mathewhe/aqua_rat huggingface dataset:
Question: If r and b are positive numbers, and r^3 + b^3 = 75, then the greatest possible value of r is between:
(A) 0 and 3
(B) 3 and 5
(C) 4 and 5
(D) 5 and 7
(E) 6 and 9
Rationale: Yes the question is ambiguous, and the answer is certainly not C between 4 and 5 .
The question stated: r and b are positive numbers but not positive integers.
so fractions are allowed to be a part of calculation.
So if the answer is C then the value 4.5 = 9/2 must comply the equation.
(9/2)^3 + b^3 = 75
so, b^3 = -129/8 , which is not possible according to the question.
Moreover the question didn't mentioninclusive or not, so we can't assume that b is 4 .
hi asif,
question is correct IMO.
Sincemaximumvalues areuniqueso you cant take any value and make it satisfy with equation
question is asking that maximum value ofa(means that unique value ofa) is between...
its not saying all value of that range will satisfy.
Answer: (C) 4 and 5
Question: In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?
(A) 6.25
(B) 6.5
(C) 6.75
(D) 7
(E) 5
Rationale: Required run rate = (282 - (3.2 x 10))/40	=	250/40 = 6.25
Answer : A
Answer: (A) 6.25
Question: If two integers x,y (x>y) are selected from -4 to 4 (inclusive), how many cases are there?
(A) 27
(B) 30
(C) 33
(D) 36
(E) 39
Rationale: There are 9 integers from -4 to 4 inclusive.
9C2 = 36.
The answer is D.
Answer: (D) 36
Question: Find how many positive integers less than 10,000 are there suchthat the sum of the digits of the no. is divisible by 3?
(A) 1324
(B) 1456
(C) 1567
(D) 3334
(E) 2346
Rationale: If sum of the digits is divisible by 3, the number is divisible by 3.
Therefore, required number of non-negative integers is equal to count of numbers less than 10,000 which are divisible by 3.
Such numbers are (3, 6, 9, ... , 9999) (arithmetic progression with first term=3, last term=9999, common difference=3).
Count of such numbers =
9999
3
=
3333
99993=3333
But zero is also divisible by 3.
This makes our total count 3334
D
Answer: (D) 3334
Question: In the third grade of Windblown School there are 84 students, one third of them failed the math test and 1/6 failed that literature test. At least how many students failed both tests?
(A) 0.
(B) 6.
(C) 8.
(D) 10.
(E) 12.
Rationale: Total = 84
failed in math = 84/3=28
failed in literature=84/6=14
the least failed in both can be 0
while max can be 14
Answer A
Answer: (A) 0.
Question: At The KHOOL Company, high quality and low quality solar reflecting sunglasses are made, where 70 percent of the sunglasses made are high quality and 25 percent are low quality (defective sunglasses are tossed away into the recycle bin, but must be counted as product produced). If there are 50 sunglasses made per day that are defective and can't be sold as low or high quality sunglasses, how many sunglasses does The KHOOL Company make total per day?
(A)  100
(B)  1,800
(C)  1,090
(D)  200
(E)  1,000
Rationale: Let the total number of sunlasses produced be x
% of high quality sunglasses = 70%
% of low quality sunglasses = 25%
% of sunglasses defective = 100% - 95% = 5%
But this number is given as 50
so 5% of x = 50 and x = (50)(100/5))
x = 180
Therefore there a total of 1,000 sunglasses made per day.
Correct answer - E
Answer: (E)  1,000
Question: A boat can move upstream at 30 kmph and downstream at 35 kmph, then the speed of the current is?
(A) 5
(B) 2.5
(C) 7
(D) 4
(E) 32
Rationale: US = 30
DS = 35
M = (35 - 30)/2 = 2.5
Answer: B
Answer: (B) 2.5
Question: Ram and Shyam can do together a piece of work in 20 days. After they have worked together for 12 days Matt stops and Peter completes the remaining work in 10 days. In how many days Peter complete the work separately.
(A) 29
(B) 28
(C) 27
(D) 26
(E) 25
Rationale: Together they complete the job in 20 days means they complete 12/20 of the job after 12 days.
Peter completes the remaining (8/20) of the job in 10 days which means that the whole job(1) can be completed in X days.
<=> 8/20->10 <=> X=10/(8/20)=25
E
Answer: (E) 25
Question: Find the missing in the series: 70, 54, 44, 41,___
(A) 22
(B) 287
(C) 2679
(D) 2767
(E) 277
Rationale: Answer:E
Answer: (E) 277
Question: If y is the smallest positive integer such that 8820 multiplied by y is the square of an integer, then y must be
(A) 2
(B) 5
(C) 6
(D) 7
(E) 14
Rationale: 8820 = 2^2*3^2*5*7^2
To be perfect square, we need to multiply by at least 5.
The answer is B.
Answer: (B) 5
Question: A certain high school has 500 students. Of these students, 30 are taking music, 10 are taking art, and 10 are taking both music and art. How many students are taking neither music nor art?
(A) 430
(B) 440
(C) 450
(D) 460
(E) 470
Rationale: We're given a series of facts to work with:
1) A certain high school has 500 students.
2) Of these students:
X are taking music,
Y are taking art, and
Z are taking BOTH music and art.
We're asked how many students are taking NEITHER music nor art?
Let's TEST
X = 30
Y = 10
Z = 10
So, we have 30 students taking music, 10 taking art and 10 taking BOTH music and art.
20 student taking JUST music
0 student taking JUST art
10 student taking BOTH music and art
Total = 30 students
We're asked for the total number of students who are taking NEITHER Course. That is 500 - 30 = 470.
E
Answer: (E) 470
Question: A rope can make 70 rounds of the circumference of a cylinder whose radius of the base is 14cm. how many times can it go round a cylinder having radius 20 cm?
(A) 49 rounds
(B) 42 rounds
(C) 54 rounds
(D) 52 rounds
(E) None of these
Rationale: Explanation :
Let the required number of rounds be x
More radius, less rounds(Indirect proportion)
Hence we can write as
radius14:20}::x:70
⇒ 14 × 70 = 20x
⇒ 14 × 7 = 2x
⇒ x = 7 × 7 = 49. Answer : Option A
Answer: (A) 49 rounds
Question: A and B can finish a work in 16 days while A alone can do the same work in 24 days. In how many days B alone will complete the work?
(A) 38
(B) 48
(C) 27
(D) 21
(E) 20
Rationale: B = 1/16 – 1/24 = 1/48 => 48 days . Answer: B
Answer: (B) 48
Question: Insert the missing number.
8, 7, 11, 12, 14, 17, 17, 22,20,27,23 (....)
(A) 27
(B) 20
(C) 22
(D) 24
(E) 26
Rationale: There are two series (8, 11, 14, 17, 20,23,26) and (7, 12, 17, 22,27) increasing by 3 and 5 respectively.
answer : E
Answer: (E) 26
Question: In measuring the sides of a rectangle, one side is taken 16% in excess and other 5% in deficit. Find the error percentage in the area calculated from these measurements.
(A) 3.5%
(B) 2.4%
(C) 10.2%
(D) 5%
(E) 2.6%
Rationale: Say both sides of the rectangle are equal to 100 (so consider that we have a square). In this case the area is 100*100=10,000.
Now, the area obtained with wrong measurements would be 116*95=11,020, which is 10.2% greater than the actual area.
Answer: C.
Answer: (C) 10.2%
Question: The sale price shirts listed f or Rs.400 after successive discount is 10% and 5% is?
(A) 280
(B) 290
(C) Rs.342
(D) 250
(E) 253
Rationale: 400*(90/100)*(95 / 100) = 342
C
Answer: (C) Rs.342
Question: Find the fraction which has the same ratio to 2/13 that 5/34 has to 7/48.
(A) 240/1577
(B) 240/1527
(C) 240/1547
(D) 240/1518
(E) 240/1273
Rationale: P : 2/13 = 5/34 : 7/48
As the product of the means is equal to the product of the extremes.
P*7/48 = 2/13 * 5/34
P*7/48 = 10/442
P = 480/3094 => P = 240/1547
Answer:C
Answer: (C) 240/1547
Question: In a certain parking lot, 10% of the cars are towed for parking illegally. However 80% of the cars which are parked illegally are not towed. What percentage of cars in the parking lot are parked illegally?
(A) 30%
(B) 40%
(C) 50%
(D) 60%
(E) 70%
Rationale: Let x be the number of cars and let y be the number of cars parked illegally.
10%*x = 20%*y
y/x = 1/2 = 50%
The answer is C.
Answer: (C) 50%
Question: There are 12 red shoes, 7 green shoes. If one draw randomly a shoe what is the probability of getting a red shoe
(A) 11/19
(B) 12/19
(C) 15/19
(D) 14/19
(E) 2/3
Rationale: total 19 from take one.
19c1=19
red 12 from one
12c1=12
12/19
ANSWER:B
Answer: (B) 12/19
Question: If inflation increases at a rate of 8 p.c.p.a. what will a 20 article cost at the end of two years?
(A) Between 20 and 21
(B) Between 21 and 22
(C) Between 22 and 23
(D) Between 23 and 24
(E) None of these
Rationale: Required sum
= 20(1+8/100)2=20×27×27/25×25=23.3
Answer D
Answer: (D) Between 23 and 24
Question: If rupee one produces rupees nine over a period of 42 years, find the rate of simple interest?
(A) 22 1/7 %
(B) 22 3/2 %
(C) 21 3/7 %
(D) 22 1/2 %
(E) 22 1/2 %
Rationale: 9 = (1*42*R)/100
R = 21 3/7 %
Answer:C
Answer: (C) 21 3/7 %
Question: Two pens and three pencils cost Rs 86. four Pens and a pencil cost Rs. 112. find the cost of a pencil.
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: 1 pen cost x,let 1 pencil cost y
2x+3y=86, ...y=(86-2x)/3
again,
4x+y=112
4x+(86-2x)/3=112
12x+86-2x=336
10x=250
x=25,
y=(86-50)/3=12
ANSWER:C
Answer: (C) 12
Question: The remainder obtained when a prime number greater than 4 is divided by 4 is
(A) a) 1 or 3
(B) b) 1 or 5
(C) c) 3 or 5
(D) d) 4 or 5
(E) e) 5
Rationale: The easiest way to answer this question is probably to pick numbers. Use the next two prime numbers greater than 4, i.e. 7 and 5:
7/4 = 1 + remainder of 3
5 / 4 = 1 + remainder of 1
This is already sufficient to see that answer choice a) is correct.
A
Answer: (A) a) 1 or 3
Question: The batting average of a particular batsman is 60 runs in 46 innings. If the difference in his highest and lowest score is 160 runs and his average excluding these two innings is 58 runs, find his highest score.
(A) 184
(B) 367
(C) 269
(D) 177
(E) 191
Rationale: Explanation:
Total runs scored by the batsman = 60*46 = 2760 runs
Now excluding the two innings the runs scored = 58*44 = 2552 runs
Hence the runs scored in the two innings = 2760 â€“ 2552 = 208 runs.
Let the highest score be x, hence the lowest score = x â€“ 160
x + (x - 160) = 208
2x = 368
x = 184 runs
ANSWER: A
Answer: (A) 184
Question: If r and s are positive integers and r-s=6, which of the following has the greatest value J?
(A) 2r
(B) 2s
(C) r +s
(D) 2r-s
(E) 2s-r
Rationale: You can answer this question by using Number Properties and logic or by TESTing VALUES.
We're told that R and S are POSITIVE INTEGERS and that R-S = 6. We're asked which of the 5 answers has the GREATEST value.
IF....
R = 8
S = 2
Answer A: 2R = 2(8) = 16
Answer B: 2S = 2(2) = 4
Answer C: R+S = 8+2 = 10
Answer D: 2R-S = 2(8) - 2 = 14
Answer E: 2S-R = 2(2) - 8 = -4
Final Answer:
A
Answer: (A) 2r
Question: It takes 35 identical printing presses 12 hours to print 500,000 papers. How many hours would it take 30 of these printing presses to print 500,000 papers?
(A) 14
(B) 15
(C) 16
(D) 18
(E) 20
Rationale: 35 printing presses can do 1/12 of the job each hour.
30 printing presses can do 6/7*1/12 = 1/14 of the job each hour.
The answer is A.
Answer: (A) 14
Question: Salesperson A's compensation for any week is $300 plus 6 percent of the portion of A's total sales above $1,000 for that week. Salesperson B's compensation for any week is 8 percent of B's total sales for that week. For what amount of total weekly sales would both salepeople earn the same compensation?
(A) $21,000
(B) $12,000
(C) $15,000
(D) $ 4,500
(E) $4,000
Rationale: sometime, setting up an equation is an easy way to go with:
300 + 0.06 (x - 1000) = 0.08 x
x = 12,000
Ans : B
Answer: (B) $12,000
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) 1/3
(B) 1/5
(C) 2/5
(D) 3/7
(E) 4/9
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 train 600 m long can cross an electric pole in 20 sec and then find the speed of the train?
(A) 117 Kmph
(B) 178 Kmph
(C) 172 Kmph
(D) 108 Kmph
(E) 109 Kmph
Rationale: Length = Speed * time
Speed = L/T
S = 600/20
S = 30 M/Sec
Speed= 30*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 108 Kmph
Answer: D
Answer: (D) 108 Kmph
Question: The area of one square is x^2 + 8x + 16 and the area of another square is 4x^2 − 28x + 49. If the sum of the perimeters of both squares is 72, what is the value of x?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: The areas are (x+4)^2 and (2x-7)^2.
The lengths of the sides are x+4 and 2x-7.
If we add the two perimeters:
4(x+4) + 4(2x-7) = 72
12x = 84
x = 7
The answer is E.
Answer: (E) 7
Question: The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along theoundary of the park at the speed of 12 km/hr completes one round in 8 min, then thearea of the park (in sq. m) is?
(A) 124545 m
(B) 134561 m
(C) 156787 m
(D) 15450 m
(E) 153600 m
Rationale: Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m.
60
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
Length = 480 m and Breadth = 320 m.
Area = (480 x 320) m2 = 153600 m
E
Answer: (E) 153600 m
Question: A rectangular tiled patio is composed of 30 square tiles. The rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles. After the change in layout, the patio will still have 30 tiles, and it will still be rectangular. How many rows are in the tile patio before the change in layout?
(A) 5
(B) 6
(C) 10
(D) 13
(E) 28
Rationale: Suppose there are c columns and there are r rows
Original Situation
So, Number of tiles = c*r = 30
Also. Reach column has r tiles and each row has c tiles
New Situation
Number of tiles in each column is r-2 and number of tiles in each row is c+4
So, number of rows = r-2 and number of columns is c+4
So, Number of tiles = (r-2)*(c+4) = 30
Comparing both of them we get
c*r = (r-2)*(c+4)
=> 4r -2c = 8
c = 2r - 4
Putting it in c*r=30
(2r-4)*r = 30
2r^2 - 4r - 30=0
r cannot be negative so r =5
and c = 6
So, Answer will be A
Answer: (A) 5
Question: If 1+2+3+...+n=n (n+1), then
2 (1+3+5+....+89)=?
(A) 4100
(B) 4050
(C) 4250
(D) 4350
(E) 4450
Rationale: Explanation :
To solve this use the formula of AP,
Sn= (n/2)(a+l) ................(1)
To find n, use
=> Tn= a+(n-1)d
=> 89=1+(n-1)2
=> n=45
Use value of n in (1)
then,
Sn = (45/2)(1+89) = 2025
Ans:- 2(Sn) = 4050
Answer : B
Answer: (B) 4050
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
(A) 186 m
(B) 176 m
(C) 872 m
(D) 150 m
(E) 765 m
Rationale: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train
= (Speed x Time) = (50/3 * 9) m
= 150 m.
Answer: D
Answer: (D) 150 m
Question: There are 9 days of school left. Cassie has $50. How much money does Cassie's mom need to give her in order for Cassie to spend $6 on lunch for each of the nine remaining school days?
(A) $1
(B) $2
(C) $4
(D) $6
(E) $8
Rationale: For Cassie to spend $6 a day for nine days, she must multiply 9 days by $6 = $54. $54 minus $50 = $4. Hence the answer : C.
Answer: (C) $4
Question: John had a stock of 1200 books in his bookshop. He sold 75 on Monday, 50 on Tuesday, 64 on Wednesday, 78 on Thursday and 135 on Friday. What percentage of the books were not sold?
(A) 50.4%
(B) 23.8%
(C) 66.5%
(D) 34.9%
(E) 43.5%
Rationale: Let N be the total number of books sold. Hence
N = 75 + 50 + 64 + 78 + 135 = 402
Let M be the books NOT sold
M = 1200 - N = 1200 - 402 = 798
Percentage
Books not sold / total number of books = 798/1200 = 0.665 = 66.5%
correct answer C
Answer: (C) 66.5%
Question: The proportion of water to alcohol in Solution A is 2:1 and the proportion of water to alcohol in Solution B is 2:3. If an equal amount of each solution is mixed together, what is the concentration of alcohol in the new solution?
(A) 46.7%
(B) 47.3%
(C) 48.4%
(D) 50.6%
(E) 51.8%
Rationale: Let V be the total volume of the new solution.
Then a volume of V/2 was added from each solution A and B.
The amount of alcohol added to the new solution was:
(1/3)(V/2)+(3/5)(V/2)=V/6+3V/10=14V/30=7V/15.
The concentration of alcohol is 7/15=46.7%
The answer is A.
Answer: (A) 46.7%
Question: Three numbers are in the ratio 3:5:7. The largest number value is 49. Find difference between Smallest & largest number is?
(A) 20
(B) 24
(C) 26
(D) 28
(E) 30
Rationale: == 3:5:7
Total parts = 15
= The largest number value is 49
= The largest number is = 7
= Then 7 parts -----> 49 ( 7 * 7 = 49 )
= smallest number = 3 & Largest number = 7
= Difference between smallest number & largest number is = 7 - 3 = 4
= Then 4 parts -----> 28 (4 * 7 = 28)
D
Answer: (D) 28
Question: A girlscout is selling cookies in her neighborhood. She has a goal to sell $150 worth of cookies. Each box costs $2.50 each. How many boxes will she need to sell in order to reach 75% of her goal?
(A) 25
(B) 35
(C) 50
(D) 40
(E) 45
Rationale: 150*.75=112.50= dollar amount to reach 75 percent of her goal
112.50/2.50=45= amount of.boxes to sell
The answer is E.
Answer: (E) 45
Question: A certain company has records stored with a record storage firm in 15-inch by 12-inch by 10-inch boxes. The boxes occupy 1.08 million cubic inches of space. If the company pays $0.8 per box per month for the record storage, what is the total amount that the company pays each month for record storage?
(A) a. 480
(B) b. 300
(C) c. 600
(D) d. 410
(E) e. 240
Rationale: Volume Per Box: 15x12x10 = 1,800
Total Volume: 1,080,000
Number of Boxes: Total Volume / Volume Per Box = 1,080,000 / 1,800 = 600
Price Per Month: Number of Boxes * Price Per Box = 600 * 0.8 = 480
Answer: A
Answer: (A) a. 480
Question: Two numbers are respectively 20% and 25% more than a third number. The percentage that is first of the second is?
(A) 86%
(B) 56%
(C) 96%
(D) 98%
(E) 95%
Rationale: I II III
120 125 100
125----------120
100-----------? => 96%
Answer:C
Answer: (C) 96%
Question: The area of a parallelogram is 450sq m and its altitude is twice the corresponding base. Then the length of the base is?
(A) 8
(B) 9
(C) 7
(D) 6
(E) 15
Rationale: 2x * x = 450 => x= 15
Answer: E
Answer: (E) 15
Question: The number 0.127 is how much greater than 1/8 ?
(A) 1/100
(B) 1/1500
(C) 1/2
(D) 1/500
(E) 1/600
Rationale: Explanation:
0.127 expressed as a fraction = 127/1000
1/8 can also be expressed as (1 x 125) / (8 x 125) = 125/1000
The difference is 2/1000, which is 1/500
ANSWER IS D
Answer: (D) 1/500
Question: What quantity of water should be added to reduce 9 liters of 50% acidic liquid to 30% acidic liquid?
(A) 6liters
(B) 8liters
(C) 10liters
(D) 12liters
(E) 15liters
Rationale: Acid in 9 liters = 50% of 9 = 4.5 liters
Suppose x liters of water be added.
Then 4.5 liters of acid in 9+x liters of diluted solution
30% of 9+x = 4.5
27+3x = 45
x = 6liters
Answer is A
Answer: (A) 6liters
Question: The average salary of workers in an industry is Rs.300 the average salary of technicians being Rs.400 and that of non-technicians being Rs.125. What is the total number of workers?
(A) 230
(B) 234
(C) 250
(D) 547
(E) 484
Rationale: 400 125
\ /
300
/ \
175 100
7:4
7->150
11->?
=>234
ANSWER:B
Answer: (B) 234
Question: The edges of three metal cubes are 1 cm, 2 cm, and 4 cm respectively. A new cube is made by melting these three cubes together. What is the edge of the new cube (in centimeters)?
(A) 3.8
(B) 4.2
(C) 4.6
(D) 5.0
(E) 5.4
Rationale: The total volume is 1^3+2^3+4^3=73
The edge of the new cube is the cube root of 73 which is about 4.2 cm.
The answer is B.
Answer: (B) 4.2
Question: Albert buys 4 horses and 9 cows for Rs. 13,400. If he sells the horses at 10% profit and the cows at 20% profit, then he earns a total profit of Rs. 1880. The cost of a horse is?
(A) 2888
(B) 2000
(C) 7768
(D) 1551
(E) 1991
Rationale: Let C.P. of each horse be Rs. x and C.P. of each cow be Rs. y.
Then, 4x + 9y = 13400 -- (i)
And, 10% of 4x + 20% of 9y = 1880
2/5 x + 9/5 y = 1880 => 2x + 9y = 9400 -- (ii)
Solving (i) and (ii), we get : x = 2000 and y = 600.
Cost price of each horse = Rs. 2000.
Answer:B
Answer: (B) 2000
Question: A shopkeeper purchased 70 kg of potatoes for Rs. 420 and sold the whole lot at the rate of Rs. 6.30 per kg. What will be his gain percent?
(A) 8 1/7 %
(B) 2 1/3 %
(C) 5 %
(D) 8 1/8 %
(E) 8 1/9 %
Rationale: C.P. of 1 kg = 420/70 = Rs. 6
S.P. of 1 kg = Rs. 6.30
Gain % = 0.30/6 * 100 = 5
= 5 %
Answer:C
Answer: (C) 5 %
Question: A, B and C have Rs.500 between them, A and C together have Rs.200 and B and C Rs.330. How much does C have?
(A) 50
(B) 78
(C) 30
(D) 29
(E) 27
Rationale: A+B+C = 500
A+C = 200
B+C = 330
--------------
A+B+2C = 530
A+B+C = 500
----------------
C = 30
Answer: C
Answer: (C) 30
Question: Jo's collection contains US, Indian and British stamps. If the ratio of US to Indian stamps is 7 to 2 and the ratio of Indian to British stamps is 5 to 1, what is the ratio of US to British stamps?
(A) 5 : 1
(B) 10 : 5
(C) 15 : 2
(D) 20 : 2
(E) 35 : 2
Rationale: U/I = 7/2
I/B = 5/1
Since I is multiple of both 2 (as per first ratio) and 5 (as per second ratio) so let's assume that I = 10
i.e. Multiplying teh first ratio by 5 and second ration by 2 in each numerator and denominator
then, U : I : B = 35 : 21 : 2
i.e. U : B = 35 : 2
Answer: Option E
Answer: (E) 35 : 2
Question: How many integers Z are prime numbers in the range 200 < Z < 220?
(A)  1
(B)  2
(C)  3
(D)  4
(E)  5
Rationale: My friend, every single odd number greater than can be written either as 4Z+1 or as 4Z+3. If you divide any odd number by 4, you will get a remainder of either 1 or 3. That's not a rule unique to prime numbers at all.
The 6Z+1 or 6Z-1 rule is basically every odd number that is not divisible by three, so it narrows the search a little.
Here's how I thought about the problem. First, eliminate all the even numbers and the odd multiples of 5 in that range. That leaves us with:
{201, 203, 207, 209, 211, 213, 217, 219}
Eliminate the four multiples of 3. Notice that 21 is a multiple of 3, so 210 is also a multiple of 3. If we add or subtract 3 or 9, we get more multiples of three. When we eliminate those, we are left with.
{203, 209, 211, 217}
Now, notice that a cool thing about this range is that 210 is also a multiple 7 (again, because 21 is a multiple of 7). This means that
210 - 7 = 203
210 + 7 = 217
Those two numbers are also multiples of 7, so eliminate them from the list. Now, we are left with
{209, 211}.
We've already checked all the prime numbers less than 10, so we know that neither of these numbers is divisible by anything less than 10. We have to check 11 now. We know that 22 is a multiple of 11, so 220 is also a multiple of 11. This means that
220 - 11 = 209
is also a multiple of 11. We can eliminate this from the list also.
That leaves us with just 211. There's no zero option in the question, so this must be a prime number.
Answer = (A)
Answer: (A)  1
Question: A invested $150 in a business after 6 months B invested $200 in the business. End of the year if they got $100 as profit. Find A shares?
(A) $100
(B) $75
(C) $20
(D) $120
(E) $60
Rationale: A:B = 150*12:200*6
A:B = 3:2
A's share = 100*3/5 = $60
Answer is E
Answer: (E) $60
Question: The average of 6 observations is 12. A new seventh observation is included and the new average is decreased by 1. The seventh observation is :
(A) 1
(B) 3
(C) 5
(D) 6
(E) 8
Rationale: Explanation:
Seventh observation = (7××11-6××12)=5
Correct Option: C
Answer: (C) 5
Question: Two numbers N and 16 have LCM = 48 and GCF = 8. Find N.
(A) 11
(B) 32
(C) 24
(D) 48
(E) 50
Rationale: The product of two integers is equal to the product of their LCM and GCF. Hence.
16 * N = 48 * 8
N = 48 * 8 / 16 = 24
correct answer C
Answer: (C) 24
Question: A began a business with Rs. 85,000. He was joined afterwards by B with Ks. 42,500. For how much period does B join, if the profits at the end of the year are divided in the ratio of 6 : 1 ?
(A) 6 months
(B) 4 months
(C) 2 months
(D) 8 months
(E) 9 months
Rationale: Suppose B joined for x months . Then, ( 85000 * 12 )/(42500 * x) = 6. or x = (85000 * 12) / (42500 * 6) = 4.
So, B joined for 4 months.
Answer: B
Answer: (B) 4 months