mathewhe/aqua_rat huggingface dataset:
Question: In how many ways 5 boys and 5 girls can be seated in a row so that boys and girls are alternate?
(A) 28400
(B) 28500
(C) 28600
(D) 28700
(E) 28800
Rationale: number of ways = 2*5!*5! = 28800
Answer is E
Answer: (E) 28800
Question: For how many integers k is (k^2)+3 = 3+(2^k) ?
(A) None
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: (2^2)+3= 3+(2^2)
(2^4)+3= 3+(4^2)
For k= 2 and 4 the above equality holds true.
Answer:Option C
Answer: (C) 2
Question: There are two pipes which are functioning simultaneouly to fill a tank in 12 hours, if one pipe fills the tank 10 hours faster than other then how many hours second pipe will take to fill the tank ?
(A) 30 hours
(B) 35 hours
(C) 40 hours
(D) 42 hours
(E) 41 hours
Rationale: Explanation:
Lets suppose tank got filled by first pipe in X hours,
So, second pipe will fill the tank in X + 10 hours.
=>1/X+1/X+10=1/12
=>X=20
ANSWER IS A
Answer: (A) 30 hours
Question: A train of length 180 metres takes 54 seconds to cross a tunnel of length 270 metres. What is the speed of the train in km/hr?
(A) 50 km/hr.
(B) 20 km/hr.
(C) 30 km/hr.
(D) 40 km/hr.
(E) None
Rationale: Sol.
Speed = [180 + 270 / 54] m/sec = [450 / 54 * 18/5] km/hr =30 km/hr.
Answer C
Answer: (C) 30 km/hr.
Question: If 7 ministers are to be seated at a round table conference, then how many different ways can they be seated?
(A) 24
(B) 60
(C) 720
(D) 520
(E) 180
Rationale: Simple formula:
There are (n - 1)! ways to arrange n distinct objects in a circle.
so its (7-1)! = 6! = 720=C
Answer: (C) 720
Question: The number which exceeds 12% of it by 52.8 is:
(A) 60
(B) 77
(C) 269
(D) 26
(E) 91
Rationale: Explanation:
Let the number be x. Then, x – 12% of x = 52.8
x – (12/100)x = 52.8
x (1– 12/100) = 52.8
(88/100)x = 52.8
x = (100 X 52.8) / 88 = 60
ANSWER: A
Answer: (A) 60
Question: How many prime numbers are between 15/7 and 131/6?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: 15/7= 3-
131/6= 22-
Prime numbers between 3 and 22 are 5, 7, 11, 13, 17, and 19
- sign signifies that the number is marginally less .
Answer D
Answer: (D) 6
Question: A boy has Rs. 320 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
(A) 60
(B) 110
(C) 140
(D) 130
(E) 120
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 320
16x = 320
x = 20.
Hence, total number of notes = 3x = 60.
A
Answer: (A) 60
Question: Find the odd man out. 1, 3, 10, 13, 19, 29
(A) 12
(B) 9
(C) 1
(D) 3
(E) 10
Rationale: 10 is an even number. All other given numbers are odd
Answer : Option E
Answer: (E) 10
Question: What is the probability that their sum of two numbers, randomly selected from the set {3,6,9,12,15,18} will be greater than 9?
(A) 7/6
(B) 7/9
(C) 7/8
(D) 7/10
(E) 6/7
Rationale: First7 problem is 6C2 = 12 .. Not 20..
Point 2, you sum should be greater than 9, so these are the following possibilities you have
({3,9},{3,12},{3,15},{3,18},{6,9},{6,12},{6,15},{6,18},{9,12},{9,15},{9,18},{12,15},{12,18},{15,18}) which leads to 14 pairs
So the probability is 14 on 12 or 7/6..
ANSWER:A
Answer: (A) 7/6
Question: Two letters from the word KHANTKAR are selected at random. What is the probability that at least one of the selected letters is a consonant?
(A) 25/28
(B) 27/28
(C) 30/28
(D) 40/28
(E) 50/28
Rationale: There are 6 consonants and 2 vowels in KHANTKAR .
probability that at least one of the selected letters is a consonant = 1 - (Probability of both vowels)
Probability of both vowels = 2C2/8C2 = 1/28
So,Answer is 1 - 1/28 = 27/28
Answer : B
Answer: (B) 27/28
Question: Working alone, Jim finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone. Jim alone cleans the entire house in 6 hours. How many hours will it take Nick and Jim to clean the entire house if they work together?
(A) 1.5
(B) 2
(C) 2.4
(D) 3
(E) 3.6
Rationale: Answer is 3.6 hours.
Jim does the complete house in 6 hours while Nick does it in 9 hours. 1/ (1/6+1/9)= 3.6
answer is E
Answer: (E) 3.6
Question: In a partnership between A, B and C. A's capital is Rs.5000. If his share of a profit of Rs.800 is Rs.200 and C's share is Rs.130, what is B's capital?
(A) 11758
(B) 11759
(C) 11755
(D) 11750
(E) 11751
Rationale: 200 + 130 = 330
800 - 330 = 470
200 ---- 5000
470 ---- ? => 11750
Answer: D
Answer: (D) 11750
Question: Choose the missing terms out of the given alternatives.
CMW, HRB, ?, RBL, WGQ, BLV
(A) MWS
(B) MWG
(C) SJE
(D) HHW
(E) YSH
Rationale: B
MWG
The letters move five steps forward.
Answer: (B) MWG
Question: Which of the following will divide evenly into 407,406,520?
(A) 11
(B) 21
(C) 4
(D) 31
(E) 41
Rationale: Rule:
4: Last two digits should be divisible by 4
the last two digits are 00, which are divisible by 4
Answer: C
Answer: (C) 4
Question: Two trains are running in opposite directions in the same speed. The length of each train is 120 meter. If they cross each other in 12 seconds, the speed of each train (in km/hr) is
(A) 30 Km/hr
(B) 36 Km/hr
(C) 80 Km/hr
(D) 90 Km/hr
(E) None of these
Rationale: Explanation:
Distance covered = 120+120 = 240 m
Time = 12 s
Let the speed of each train = x.
Then relative velocity = x+x = 2x
2x = distance/time = 240/12 = 20 m/s
Speed of each train = x = 20/2 = 10 m/s
= 10*18/5 km/hr = 36 km/hr
Option B
Answer: (B) 36 Km/hr
Question: A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is?
(A) 128
(B) 177
(C) 199
(D) 178
(E) 150
Rationale: Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 15 => y = x/15
x + 100 / 25 = x / 15
x = 150 m.
Answer:E
Answer: (E) 150
Question: Two employees X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
(A) Rs.200
(B) Rs.250
(C) Rs.300
(D) Rs.350
(E) Rs.370
Rationale: Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 550
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 550
⇒ y[12/10 + 1] = 550
⇒ 22y/10 = 550
⇒ 22y = 5500
⇒ y = 5500/22 = 500/2 = Rs.250
B)
Answer: (B) Rs.250
Question: The area of playground is 5700 sq. meters. What will be the cost of covering it with grass sheet 1cm deep, if cost of grass sheet is $2.80 per cubic meter.
(A) a) $144
(B) b) $150.50
(C) c) $159.6
(D) d) $158.60
(E) e) $160.70
Rationale: total volume * unit cost = total cost
or, 5700 * 0.01 * 2.8 = total cost = 159.6=C
Answer: (C) c) $159.6
Question: A man has Rs. 400 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
(A) 45
(B) 60
(C) 75
(D) 90
(E) 105
Rationale: Answer : C
Let number of notes of each denomination be x.
Then, x + 5x + 10x = 400
16x = 400
x = 25.
Hence, total number of notes = 3x = 75.
Answer: (C) 75
Question: An design manager has 10patterns of chairs & 9patterns of tables. In how many ways can he make a pair of table & chair?
(A) 20
(B) 40
(C) 80
(D) 90
(E) 100
Rationale: He has has ten patterns of chairs and eight patterns of tables
Hence, A chair can be arranged in 10 ways and
A table can be arranged in 9 ways
Hence one chair and one table can be arranged in 10 x 9 ways = 90 ways
D
Answer: (D) 90
Question: The perimeter of a square is 52 m. Find the area of the square.
(A) 161 m².
(B) 164 m².
(C) 166 m².
(D) 169 m².
(E) 273 m².
Rationale: Perimeter of square = 52 m
But perimeter of square = 4 × side
Therefore, 4 × side = 52 m
Therefore, side= 52/4 m = 13m
Now, the area of the square = (side × side)
Therefore, area of the square = 13 × 13 m² = 169 m².
ANSWER : OPTION D
Answer: (D) 169 m².
Question: Find the distance covered by a man walking for 36min at a speed of 10km/hr?
(A) 1km
(B) 3km
(C) 6 km
(D) 5km
(E) 6km
Rationale: Distance = 10*36/60 =6 km
Answer is C
Answer: (C) 6 km
Question: A train 2500 m long can cross an electric pole in 100 sec and then find the speed of the train?
(A) 90
(B) 60
(C) 120
(D) 180
(E) 360
Rationale: Length = Speed * time
Speed = L/T
S = 2500/100
S = 25 M/Sec
Speed= 25*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 90 Kmph
Answer:A
Answer: (A) 90
Question: The list price of an article is Rs.70. A customer pays Rs.59.22 for it. He was given two successive discounts, one of them being 10%. The other discount is?
(A) 8%
(B) 7%
(C) 10%
(D) 12%
(E) 6%
Rationale: Option E
Explanation:
70*(90/100)*((100-x)/100) = 59.22
x = 6%
Answer: (E) 6%
Question: Sushil got thrice as many marks in English as in Science. His total marks in English, Science and Maths are 162. If the ratio of his marks in English and Maths is 3:5, find his marks in Science?
(A) 18
(B) 68
(C) 67
(D) 55
(E) 56
Rationale: S:E = 1:3
E:M = 3:5
------------
S:E:M = 3:9:15
3/27 * 162
= 18
Answer:A
Answer: (A) 18
Question: Kail purchased n items from a catalog for $10 each. Postage and handling charges consisted of $4 for the first item and $1 for each additional item. Which of the following gives the total dollar amount for Kim’s purchase, including postage and handling, in terms of n ?
(A) 11n + 2
(B) 11n + 4
(C) 11n + 3
(D) 9n + 3
(E) 9n + 4
Rationale: its C
n items for $10 each
total price $10n
postage and handling of $4 for 1st item and $1 for the rest
total postage and handling = $ [4+ (n-1)]
= $ n+3
total cost
10n+n+3 = 11n+3
Answer: (C) 11n + 3
Question: In a school of 850 boys, 46% of Muslims, 28% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities?
(A) A)136
(B) B)627
(C) C)153
(D) D)721
(E) E)159
Rationale: 46 + 28 + 10 = 84%
100 – 84 = 16%
850 * 16/100 = 136
Answer:A
Answer: (A) A)136
Question: A tank can be filled by pipe A in 5 hours and by pipe B in 8 hours, each pump working on its own. When the tank is full and a drainage hole is open, the water is drained in 20 hours. If initially the tank was empty and someone started the two pumps together but left the drainage hole open, how long does it take for the tank to be filled?
(A) 2.6 hours
(B) 3.6 hours
(C) 4.6 hours
(D) 5.6 hours
(E) None of these
Rationale: Let's first find the rates of the pumps and the drainage hole
pump A: 1 / 5 , pump B: 1 / 8 , drainage hole: 1 / 20
Let t be the time for the pumps to fill the tank. The pumps ,add water into the tank however the drainage hole drains water out of the tank, hence
t ( 1 / 5 + 1 / 8 - 1 / 20) = 1
Solve for t
t = 3.6 hours
Answer B
Answer: (B) 3.6 hours
Question: A certain company’s profit in 1996 was 15 percent greater than its profit in 1995, and its profit in 1997 was 20 percent greater than its profit in 1996. The company’s profit in 1997 was what percent greater than its profit in 1995?
(A) 5%
(B) 18%
(C) 33%
(D) 35%
(E) 38%
Rationale: Soln:-
Profit in 1995 - 100
Profit in 1996 - 115
%increase Profit in 1997 in comparison to 1995 = 15 + 115*20%= 38%
ANSWER:E
Answer: (E) 38%
Question: What is the value of x?
Data 1: x - 2y = 7
Data 2: 4x – 28 = 8y
(A) 89
(B) 10
(C) 12
(D) 15
(E) no solution exists
Rationale: both are same equations
4X(x-2y=7) is 4x-8y=28
so no solution exists
ANSWER:E
Answer: (E) no solution exists
Question: The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is
(A) 4/5
(B) 7/11
(C) 7/13
(D) 7/15
(E) 8/11
Rationale: Let the required fraction be x. Then	1	- x =	9
x	20
1 - x2	=	9
x	20
20 - 20x2 = 9x
20x2 + 9x - 20 = 0
20x2 + 25x - 16x - 20 = 0
5x(4x + 5) - 4(4x + 5) = 0
(4x + 5)(5x - 4) = 0
x =	4/5
A)
Answer: (A) 4/5
Question: A box contains 8 apples, 7 of which are red. An apple is drawn from the box and its color is noted before it is eaten. This is done a total of n times, and the probability that a red apple is drawn each time is less than 0.5. What is the smallest possible value of n?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: P(choosing a red apple 5 times in a row) = 7/8*6/7*5/6*4/5*3/4 = 3/8 < 0.5
The answer is C.
Answer: (C) 5
Question: When not moving on the sidewalk, Maya can walk the length of the sidewalk in 7 minutes. If she stands on the sidewalk as it moves, she can travel the length in 4 minutes. If Maya walks on the sidewalk as it moves, how many minutes will it take her to travel the same distance? Assume she always walks at the same speed, and express your answer as a decimal to the nearest tenth.
(A) 2.9
(B) 2.5
(C) 2.7
(D) 2.1
(E) 2.2
Rationale: Explanation:
Assume distance of sidewalk "x"
Speed 1 (moving on sidewalk)
Speed 2 (moving off sidewalk)
Since both the movements are in same direction, we can do speed 1 + speed 2
Speed 1 = x4x4
Speed 2 = x7x7
Speed 1 + speed 2 = 11x2811x28 = = 0.39286x
Now new time while moving on sidewalk = x0.39286xx0.39286x = 2.54544
Hence, the answer is 2.5
Answer: B
Answer: (B) 2.5
Question: There are 21 balls in a jar: 14 red, 4 blue and 3 green. If a single ball is drawn from the jar, what is the probability of that it is either blue or red?
(A) 1/12
(B) 3/4
(C) 6/9
(D) 6/7
(E) 3/4
Rationale: Blue + Red =18
Total number of balls is 14+4+3=21
So the answer is 18/21=6/7
Answer D
Answer: (D) 6/7
Question: A train is walking at 6/7 of its usual speed, the train is 20 minutes too late. Find its usual time to cover the journey.
(A) 1 hour
(B) 30min
(C) 3 hours 20 min
(D) 2 hours 30 min
(E) 2 hours
Rationale: new speed = 6/7 of the usual speed
new time taken = 7/6 of the usual time taken
so, ( 7/6 of the usual time ) - ( usual time ) = 20min
1/6 of the usual time = 20min
usual time = 20*6 = 120 min = 2 hours
correct option is E
Answer: (E) 2 hours
Question: A boy has nine trousers and 12 shirts. In how many different ways can he select a trouser and a shirt?
(A) 109 ways
(B) 908 ways
(C) 128 ways
(D) 108 ways
(E) 104 ways
Rationale: The boy can select one trouser in nine ways.
The boy can select one shirt in 12 ways.
The number of ways in which he can select one trouser and one shirt is 9 * 12 = 108 ways.
Answer:D
Answer: (D) 108 ways
Question: How many meters are there in 770 centimeters?
(A) 770 meters
(B) 7.6 meters
(C) 700 meters
(D) 6.5 meters
(E) 7.7 meter
Rationale: Solution:
1 meter = 100 centimeters
Just divide 770 by 100
770 Ã· 100 = 7.7, so there are 7.7 meters in 770 centimeters
Option E
Answer: (E) 7.7 meter
Question: A shopkeeper sold an article at $1800 with 20% profit. Then find its cost price?
(A) $1000
(B) $1500
(C) $1850
(D) $1600
(E) $2000
Rationale: cost price = selling price *100/(100+profit)
C.P. = 1800*100/120 = $1500
Answer is B
Answer: (B) $1500
Question: For what values of k will the pair of equations 3(3x + 4y) = 36 and kx + 12y = 30 does not have a unique solution?
(A) 12
(B) 9
(C) 3
(D) 7.5
(E) 2.5
Rationale: we have 2 equations
1. 3(3x + 4y) = 36 --> 3x + 4y = 12 -- > 9x + 12y = 36
2. kx + 12y = 30
substract 1-2, we get (9-K)x = 6
i.e. x = 6/(9-k)
then, by looking at options, we get some value of x except for B. When we put k=9, x becomes 6/0 and hence answer is B
Answer: (B) 9
Question: A and B invests Rs.8000 and Rs.9000 in a business. After 4 months, A withdraws half of his capital and 2 months later, B withdraws one-third of his capital. In what ratio should they share the profits at the end of the year?
(A) 32:45
(B) 32:47
(C) 32:45
(D) 32:41
(E) 32:42
Rationale: A : B
(8000*4)+(4000*8) : (9000*6)+(6000*6)
64000 : 90000
32 : 45.Answer: A
Answer: (A) 32:45
Question: Workers decided to raise Rs.3lacs by equal contribution from each. Had they contributed Rs.50 eachextra, the contribution would have been Rs.3.25lacs. How many workers were they?
(A) 350
(B) 400
(C) 500
(D) 550
(E) 590
Rationale: N * 50 = (325000 - 300000) = 25000
N = 25000 / 50
= 500
C
Answer: (C) 500
Question: In how many ways can 12 different gifts be divided among four children such that each child receives exactly three gifts?
(A) 16^3
(B) (4!)^3
(C) 12!/(3!)^4
(D) 12!/4!
(E) 4^12
Rationale: Total 12 different Gifts, and 4 children.
Thus any one child gets 12C3 gifts,
then the other child gets 9C3 gifts(12 total - 3 already given),
then the third one gets 6C3 gifts,
and the last child gets 3C3 gifts.
Since order in which each child gets the gift is not imp, thus, ans :
12C3 * 9C3 * 6C3 * 3C3 = 12! / (3!)^4
Ans : C.
Answer: (C) 12!/(3!)^4
Question: Find the value of x in (8x-6)=10.
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: (8x-6)=10
Adding both sides with 6 gives 8x=16
Dividing both sides with 8 gives x=2
Answer: B
Answer: (B) 2
Question: The sum of three integers A, B and C is 180. A is one third of the sum of B and C and B is one fifth of the sum of A and C. What is C?
(A) 120
(B) 125
(C) 105
(D) 115
(E) 110
Rationale: A is one third of the sum of B and C..
or A=1/3(B+C)...
But A+B+C=180.
so 1/3(B+C)+B+C=180
4(B+C)/3= 180
B+C =180*3/4 = 135
A=180-135=45
2)B is one fifth of the sum of A and C
or B=1/5(A+C)...
But A+B+C=180
so 1/5(A+C)+A+C=180
A+C=180*5/6=150
but A=45, so C=150-45=105
Answer : B
Answer: (B) 125
Question: What is (24^7+24) / 24?
(A) 159202573
(B) 160902641
(C) 172502765
(D) 182302834
(E) 191102977
Rationale: (24^7+24) / 24 =
24*(24^6+1) / 24 =
24^6 + 1
Clearly this is a number which ends with a 7 in the units place.
The answer is E.
Answer: (E) 191102977
Question: A man gets a simple interest of Rs.400 on a certain principal at the rate of 5% p.a in eight years. Find the compound interest the man will get on twice the principal in two years at the same rate?
(A) s.256.27
(B) s.256.29
(C) s.205.00
(D) s.256.22
(E) s.256.25
Rationale: Let the principal be Rs.P
S.I at 5% p.a in 8 years on Rs.P = Rs.400
(P)(8)(5)/100 = 400
P = 1000
C.I on Rs.2P i.e., Rs.2000 at 5% p.a in two years
=2000{ [1 + 5/100]^2 - 1} =
= 2000(41/ 400)
= Rs.205
Answer:C
Answer: (C) s.205.00
Question: A bag contains 3 blue and 5 white marbles. One by one, marbles are drawn out randomly until only two are left in the bag. What is the probability C that out of the two, one is white and one is blue?
(A) 15/56
(B) 41/56
(C) 13/28
(D) 15/28
(E) 5/14
Rationale: The required probability C= probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls.
Ways to select 6 out of total 8 = 8C6
Ways to select 4 out of 5 white balls = 5C4
Ways to select 2 out of 3 blue balls = 3C2
Thus the required probability = (5C4*3C2)/8C6 = 15/28.
D is thus the correct answer.
Answer: (D) 15/28
Question: Of 120 applicants for a job, 56 had at least 4 years' experience, 72 had degrees, and 12 had less than 4 years' experience and did not have a degree.How many of the applicants had at least 4 years' experience and a degree?
(A) 10
(B) 15
(C) 22
(D) 20
(E) 24
Rationale: 120 - 12 = 108
108 - 56 - 72 = -20
Then 20 are in the intersection between 4 years experience and degree.
Answer : D
Answer: (D) 20
Question: Eleven books consisting of 5 financial management, 4 marketing management and 2 system management are placed on a shelf at random order. What is the probability that the books of each kind are all together.
(A) 1/1155
(B) 1/1255
(C) 1/1355
(D) 1/1455
(E) 1/1555
Rationale: (Probability of an event) = (Favorable) / (Total)
The total number of ways to arrange 11 books in a row is 11!.
3 groups of books: financial management (F), marketing management (M) and system management (S), can be arranged in 3! ways: FMS, FSM, MFS, MSF, SFM, and SMF (this way all the books of each kind will be together). Now, books in F itself can be arranged in 5! ways, in M in 4! ways and in S in 2! ways. Hence, the total number of ways to arrange books so that books of each kind are together is 3!*5!*4!*2!.
P = (3!*5!*4!*2!) / 11! = 1/1155.
Answer: A
Answer: (A) 1/1155
Question: The inverse ratio of 3: 2: 1 is?
(A) 2:3:8
(B) 4:3:6
(C) 2:3:2
(D) 2:3:6
(E) 2:3:1
Rationale: 1/3: 1/2: 1/1
= 2:3:6
Answer: D
Answer: (D) 2:3:6
Question: Which of the following MUST yield an integer when divided by 11?
(A) The sum of eleven consecutive positive integers.
(B) The square of a prime number.
(C) The sum of two odd integers.
(D) The product of three consecutive odd numbers.
(E) The difference between a multiple of 8 and a multiple of 3.
Rationale: For option A: Let the numbers be (x-5), (x-4), (x-3), (x-2), (x-1), (x), (x+1), (x+2), (x+3), (x+4), (x+5).
Now, (x-5)+(x-4)+(x-3)+(x-2)+(x-1) + (x) + (x+1) + (x+2)+(x+3)+(x+4)+(x+5) = 11(x). Hence A is true. No need to check other answers since there can only be one correct answer.
So, Ans(A).
Answer: (A) The sum of eleven consecutive positive integers.
Question: A coach must choose five starters from a team of 12 players. How many different ways can the coach choose the starters ?
(A) 722
(B) 729
(C) 278
(D) 299
(E) 271
Rationale: Explanation:
Choose 5 starters from a team of 12 players. Order is not important.
\inline {\color{Black} 12C_{5}}= 729
Answer: B) 729
Answer: (B) 729
Question: Barbata invests $2400 in the National Bank at 5%. How much additional money must she invest at 8% so that the total annual income will be equal to 8% of her entire investment?
(A) 1200
(B) 3000
(C) 1000
(D) 3600
(E) 2400
Rationale: Let the additional invested amount for 8% interest be x;
Equation will be;
2400+0.05*2400+x+0.08x = 2400+x+0.08(2400+x)
0.05*2400+0.08x = 0.06x+0.08*2400
0.02x = 2400(0.08-0.05)
x = 2400*0.03/0.02 = 3600
Ans:D
Answer: (D) 3600
Question: One side of the bottom layer of a triangular pyramid has 12 balls. How many are there in the whole pyramid?Note that the pyramid is equilateral and solid.
(A) 286
(B) 364
(C) 504
(D) 164
(E) 165
Rationale: As there are 12 balls along one side, it means that there are 12 layers of balls. The top most layer has 1 ball. The second layer has 3 (1+2) balls. The third layer has 6 (1+2+3) balls. The fourth layer has 10 (1+2+3+4) balls. The fifth layer has 15 (1+2+3+4+5) balls. Similarly, there are 21, 28, 36, 45, 55, 66 and 78 balls in the remaining layers.
Hence, the total number of balls are
= 1 + 3 + 6 + 10 + 15 + 21 +28 + 36 + 45 + 55 + 66 + 78
= 364 balls
ANSWER:B
Answer: (B) 364
Question: Marcella has 25 pairs of shoes. If she loses 9 individual shoes, what is the greatest number of matching pairs she could have left?
(A) 21
(B) 20
(C) 19
(D) 16
(E) 15
Rationale: greatest number of paired shoes means greatest number of lost pairs
9 shoes have 4 pairs and 1 extra shoes of a pair .so a otal of 5 pairs she loses
leftover pair=20
ANSWER:B
Answer: (B) 20
Question: A welder received an order to make a 1 million liter cube-shaped tank. If he has only 4x2 meter sheets of metal that can be cut, how many metal sheets will be required for this order Y? (1 cubic meter = 1,000 liters)
(A) 92
(B) 90
(C) 82
(D) 78
(E) 75
Rationale: I get 75. A cube with 1 million liters cube would be a cube with the dimensions of 100*100*100. 4*2 covers 8 sq liters so 100/8 = 12.5.
Y=12.5*6 = 75.E
Answer: (E) 75
Question: A merchant can buy goods at the rate of Rs. 20 per good. The particular good is part of an overall collection and the value is linked to the number of items that are already on the market. So, the merchant sells the first good for Rs. 2, second one for Rs. 4, third for Rs. 6…and so on. If he wants to make an overall profit of at least 40%, what is the minimum number of goods he should sell?
(A) 24
(B) 18
(C) 27
(D) 32
(E) 34
Rationale: DETAILED SOLUTION
Let us assume he buys n goods.
Total CP = 20n
Total SP = 2 + 4 + 6 + 8 ….n terms
Total SP should be at least 40% more than total CP
2 + 4 + 6 + 8 ….n terms ≥ 1.4 * 20 n
2 (1 + 2 + 3 + ….n terms) ≥ 28n
n(n + 1) ≥ 28n
n2 + n ≥ 28n
n2 - 27n ≥ 0
n ≥ 27
He should sell a minimum of 27 goods.
Answer Choice (C)
Answer: (C) 27
Question: 65% of x = 20% of 747.50. Find the value of x?
(A) 100
(B) 230
(C) 150
(D) 180
(E) 199
Rationale: 65% of x = 20% of 747.50
Then, 65/100 * x = 20/100 * 7475/10
x = 230
Answer is B
Answer: (B) 230
Question: The sum of two numbers is 528 and their H.C.F is 33. The number of pairs of numbers satisfying the above conditions is:
(A) 4
(B) 5
(C) 6
(D) 6
(E) 1
Rationale: Let the required numbers be 33a and 33b.
Then, 33a + 33b = 528 => a + b = 16.
Now, co-primes with sum 16 are (1, 15), (3, 13), (5, 11) and (7, 9).
Required numbers are (33 * 1, 33 * 15), (33 * 3, 33 * 13), (33 * 5, 33 * 11), (33 * 7, 33 * 9).
The number of such pairs is 4.
Answer:A
Answer: (A) 4