mathewhe/aqua_rat huggingface dataset:
Question: A invested $15000 in a business after 6months B invested $18000 in the business. End of the year if they got $16000 as profit. Find B shares?
(A) $10000
(B) $12000
(C) $5000
(D) $6000
(E) $7500
Rationale: A:B = 15000*12:18000*6
A:B = 5:3
A's share = 16000*5/8 = 10000
B's share = 16000*3/8 = 6000
Answer is D
Answer: (D) $6000
Question: For a certain exam,a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean.What was the mean score W for the exam?
(A) 74
(B) 76
(C) 78
(D) 80
(E) 82
Rationale: A score of 58 was 2 standard deviations below the mean --> 58 = Mean - 2d
A score of 98 was 3 standard deviations above the mean --> 98 = Mean + 3d
Solving above for Mean W= 74.
Answer: A.
Answer: (A) 74
Question: If x and y are both odd prime numbers and x < y, how many distinct positive integer W factors does 2xy have?
(A) 3
(B) 4
(C) 6
(D) 8
(E) 12
Rationale: Since 2xy prime W factors are x^1*y^1*2^1, its total number or factors must be (1+1)(1+1)(1+1)=2^3=8. Thus, I think D would be the correct answer.
Answer: (D) 8
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow?
(A) 2/28
(B) 2/29
(C) 2/21
(D) 2/29
(E) 2/20
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = ³C₂/¹⁵C₂ = (3 * 2)/(15 * 14) = 1/35
Probability that both are yellow = ²C₂/¹⁵C₂ = (2 * 1)/(15 * 14) = 1/105
Probability that one blue and other is yellow = (³C₁ * ²C₁)/¹⁵C₂ = (2 * 3 * 2)/(15 * 14) = 2/35
Required probability = 1/35 + 1/105 + 2/35
= 3/35 + 1/105 = 1/35(3 + 1/3)
= 10/(3 * 35) = 2/21
Answer: C
Answer: (C) 2/21
Question: There are 7 players in a chess group, and each player plays each of the others once. Given that each game is played by two players, how many total games will be played?
(A) 21
(B) 30
(C) 45
(D) 60
(E) 90
Rationale: 7 players are there.
two players play one game with one another.
so 7C2=7*6/2
=21
SO OPTION A is correct
Answer: (A) 21
Question: In e is a positive integer smaller than 200 and (14e)/60 is an integer, then e has how many different positive prime factors?
(A) 2
(B) 3
(C) 5
(D) 6
(E) 8
Rationale: 7e/30 tells us that e is a factor of 30, which has 2, 3, and 5 as its prime factors. Each of them is distinct. Moreover, all multiples of 30 less than 200 can be derived by multiplying these prime factors alone. Thus, number of different prime factors is 3.
Answer: B
Answer: (B) 3
Question: A merchant marks his goods up in such a way that the profit made on selling 30 articles is equal to the cost price of 20 articles. What is the W % profit made by the merchant?
(A) 66.67 %
(B) 50 %
(C) 200 %
(D) 100 %
(E) 33.33 %
Rationale: C.P of 1 article= $30(say)
C.P of 20 articles=30*20=$600
Now, C.P of 20 articles=Profit on 30 articles
Therefore, profit on 1 article=$600/30=$20
Profit W%=(20/30)*100=66.67%
Answer A
Answer: (A) 66.67 %
Question: A man fixed an appointment to meet the manager, Manager asked him to come two days after the day before the day after tomorrow. Today is Friday. When will the manager expect him?
(A) Sunday
(B) monday
(C) tuesday
(D) wednesday
(E) thursday
Rationale: 1 2 3 4 5 6 7
sun mon tue wed thu fri sat
today is friday=6
by question
day after tommorrow i.e.sunday
day before sunday=saturday
now 2 days after saturday i.e.monday
hence answer is monday..
ANSWER:B
Answer: (B) monday
Question: Thirty men take 20 days to complete a job working 9 hours a day.How many hour a day should 40 men work to complete the job?
(A) 8 hrs
(B) 7 1/2 hrs
(C) 7 hrs
(D) 9 hrs
(E) 19 hrs
Rationale: As it is not given, in how many days 40 men have to complete the job, so considering same days(=20) in which 30 men completes the job.
So If 40 men works for 'x' hours/day for 20 days, then Total men hours=30*20*9 = 40*20*x
x=(30*20*9)/40*20)= 27/4= 6 3/4
ANSWER:E
Answer: (E) 19 hrs
Question: There are 10 teams in a certain league and each team plays each of the other teams exactly once. What is the total number of games played?
(A) 30
(B) 36
(C) 42
(D) 45
(E) 50
Rationale: 10C2 = 45
The answer is D.
Answer: (D) 45
Question: A train 160 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
(A) 40 sec
(B) 50 sec
(C) 44 sec
(D) 24 sec
(E) 60 sec
Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 160 + 140 = 300 m
Required time = 300 * 2/25 = 24 sec
Answer:D
Answer: (D) 24 sec
Question: How many words can be formed by using all letters of the word ‘BEIJING’ ?
(A) 4050
(B) 720
(C) 120
(D) 5040
(E) 770
Rationale: Solution
The word BEIJING contains 7 different letters.
Required number of words = 7P7 = 7 ! = (7 x 6 x 5 x 4 x 3 x 2 x 1) = 5040
Answer D
Answer: (D) 5040
Question: Express 60 mps in kmph?
(A) 200
(B) 182
(C) 216
(D) 127
(E) 400
Rationale: 60 * 18/5 = 216 kmph
Answer:C
Answer: (C) 216
Question: Eight women can do a work in 10 days. Ten men can complete the same work in 6 days. What is the ratio between the capacity of a man and a woman?
(A) 1:2
(B) 2:1
(C) 2:3
(D) 4:3
(E) None of these
Rationale: Explanation:
(8Ã— 10) women can complete the work in 1 day.
âˆ´ 1 woman's 1 day's work = 1/80
(10 Ã— 6) men can complete the work in 1 day.
âˆ´ 1 man's 1 day's work = 1/60
so, required ratio =1/80 : 1/60= 4:3
Answer: D
Answer: (D) 4:3
Question: If 0 < y< 1 < z, which of the following must be true?
(A) 1 < 1/y < 1/z
(B) 1/y< 1 < 1/z
(C) 1/y< 1/z< 1
(D) 1/z< 1 < 1/y
(E) 1/z< 1/y< 1
Rationale: 0<y<1<z. Let y=1/2 and z=2
Substituting values:
A. 1<2<1/2 ---Wrong
B. 2<1< 1/2 ---Wrong
C. 2<1/2<1 ---Wrong
D. 1/2<1<2 ---Correct
E. 1/2<2<1 ---Wrong
Hence answer is D
Answer: (D) 1/z< 1 < 1/y
Question: The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is
(A) 22
(B) 21
(C) 28
(D) 27
(E) 31
Rationale: Lot the total number of workers be v Then,
8OOOv = (12000 * 7) + 6000 (v - 7) <=> 2000v = 42000 <=> v = 21.
Answer: B
Answer: (B) 21
Question: Rita is twice as old as Rama. Three years ago, she was three
times as old as Rama. How old is Rita now?
(A) 11 years
(B) 12 years
(C) 13 years
(D) 14 years
(E) 15 years
Rationale: If present age of Rita=x & Rama=y, then
x=2y ---(i) &
x-3=3*(y-3) or x-3y=-6 ---(ii)
On solving (i) & (ii), x=12, y=6
ANSWER:B
Answer: (B) 12 years
Question: If a and b are positive integers such that a/b = 0.68, which of the following must be a divisor of a?
(A) 12
(B) 13
(C) 22
(D) 25
(E) 17
Rationale: 1) A and B are positive INTEGERS
2) A/B = 0.68
A = 68
B = 100
68/100 = 0.68
These values are NOT the smallest possible values though (since they're both even, we can divide both by 2)...
A = 34
B = 50
34/50 = 0.68
This can be further reduced to:
A = 17
B = 25
There is no other way to reduce this fraction, so A must be a multiple of 17 and B must be an equivalent multiple of 25. At this point though, the value of B is irrelevant to the question. We're asked for what MUST divide into A....
Since A is a multiple of 17, we have to 'factor-down' 17. This gives us only 17, apart from 1. So this integer MUST be a factor of A. You'll find the match in the answer choices.
Answer: E
Answer: (E) 17
Question: If the ratio of the roots of the equation x2+px+q=0 is equal to that of the roots x2+rx+s=0, then:
(A) sq=pr
(B) qp=sr
(C) sq=p
(D) ps=qr
(E) none
Rationale: x2+px+q=0 for this eqn... roots are R1=-p R2=-q
x2+rx+s=0 for this eqn... roots are R3=-r R4=-s
As per Question, -p/-q=-r/-s
=> ps=qr
ANSWER:D
Answer: (D) ps=qr
Question: A sum of money doubles in 12 years. In how many years, it will treble at S.I.
(A) 12 years
(B) 8 years
(C) 6 years
(D) 24 years
(E) 36 years
Rationale: Explanation :
Simple Interest, SI = PRT/100
i.e, SI ∝ T when rate(R) and principal (P) are constants
Let x be the sum of money and which will treble in n years
(Please note that when the money doubles, simple interest is 2x - x = x
and when the money trebles, simple interest is 3x - x = 2x)
(2x-x) ∝ 12
=> x ∝ 12 -------------(1)
(3x-x) ∝ n
=> 2x ∝ n -------------(2)
From (1) and (2),
x/2x=12/n 1/2=12/n⇒n = 24 years
i.e, in 24 years, the money will treble
Answer : Option D
Answer: (D) 24 years
Question: If the operation ∆ is defined by a ∆ b = (b - a)^2/a^2 for all numbers a and b, and a ≠ 0, then what is the result when we evaluate this expression: (-3) ∆ (3 ∆ −3) ?
(A) 47/6
(B) 49/9
(C) 36/25
(D) 25/16
(E) 16/9
Rationale: (-3) ∆ (3 ∆ − 3) =
(-3) ∆ (6^2/3^2) =
(-3) ∆ (4) =
(-7^2) / (-3)^2 = 49/9
The answer is B.
Answer: (B) 49/9
Question: In how many ways, a committee of 5 members can be selected from 9 men and 5 ladies, consisting of 3 men and 2 ladies?
(A) 75
(B) 552
(C) 775
(D) 840
(E) 912
Rationale: (3 men out 9) and (2 ladies out of 5) are to be chosen
Required number of ways = (9C3 * 5C2) = 840
Answer is D
Answer: (D) 840
Question: A certain plant was 11 feet long on the day it was plantedthe length grows by a constant amount everyday(inc. the first day it was planted).
if this plant grew by 70% b/w the 4th day and 10 th day after it was planted ,how many feet per day does the plant grow
(A) a) 2
(B) b) 4.5
(C) c) 2.41
(D) d) 5.5
(E) e) 3
Rationale: If the plant is 11 feet tall when it is planted, it will be 11 + k feet tall at the end of the day (where k is the constant length it grows by every day).
Similarly, at the end of the 4th day the plant must be 11 + 4k feet tall and at the end of the 10th day it must be 11 + 10k feet tall.
Therefore 6k = 0.7 (11 + 4k)
=> k = 2.41
Therefore the plant grows by 1 feet every day.
Option (C)
Answer: (C) c) 2.41
Question: A person bought 115 glass bowls at a rate of Rs. 18 per bowl. He sold 104 of them at Rs. 20 and the remaining broke. What is the percentage gain for A?
(A) 40
(B) 300/11
(C) 243/7
(D) 279/11
(E) 100/207
Rationale: CP=115*18=2070 and SP=104*20=2080
Gain %= 100*(2080-2070)/2070= 100/207
ANSWER:E
Answer: (E) 100/207
Question: When 242 is divided by a certain divisor the remainder obtained is 11. When 698 is divided by the same divisor the remainder obtained is 18. However, when the sum of the two numbers 242 and 698 is divided by the divisor, the remainder obtained is 9. What is the value of the divisor?
(A) 11
(B) 17
(C) 13
(D) 20
(E) None of these
Rationale: let that divisor be x
since remainder is 11 or 18 it means divisor is greater than 18.
now 242-11=231 =kx (k is an integer and 234 is divisble by x)
similarly 698-18=680 = lx (l is an integer and 689 is divisible by x)
adding both 698 and 242
= (231+680)+11+18
=x(k+l) + 29
when we divide this number by x then remainder will be equal to remainder of (29 divided by x) = 9 hence x = 29-9 = 20
hence D
Answer: (D) 20
Question: 9 students bought burgers for $143 dollars. If the bill has to be divided among these students, how much amount should be added to the amound to make it
divided amoung them equally in dollars(in whole number of dollars)
(A) $1
(B) $2
(C) $3
(D) $4
(E) $5
Rationale: In order to divide the sum in 9 parts, the amount must be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 143 = 8 and 9 is divisible by 9.
Hence, we need to add 1 to this number for it to be divisible by 9
Correct Option: A
Answer: (A) $1
Question: In what time will a train 125 m long cross an electric pole, it its speed be 130 km/hr?
(A) 3.5
(B) 2.7
(C) 2.9
(D) 2.3
(E) 2.1
Rationale: Speed = 130 * 5/18 = 36 m/sec
Time taken = 125/36
= 3.5 sec.
Answer: A
Answer: (A) 3.5
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
(A) 22
(B) 88
(C) 48
(D) 99
(E) 22
Rationale: Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 * 6/125 = 48 sec
Answer: C
Answer: (C) 48
Question: In the quadrilateral PQRS d=10 cm, h1=4.6 cm and
h2=2.3 cm. Find the area
(A) 21
(B) 22
(C) 23
(D) 34.5
(E) 25
Rationale: area of quad.=1/2*any diagonal*(sum of 2 perpendiculars which is drawn on that diagona)
so 1/2*10*(4.6+2.3)=34.5
ANSWER:D
Answer: (D) 34.5
Question: Which of the following numbers is two more than the square of an odd integer?
(A) 14,173
(B) 14,361
(C) 15,253
(D) 15,737
(E) 16,131
Rationale: If a square has an odd unit's digit, then its ten's digit must be even.
Only 16,131-2 = 16,129 satisfies this condition.
The answer is E.
Answer: (E) 16,131
Question: Find the odd man out. 6, 13, 18, 25, 30, 37, 40
(A) 40
(B) 30
(C) 37
(D) 25
(E) 15
Rationale: Explanation :
The difference between two successive terms from the beginning are 7, 5, 7, 5, 7, 5
Hence, in place of 40, right number is 37 + 5=42, Answer : Option A
Answer: (A) 40
Question: In the infinite sequence 2, 4, 6, 8, 10, . . . , where each term is 2 greater than the previous term, the 72th term is
(A) 144
(B) 263
(C) 176
(D) 344
(E) 287
Rationale: T(n) = a + (n-1) d
Here d =2, a=2, n=72
Solving we get T(n) =144.
Answer: A
Answer: (A) 144
Question: A and B go around a circular track of length 600 m on a cycle at speeds of 24 kmph and 60 kmph. After how much time will they meet for the first time at the starting point?
(A) 120 sec
(B) 176 sec
(C) 178 sec
(D) 180 sec
(E) 189 sec
Rationale: Time taken to meet for the first time at the starting point
= LCM { length of the track / speed of A , length of the track / speed of B}
= LCM { 600/ (24 * 5/18) , 600/ (60 * 5 /18) }
=180 sec.
Answer: D
Answer: (D) 180 sec
Question: 3 candidates in an election and received 3136, 7636 and 11628 votes respectively. What % of the total votes did the winning candidate got in that election?
(A) 45%
(B) 49%
(C) 52%
(D) 59%
(E) 61%
Rationale: Total number of votes polled = (3136 + 7636 + 11628) = 22400
So, Required percentage = 11628/22400 * 100 = 52%
C
Answer: (C) 52%
Question: By selling 22 pens for a rupee a woman loses 10%. How many for a rupee should he sell in order to gain 50%?
(A) 12
(B) 14
(C) 45
(D) 13
(E) 65
Rationale: D
90% --- 22
150% --- ?
90/150 * 22 = 13
Answer: (D) 13
Question: The edges of three iron cubes are 6cm; 8cm; 10cm respectively. A new cube was made by melting them. Find the edge of the new cube?
(A) 8 cm
(B) 12 cm
(C) 14 cm
(D) 10 cm
(E) 15 cm
Rationale: 63 + 83 + 103 = a3 => a = 12
ANSWER:B
Answer: (B) 12 cm
Question: Sheik Abdullah decides to buy 3 new cars for his collection. If he has to choose between nine different cars, what is the number of purchasing possibilities he has?
(A) A)304
(B) B)404
(C) C)504
(D) D)604
(E) E)704
Rationale: Sheik Abdullah decides to buy 3 new cars for his collection. He has to choose between nine different cars
8C3= 9*8*7*6/(3*2*1) = 504 ANS:C
Answer: (C) C)504
Question: A string of 25 light bulbs is wired in such a way that if any individual light bulb fails, the entire string fails. If for each individual light bulb the probability of failing during time period T is 0.06, what is the probability that the string of light bulbs will fail during the time period T?
(A) 0.06
(B) (0.06)^25
(C) 1 - (0.06)^25
(D) 1 - (0.94)^25
(E) (0.94)^25
Rationale: The string of light bulbs will fail if at least one light bulb fails. So, let's find the probability of the opposite event and subtract that value from 1.
The opposite event is when none of the 25 light bulbs fails, since the probability of each light bulb not to fail is 1-0.06=0.94 the probability that none of the 25 light bulbs fails is 0.94^25.
Hence, the probability that at least one light bulb fails is 1-0.94^25.
Answer: D.
Now, you should have spotted that your reasoning was not right because of one simple thing, consider the case when we have 100 light bulbs instead of 25, then according to your logic the probability that the string of light bulbs will fail would be 100*0.06=6, which is not possible since the probability of an event cannot be more than 1 (100%).
Answer: (D) 1 - (0.94)^25
Question: The distance between A&B is 750km. A person is traveling from A to B at 80km/hr started at 10AM and another person is traveling from B to A at 70km/hr and started at same time. Then at what time they meet together.?
(A) A)2PM
(B) B)4PM
(C) C)3PM
(D) D)1PM
(E) E)5PM
Rationale: Let x hours be they will meet together
distance covered by 1st person+distance covered by 2nd person = 750km
70x+80x = 750
x= 5 hr
They will meet = 10AM +5hr = 3PM
Answer is C
Answer: (C) C)3PM
Question: A milk man has 40 liters of milk. If he mixes 5 liters of water, which is freely available, in 20 liters of pure milk.If the cost of pure milk is Rs.18 per liter,then the profit of the milkman, when he sells all the mixture at cost price is:
(A) 20%
(B) 25%
(C) 45%
(D) 18%
(E) None of these
Rationale: Explanation:
when the water is freely available and all the water is sold at the price of the milk, then the water gives the profit on the cost of 40 liters of milk.
Therefore, profit percentage = 45 %. Answer: C
Answer: (C) 45%
Question: In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can?
(A) 65
(B) 44
(C) 86
(D) 29
(E) 26
Rationale: Let the capacity of the can be T litres.
Quantity of milk in the mixture before adding milk = 4/9 (T - 8)
After adding milk, quantity of milk in the mixture = 6/11 T.
6T/11 - 8 = 4/9(T - 8)
10T = 792 - 352 => T = 44.
Answer: B
Answer: (B) 44
Question: The juice stall at the circus stocked just 2 brands of orange juice tetra packs. Brand A costs $1 per pack and brand B costs $1.5 per pack. Last week , brand A contributed to a% of stall’s revenue and accounted for b% of sales of juice tetra packs. Which of the following expresses a in terms of b?
(A) 100b/(150 – b)
(B) 200b/(250-b)
(C) 200b/(300-b)
(D) 250b/(400-b)
(E) 300b/(500-b)
Rationale: 1. Let the number of units sold be 100. Then n units of A are sold and (100-n) units of B are sold.
Total revenue= Revenue due to A + Revenue due to B
= (No.of units of A sold * Cost/unit of A) + (No.of units of B sold * cost/unit of B)
= b *1 + (100-b) *1.5
= b + (150-1.5b) --- (1)
2. But we know, revenue due to A = a%. of the total revenue --- (2)
3. To express a in terms of b we need to relate (1) and (2)
4. a% = b / ( b + (150-1.5b))
or a= 100b / 150-0.5b = 200b/(300-b)
C
Answer: (C) 200b/(300-b)
Question: Arun purchased 30 kg of wheat at the rate of Rs. 11.50 per kg and 20 kg of wheat at the rate of 14.25 per kg. He mixed the two and sold the mixture. Approximately what price per kg should be sell the mixture to make 10% profit?
(A) 13.86
(B) 16.33
(C) 16.35
(D) 16.3
(E) 16.32
Rationale: C.P. of 50 kg wheat = (30 * 11.50 + 20 * 14.25) = Rs. 630.
S.P. of 50 kg wheat = 110% of Rs. 630 = 110/100 * 630 = Rs.693
S.P. per kg = 693/50 = Rs. 13.86
Answer: A
Answer: (A) 13.86
Question: The post office processed lots of packages every weekday. The numbers of packages it processed per day were 80, 30, 100, 90 and x. If the median number of packages was 10 higher than the average (arithmetic mean) number of packages, which of the following could be x?
(A) 40
(B) 45
(C) 50
(D) 55
(E) 60
Rationale: Look at the options available
Value of x seems to 40 < = x < = 60
A. 40
B. 45
C. 50
D. 55
E. 60
So position of x is second
30 , x , 75 , 85 , 95
Median = 75
Median number of packages was 10 points higher than the average, so average = 65
30 + x + 75 + 85 + 95 = 325
x = 40 = Answer = A
Answer: (A) 40
Question: What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58?
(A) Rs.3944
(B) Rs.3943
(C) Rs.3928
(D) Rs.3929
(E) Rs.3925
Rationale: Let the side of the square plot be a ft.
a2 = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 * 58
= Rs.3944.
Answer:A
Answer: (A) Rs.3944
Question: If (1/3)A = (1/4)B = (1/5)C. Then A : B : C is
(A) 4 : 3 : 5
(B) 5 : 4 : 3
(C) 3 : 4 : 5
(D) 20 : 15 : 12
(E) None of these
Rationale: (A/3) = (B/4) = (C/5) = K
=> A = 3K, B = 4K, C = 5K
Therefore, A : B : C = 3K : 4K : 5K = 3 : 4 : 5
ANSWER:C
Answer: (C) 3 : 4 : 5
Question: If there are 5 seats and 2 students, in how many ways can they be seated?
(A) 12
(B) 16
(C) 20
(D) 24
(E) 28
Rationale: The first student has 5 choices and the second student has 4 choices.
The number of ways to sit is 5*4 = 20.
The answer is C.
Answer: (C) 20
Question: When positive integer x is divided by positive integer y, the result is 59.32. What is the sum W of all possible 2-digit remainders for x/y?
(A) 560
(B) 616
(C) 672
(D) 728
(E) 784
Rationale: ans B 616...
remainders = .32=32/100=8/25=16/50 and so on..
so two digit remainders are 16+24+32+....+96..
W=8(2+3+4....+12)=616
Answer: (B) 616
Question: A corporation triples its annual bonus to 50 of its employees. What percent E of the employees’ new bonus is the increase?
(A) 50%
(B) 662⁄3%
(C) 100%
(D) 200%
(E) 300%
Rationale: E of the employees’ new bonus is the increase Hence B.
Answer: (B) 662⁄3%
Question: The ratio of 2 numbers is 1:2 and their H.C.F. is 10. Their L.C.M. is ?
(A) 10
(B) 20
(C) 30
(D) 50
(E) 40
Rationale: Let the numbers be x and 2x
Their H.C.F. = 10
so the numbers are 1*10 , 2*10 = 10,20
L.C.M. = 20
Answer is B
Answer: (B) 20
Question: If 14,444 – n is divisible by 11, and 0 < n < 11, what is n?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: 14,444 / 11 = 1313 with a remainder of 1.
We need to subtract the remainder to get a multiple of 11.
The answer is A.
Answer: (A) 1
Question: Tea worth Rs. 126 per kg are mixed with a third variety in the ratio 1: 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg
(A) 175.59
(B) 175.5
(C) 175.57
(D) 175.52
(E) 175.11
Rationale: Explanation:
Since first second varieties are mixed in equal proportions, so their average price = Rs.(126+135/2) = Rs.130.50
So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.
Cost of 1 kg tea of 1st kind Cost of 1 kg tea of 2nd kind
x-153/22.50 = 1 => x - 153 = 22.50 => x=175.50.
Hence, price of the third variety = Rs.175.50 per kg.
Answer: C) Rs. 175.50
Answer: (C) 175.57
Question: The 1:30 pm train leaves the station as a prospective passenger reaches the platform. Assuming that the train is going at 40 kmph, and the next train is an Express leaving half an hour later, which will go 50 kmph, when will the passenger reach the same place as the train he missed?
(A) 2:00 pm
(B) 2:30 pm
(C) 3:45 pm
(D) 4:00 pm
(E) 5:15 pm
Rationale: Distance covered by the original train in 1/2 hour = 20 km
10 km is compensated for in 1 hour, therefore 20 km will be compensated in 2 hours
So, the Express overtakes the original train at 4 p.m.
Correct Answer: D
Answer: (D) 4:00 pm
Question: If y is the smallest positive integer such that 6300 multiplied by y is the square of an integer, then y must be
(A) 5
(B) 7
(C) 15
(D) 35
(E) 45
Rationale: 6300 = 2^2*3^2*5^2*7
To be perfect square, we need to multiply by at least 7.
The answer is B.
Answer: (B) 7
Question: From January through June, 46200 immigrants applied for citizenship. During this same period last year, 120000 immigrants applied. What is the percentage of decrease?
(A) 38.5
(B) 38.6
(C) 38.7
(D) 38.8
(E) None
Rationale: Solution:
(46200/120000) * 100 = 462/12 = 38.5
Answer A
Answer: (A) 38.5
Question: If x ¤ y = (x + y)^2 - (x - y)^2. Then √5 ¤ √5 =
(A) 0
(B) 5
(C) 10
(D) 15
(E) 20
Rationale: X = √5 and Y also =√5
Applying the function (√5+√5)^2 - (√5-√5)^2 = (2√5)^2 - 0 = 4 x 5 = 20.
Note: Alternative Approach is the entire function is represented as X^2 - Y^2 = (X+Y)(X-Y) which can be simplified as (x+y+x-y)(x+y-(x-y)) = (2x)(2y)=4xy. Substituting x=√5 and y = √5 you get the answer 20
Answer is E.
Answer: (E) 20
Question: The ratio between the sale price and the cost price of an article is 7:5. What is the ratio between the profit and the cost price of that article?
(A) 23
(B) 1:2
(C) 2:5
(D) 3:5
(E) 25
Rationale: C
C.P. = Rs. 5x and S.P. = Rs. 7x.
Then, Gain = Rs. 2x
Required ratio = 2x : 5x = 2:5
Answer: (C) 2:5