edges of a square piece of cloth, and 5 feet from the other two edges. If 45 square feet of cloth remain, what was the length of a side of the original piece of cloth?
(A) 13
(B) 15
(C) 17
(D) 19
(E) 21
Rationale: Let the original side of the square be x.
(x-14)*(x-10) = 45 = 5*9
x = 19
The answer is D.
Answer: (D) 19
Question: If z is not equal to zero, and z=6zs−9s2−−−−−−−−√z=6zs−9s2, then z equals:
(A) s
(B) 3s
(C) 4s
(D) -3s
(E) -4s
Rationale: squaring on both the sides gives Z^2 = 6ZS -9S^2
= Z^2-6ZS+9S^2
= Z(Z-3S) -3S(Z-3S)
= (Z-3S) (Z-3S)
= Z = 3S
Answer = B
Answer: (B) 3s
Question: 9, 12, 11, 14, 13, ?, 15
(A) 12
(B) 16
(C) 15
(D) 17
(E) 10
Rationale: Alternatively, 3 is added and one is subtracted.
Answer : B.
Answer: (B) 16
Question: For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when m is even. What is [7]*[4] equivalent to?
(A) [28]
(B) [84]
(C) [42]
(D) [48]
(E) [14]
Rationale: [7]*[4] = 21*2 = 42 = (1/2)(84) = [84]
The answer is B.
Answer: (B) [84]
Question: A 6 litre sol is 25% alcohol .How many litres of pure alcohol must be added to produce a sol that is 50% alcohol ?
(A) A.0.6
(B) B.1
(C) C.2.1
(D) D.3
(E) E.5.4
Rationale: 25% of 6 = 1.5
50% of 6 = 3
shortage is 1.5
so we need to have 1.5/50% to get 50% alcohol content.
= 3 D
Answer: (D) D.3
Question: How many digits 2^300 has?
(A) 31
(B) 35
(C) 50
(D) 91
(E) 101
Rationale: 2^10 = 1.024 * 10^3 => 2^100 = (1.024)^10 * 10^90
therefore 91 digits would be my best guess
D
Answer: (D) 91
Question: 6 wires are by average 80 cm long each. If the average length of one third of the wires is 70 cm, what is the average of the other wires?
(A) 75.
(B) 85.
(C) 90.
(D) 94.
(E) 100.
Rationale: Edit:
Given ( X1 + X2 ... + X6 ) / 6 = 80
( X1 + X2 ... + X6 ) = 480 --> Eq 1.
Now given avg length of one third wires is 70. That means out 6 / 3 = 2 wires.
let the avg length of two wires be ( X1 + X2 ) / 2 = 70 .
( X1 + X2 ) = 140. --> eq 2.
Now we are asked to find the average of the remaining i.e. ( X3 + X4 + X5 + X6 )
Substitute eq 2 in eq 1 then we get
140 + X3 + X4 + X5 + X6 = 480
=> X3 + X4 + X5 + X6 = 340
Now divide 340 by 4 we get 85.
=> ( X3 + X4 + X5 + X6) / 4 = 85 = avg length of remaining wires.
IMO correct option is B.
Answer: (B) 85.
Question: Three numbers are in the ratio 4 : 5 : 6 and their average is 36 . The largest number is:
(A) 28
(B) 32
(C) 43.2
(D) 42
(E) 45
Rationale: Explanation:
Let the numbers be 4x, 5x and 6x. Therefore,
(4x+5x+6x)/3 = 36
15x = 108
x = 7.2
Largest number = 6x = 43.2.
ANSWER C
Answer: (C) 43.2
Question: If A and B together can finish a work in 16 days.A can finish same work alone in 24 days then B alone can finish same work alone in how many days?
(A) 30 days
(B) 48 days
(C) 40 days
(D) 36 days
(E) 50 days
Rationale: (A+B) work in 1 day = 1/16, A work in 1 day= 1/24
B work in 1 day=[1/16-1/24]=1/48.
B alone can finish same work in 48 days.
Answer B
Answer: (B) 48 days
Question: A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.1 m and its walls are 5 cm thick. The thickness of the bottom is:
(A) 90 cm
(B) 1 dm
(C) 1 m
(D) 1.1 cm
(E) None of these
Rationale: Explanation:
Let the thickness of the bottom be x cm.
Then , [(330 - 10) × (260 - 10) × (110 - x)] = 8000 × 1000
=> 320 × 250 × (110 - x) = 8000 × 1000
=> (110 - x) = 8000×1000/320=
100
=> x = 10 cm = 1 dm.
Answer: B
Answer: (B) 1 dm
Question: A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length.
(A) 20 seconds
(B) 27 seconds
(C) 30 seconds
(D) 40 seconds
(E) 50 seconds
Rationale: Speed = 45 Km/hr = 45*(5/18) m/sec
= 25/2 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
=500∗2/25=40seconds
answer :D
Answer: (D) 40 seconds
Question: In an examination, 40% of total students failed in Hindi, 40% failed in English and 15% in both. The percentage of these who passed in both the subjects is :
(A) 10%
(B) 20%
(C) 30%
(D) 40%
(E) 50%
Rationale: pass percentage = 100 - (40+45-15) = 100-70 = 30
ANSWER:C
Answer: (C) 30%
Question: The speed of a car is 60 km in the first hour and 30 km in the second hour. What is the average speed of the car?
(A) 45 kmph
(B) 65 kmph
(C) 75 kmph
(D) 85 kmph
(E) 90 kmph
Rationale: Explanation:
S = (60 + 30)/2 = 45 kmph
A)
Answer: (A) 45 kmph
Question: K-numbers are positive integers with only 2's as their digits. For example, 2, 22, and 222 are K-numbers. The K-weight of a number n is the minimum number of K-numbers that must be added together to equal n. For example, the K-weight of 50 is 5, because 50 = 22 + 22 + 2 + 2 + 2. What is the K-weight of 550?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 15
Rationale: 550 = 2*222 + (22*4) + 9*2
K weight of 600 = 2 +4+9 = 15
Answer E
Answer: (E) 15
Question: For all positive integers m and v, the expression m Θ v represents the remainder when m is divided by v. What is the value of (( 96 Θ 33 ) Θ 17 ) - ( 94 Θ (33 Θ 17)) ?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: (( 96 Θ 33 ) Θ 17 )
The remainder of 96 divided by 33 is 30;
The remainder of 30 divided by 17 is 13;
( 97 Θ (33 Θ 17))
The remainder of 33 divided by 17 is 16;
The remainder of 94 divided by 16 is 1.
13 - 2 = 11.
Answer: D.
Answer: (D) 11
Question: An amount of money is to be distributed among Faruk, Vasim and Ranjith in the ratio 3 : 5 : 9. If Vasims share is Rs. 1500, what is the difference between Faruk's and Ranjith's shares?
(A) s 1800
(B) s 1500
(C) s 1600
(D) s 1900
(E) s 1700
Rationale: Explanation :
Let P = Faruk, Q = Vasim, R = Ranjith
Let P = 3x, Q = 5x and R = 9x.
Then, 5x = 1500 ? x = 300. P=900,Q=1500 and R = 2700.
Hence, (R - p) = (2700 - 900) = 1800
Answer : A
Answer: (A) s 1800
Question: The length of a rectangular floor is more than its breadth by 200%. If Rs. 100 is required to paint the floor at the rate of Rs. 2 per sq m, then what would be the length of the floor?
(A) 12.25
(B) 44
(C) 18
(D) 16
(E) 14
Rationale: Let the length and the breadth of the floor be l m and b m respectively.
l = b + 200% of b = l + 2b = 3b
Area of the floor = 100/2 = 50 sq m
l b = 50 i.e., l * l/3 = 150
l2 =150 => l = 12.25
Answer:A
Answer: (A) 12.25
Question: Seven children — A, B, C, D, E, F, and G — are going to sit in seven chairs in a row. Child C must be somewhere to the left of child D. How many possible configurations are there for the children?
(A) 630
(B) 1260
(C) 2520
(D) 3780
(E) 5040
Rationale: The number of ways to seat 7 people is 7! = 5040.
Child C will sit to the left of Child D in exactly half of these arrangements.
The total number of possible arrangements is 5040/2 = 2520
The answer is C.
Answer: (C) 2520
Question: When tossed, a certain coin has equal probability of landing on either side. If the coin is tossed 4 times, what is the probability that it will land on the same side each time?
(A) 1/8
(B) 1/4
(C) 1/16
(D) 1/2
(E) 1/32
Rationale: Must be either 4 tails or 4 heads
1/2*1/2*1/2*1/2+1/2*1/2*1/2*1/2
1/16 + 1/16 = 1/8
Answer: A
Answer: (A) 1/8
Question: The length of the longest rod that can fit in a cubical room of 4 m side is?
(A) 100%
(B) 108%
(C) 120%
(D) 110%
(E) 101%
Rationale: 100%
Answer:A
Answer: (A) 100%
Question: A, B and C are entered into a partnership. A invested Rs.6500 for 6 months, B invested Rs.8400 for 5 months and C invested for Rs.10000 for 3 months. A is a working partner and gets 5% of the total profit for the same. Find the share of C in a total profit of Rs.7400?
(A) 2998
(B) 1900
(C) 2788
(D) 2662
(E) 1122
Rationale: 65 * 6 : 84 * 5 : 100 * 3
26:28:20
C share = 74000 * 95/100 = 7030 * 20/74
=> 1900
Answer:B
Answer: (B) 1900
Question: In the coordinate plane, points (x, 2) and (10, y) are on line k. If line k passes through the origin and has slope 1/2, then x + y =
(A)  4.5
(B)  7
(C)  9
(D)  11
(E)  12
Rationale: Line k passes through the origin and has slope 1/2 means that its equation is y=1/2*x.
Thus: (x, 2)=(4, 2) and (10, y) = (10,5) --> 4+5=2+5=9.
Answer: C.
Answer: (C)  9
Question: Rani bought more apples than oranges. She sells apples at ₹23 apiece and makes 15% profit. She sells oranges at ₹10 apiece and makes 25% profit. If she gets ₹653 after selling all the apples and oranges, find her profit percentage X.
(A) 16.8%
(B) 17.4%
(C) 17.9%
(D) 18.5%
(E) 19.1%
Rationale: Given: Selling price of an Apple = 23 --> Cost price = 23/1.15 = 20
Selling price of an orange = 10 --> Cost price = 10/1.25 = 8
A > O
23*(A) + 10*(O) = 653
653 - 23*(A) has to be divisible by 10 --> Units digit has to be 0
Values of A can be 1, 11, 21, 31, .... --> 1 cannot be the value
Between 11 and 21, If A = 11, O = 30 --> Not possible
If A = 21, O = 17 --> Possible
Cost price = 20*21 + 8*17 = 420 + 136 = 556
Profit = 653 - 556 = 97
Profit% X= (97/556)*100 = 17.4%
Answer: B
Answer: (B) 17.4%
Question: Leo has an average price of Rs.57 on every item in his shopping cart. At the last minute he decided to get rid of apple juice worth Rs. 80 and get orange juice worth Rs. 60. If his shopping cart has 4 items, what is his new average?
(A) 48
(B) 52
(C) 56
(D) 57
(E) 60
Rationale: Sum of prices of items before replacement= 57x4=228
Sum of ages of employees after replacement=(57x4)+60-80=208
The new average age=208/4=52
Answer: B
Answer: (B) 52
Question: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
(A) 2356
(B) 3467
(C) 4567
(D) 5189
(E) 5184
Rationale: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62
E
Answer: (E) 5184
Question: If in the word 'DISTURBANCE', the first letter is interchanged with the last letter, the second letter is interchanged with the tenth letter and so on, which letter would come after the letter T in the newly formed word ?
(A) S
(B) C
(C) T
(D) R
(E) U
Rationale: The new letter sequence is E C N A B R U T S I D
Clearly, S comes after T
ANSWER A
Answer: (A) S
Question: A person travels 12 km in the southward direction and then travels 5km to the right and then travels 15km toward the right and
finally travels 5km towards the east, how far is he from his starting place?
(A) 5.5 kms
(B) 3 km
(C) 13 km
(D) 6.4 km
(E) 7.4 km
Rationale: 12 km south then 5km right means in west direction again he moves 15 km towards right means north direction then he moves 5 km east....In this 5km in both east &west directions will cancel with each other.Remaining is in north and south directions,as he moves 15km,12km in the respective directions.The distance (15-12)=3km
ANSWER:B
Answer: (B) 3 km
Question: Company A imported 10,500 widgets made of either brass or aluminum. The widgets are painted blue, red or green. If 10 percent of the widgets are made of brass and of those 20 percent are painted red and 40 percent are painted blue how many brass widgets painted green were imported?
(A) 480
(B) 840
(C) 1050
(D) 420
(E) 2100
Rationale: Answer A.
We are told that 10% of all imported widgets are made of brass and of those, 20% are red and 40% are blue. Since we know that there are only three colors, the remaining 40% must be green. 40% blue of 10% brass widgets leads to 4% green brass widgets out of the total 10,550 widgets.
10,500 /100 * 4 = 420.
Answer D.
Answer: (D) 420
Question: What is the characteristic of the logarithm of 0.0000134?
(A) 5
(B) -5
(C) 6
(D) -6
(E) 7
Rationale: log (0.0000134). Since there are four zeros between the decimal point and the first significant digit, the characteristic is –5.
answer : B
Answer: (B) -5
Question: A farmer has a field that measures 1000 ft wide by 2000 ft long. There is an untillable strip 20 ft wide on the inside edge of the field, and a 30 ft wide untillable strip bisects the field into two squares (approximate). Approximately what percentage of the field is tillable?
(A) 98%
(B) 93%
(C) 91%
(D) 90%
(E) 88%
Rationale: Total Area = 1000*2000
Tillable Square's side horizontally = (2000-20-30-20)/2 = 1930/2 = 965
Tillable Square's side vertically = (1000-20-20) = 960 = 960
Consider it as 960:
Why approximated to 93 and not 91 because we shortened one side from 965 to 960. Thus, in reality the squares are bigger.
Ans: "B"
Answer: (B) 93%
Question: Rectangle ABCD is constructed in the coordinate plane parallel to the x- and y-axes. If the x- and y-coordinates of each of the points are integers which satisfy 6 ≤ x ≤ 11 and -5 ≤ y ≤ 5, how many possible ways are there to construct rectangle ABCD?
(A) 396
(B) 1260
(C) 825
(D) 7920
(E) 15840
Rationale: As the rectangle is parallel to coordinate axes, the coordinates of the points of the rectangle would be
(X1, Y1), (X2, Y1), (X2, Y2), (X1,Y2)
given that X1, X2 lie between 6 and 11..ie., 6 possible numbers
Possible combinations for X1,X2 would be 6C2 = 15
Similarly, Possible combinations for Y1, Y2 would be 11C2 = 55
Possible ways of constructing rectangle is by selecting any of the combination of X1,X2 and Y1,Y2
= 15 * 55 = 825
Ans. C
Answer: (C) 825
Question: A committee has 5 men and 6 women. What are the number of ways of selecting a group of eight persons?
(A) 110
(B) 140
(C) 250
(D) 987
(E) 165
Rationale: Explanation:
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: E
Answer: (E) 165
Question: Two clocks were set right at noon on Sunday. One gains 2 min and the other loses 3 min in 24 hours. What will be the true time when the first clock indicates 3 pm on Wednesday?
(A) 2 : 38 pm
(B) 2 : 54 pm
(C) 2 : 23 pm
(D) 2 : 48 pm
(E) None of these
Rationale: Time from noon on Sunday to 3 pm on Wednesday = 75 hours.
24 hours 2 minutes of the first clock = 24 hours of the correct one.
⇒ 1 hour of the first clock = 24 × (30/721) hours of correct one.
⇒ 75 ours of the first clock
= 24 × 30 × (75/721) hours of correct one
= 54000/721 hours = 74 hours 53.7 min.
Hence the answer is 2 : 54 pm.
Answer B
Answer: (B) 2 : 54 pm
Question: In a fuel station the service costs $1.75 per car, every liter of fuel costs 0.65$. Assuming that a company owns 12 cars and that every fuel tank contains 50 liters and they are all empty, how much money total will it cost to fuel all cars?
(A) 320$
(B) 380$
(C) 420$
(D) 450$
(E) 411$
Rationale: Total Cost = ( 1.75*12 ) + ( 0.65 * 12 * 50) = 21 + 390 => 411
Hence answer will be (E)
Answer: (E) 411$
Question: Find the value of m 72519 x 9999 = m?
(A) 724533811
(B) 353654655
(C) 545463251
(D) 725117481
(E) 477899932
Rationale: 72519 x 9999 = 72519 x (10000 - 1)
= 72519 x 10000 - 72519 x 1
= 725190000 - 72519
= 725117481
D
Answer: (D) 725117481
Question: For each of her sales, a saleswoman receives a commission equal to 20 percent of the first $500 of the total amount of the sale, plus 25 percent of the total amount in excess of $500. If the total amount of one of her sales was $800, the saleswoman’s commission was approximately what percent of the total amount of the sale?
(A) 22%
(B) 24%
(C) 25%
(D) 27%
(E) 28%
Rationale: Total sales =800
Comission = (20/100)*500+ (25/100)*300
=100 + 75
=175
%Comission =(175/800)*100=21.8~ 22%
Answer is A
Answer: (A) 22%
Question: In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?
(A) 54000
(B) 50400
(C) 40500
(D) 45000
(E) None of them
Rationale: In the word 'CORPORATION', we treat the vowels OOAIO as one letter.
Thus, we have CRPRTN (OOAIO).
This has 7 (6 + 1) letters of which R occurs 2 times and the rest are different.
Number of ways arranging these letters = 7!/2! = 2520.
Now, 5 vowels in which O occurs 3 times and the rest are different, can be arranged
in 5!/3!= 20 ways.
Required number of ways = (2520 x 20) = 50400.
Answer is B.
Answer: (B) 50400
Question: The diagonals of a rhombus are 12 cm and 20 cm. Find its area?
(A) 176
(B) 186
(C) 120
(D) 179
(E) 172
Rationale: 1/2 * 12 * 20
= 120
Answer:C
Answer: (C) 120
Question: 99,997^2 - 3^2 =
(A) 10^10 - 2
(B) (10^5 – 2)^2
(C) 10^4(10^5 – 2)
(D) 10^5(10^5 – 6)
(E) 10^5(10^5 – 2)
Rationale: (99,997)^2 - (3)^2 = (100,000 -3)^2 - (3)^2 = (100,000)^2 - 2*3*100,000 + 3^2-3^2=(10^5)^2 - 2*3*(10^5) = 10^10 - 6*(10^5)=10^5(10^5 - 6) Answer D
Answer: (D) 10^5(10^5 – 6)
Question: The average of first 10 prime numbers is?
(A) 10.11
(B) 12.9
(C) 12.11
(D) 13.11
(E) 14.11
Rationale: Sum of 10 prime no. = 129
Average = 129/10 = 12.9
Answer : B
Answer: (B) 12.9
Question: Set A contains four different positive odd integers and six different positive even integers. Set B contains two different positive odd integers and three different positive even integers. If one integer from set A and one integer from set B are chosen at random, what is the probability that the product of the chosen integers is even?
(A) 3/5
(B) 4/5
(C) 17/25
(D) 21/25
(E) 43/50
Rationale: There can be an odd product only if both integers are odd.
P(odd product) = 4/10*2/5 = 4/25
P(even product) = 1 - 4/25 = 21/25
The answer is D.
Answer: (D) 21/25
Question: A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
(A) 150 m
(B) 165 m
(C) 155 m
(D) 160 m
(E) 170 m
Rationale: Length of the train be ‘X’
X + 150/15 = X + 250/20
4X + 600 = 3X + 750
X = 150m
ANSWER:A
Answer: (A) 150 m
Question: The ratio between the length and the breadth of a rectangular plot is 7 : 5. If the perimeter of the plot is 216 metres, what is its area?
(A) 1325 sq.metres
(B) 1260 sq.metres
(C) 2835 sq.metres
(D) 3380 sq.metres
(E) None of these
Rationale: Let the length and breadth be 7x and 5x respectively.
Then, P = 2(7x + 5x) = 216 â‡’ x = 9
Area = 7 Ã— 9 Ã— 5 Ã— 9 = 2835 sq.m.
Answer C
Answer: (C) 2835 sq.metres
Question: A boy was asked to find 7/9 of x. But he divided the x by 7/9, Thus he got 32more thanthe answer. Find the x.
(A) 43
(B) 45
(C) 59
(D) 63
(E) 65
Rationale: x/7/9 = 9x/7 = 32 + y
Actualy he should do 7x/9 = y
y = (9x/7) - 32
y = (9x - 224)/7
(9x - 224)/7 = 7x/9
81x - 2016 = 49x
81x - 49x = 2016
32x = 2016
x = 63
D
Answer: (D) 63
Question: A small table has a length of 12 inches and a breadth of b inches. Cubes are placed on the surface of the table so as to cover the entire surface. The maximum side of such cubes is found to be 4 inches. Also, a few such tables are arranged to form a square. The minimum length of side possible for such a square is 20 inches. Find b.
(A) 8
(B) 16
(C) 4
(D) 32
(E) 48
Rationale: From the info that the maximum sides of the cubes is 4, we know that the GCF of 12 (=2^2*3) andbis 4 (=2^2), sob=2^x, where x>=2.
From the second premise, we know that the LCM of 12 (2^2*3) andbis 20 (2^2*5), sob=2^2 or 2^2*5(4 or 20).
Combining 2 premises shows the answer is C(4).
Answer: (C) 4