mathewhe/aqua_rat huggingface dataset:
Question: In a jar there are 20 white balls, 24 green balls and 32 blue balls. How many balls must be taken out in order to make sure we have 22 balls of the same color?
(A) a)	23
(B) b)	46
(C) c)	57
(D) d)	63
(E) e)	67
Rationale: Here, we need to find minimum number of marbles to be taken out to get 22 marbles of same color.
For a instance, if we take 21 white marbles 1st and followed by 22 Green and then 22 Blue.
Total will be 20 + 21+ 21= 62 draws.
If we choose either Green or Blue next time. This will bring the total of either of these colored marble to 22.
So Minimum we need to take 62+1 = 63 Times to get 22 marbles of same color(either Green or Blue).
Answer : D.
Answer: (D) d)	63
Question: Free notebooks were distributed in a class among all the students. Each student got notebooks which were one-eighth of the number of student. If number of student been half, then each child would have received 16 notebooks in total. Find the total number of books distributed among students?
(A) 456
(B) 534
(C) 457
(D) 567
(E) 512
Rationale: Let suppose total number of students in class are X.
Then from the question we can conclude it that,
X∗18X=X2∗16=>X=64Total notebooks,=18X2=(18∗64∗64)=512
E
Answer: (E) 512
Question: In a fort, there are 1200 soldiers. If each soldier consumes 3 kg per day, the provisions available in the fort will last for 30 days. If some more soldiers join, the provisions available will last for 25 days given each soldier consumes 2.5 kg per day. Find the number of soldiers joining the fort in that case?
(A) 568
(B) 528
(C) 567
(D) 872
(E) 623
Rationale: Assume X soldiers join the fort. 1200 soldiers have provision for 1200(days for which provisions last them)(rate of consumption of each soldier)
= 1200(30)(3) kg
Also provisions available for (1200 + x) soldiers is (1200 + x)(25)(2.5) kg
As the same provisions are available
=> 1200(30)(3) = (1200 + x)(25)(2.5)
x = [1200(30)(3)]/[(25)(2.5)] - 1200
Answer: B
x = 528
Answer: (B) 528
Question: The variable x is inversely proportional to the square of the variable y. If y is divided by 5a, then x is multiplied by which of the following?
(A) a. 1/25a
(B) b. 1/25a^2
(C) 1/5a
(D) 25a
(E) 25a^2
Rationale: initially - did x= 1/y^2
But this yielded the wrong answer,
I then re examined the question and tried y^2/x =1
Which I then got y = SQR(X)
subbing into y/5a I got answer E)
Answer: (E) 25a^2
Question: If the terms of a series are either2or24and the sum of all the terms G of the series is 124, then which of the following could be the number of2sin the series?
(A) 26
(B) 29
(C) 35
(D) 40
(E) 48
Rationale: Ans: A
Solution: we are not certain how many 2 or 24 are there. but as given sum of all the terms G is 124 means 24*5= 120 so number of 24 can't be more than 5
so 24x +2y = 124
24*5 + 2y =124 then y=2
24*4 + 2y = 124 then y=14
24*3 +2y = 124 then y= 26
24*2 +2y =124 then y = 38
24 +2y = 124 then y= 50
26 is the ans.A
Answer: (A) 26
Question: A sum of money invested at compound interest to Rs. 800 in 3 years and to Rs 820 in 4 years. The
rate on interest per annum is.
(A) 0.4%
(B) 5.0%
(C) 2.5%
(D) 7%
(E) 8%
Rationale: Explanation:
S.I. on Rs 800 for 1 year = 20
Rate = (100*20)/(800*1) = 2.5%
Answer: C
Answer: (C) 2.5%
Question: Consider a sequence of numbers given by the expression 7 + (q - 1) * 5, where n runs from 1 to 80.What is the sum of this series ?
(A) 409
(B) 1636
(C) 16360
(D) 16000
(E) 15360
Rationale: terms in this sequence are 7,12,17----402
now since this is an a.p. with a common difference of 5. therefore its sum can be given as
q(a+l)/2----------------1)
q= total no. of terms =80
a= first term=7
l= last term=402
subsituting values in the expression 1 we have
80(7+402)/2
= 40(409)
=16360=C
Answer: (C) 16360
Question: Find all integers x NOT EQUAL TO 3 such that X-3|X^3-3
(A) 1,2,3,4,5
(B) -21,-9,-5,-3,-1,0,1,2,4,5,6,7,9,11,15,27
(C) 1
(D) 6
(E) -1,0,1
Rationale: Let x-3=t. Thus, t is an integer not equal to such'that t|(t+3)^2-3,
which is equivalent to the condition t|3^3-3, or t|24. Therefore, it is necessary
and sufficient for t to be an integer divisor of 24, hence t must be equal
to one of the numbers +or-1, +or-2, +or-3, +or-4, +or-6, +or-8, +or-12, +or-24. For x
= t+3 we obtain the values -21, -9, -5, -3, -1,0,1,2,4,5,6,7,
9, 11, 15, and 27.
Correct Answer B -21,-9,-5,-3,-1,0,1,2,4,5,6,7,9,11,15,27
Answer: (B) -21,-9,-5,-3,-1,0,1,2,4,5,6,7,9,11,15,27
Question: How long does a train 140 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length?
(A) 13.6 sec
(B) 12.1 sec
(C) 17.9 sec
(D) 16.8 sec
(E) 14.9 sec
Rationale: Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 140 + 132 = 272 m.
Required time = 272/20 = 13.6 sec.
Answer: A
Answer: (A) 13.6 sec
Question: a is what percent of b percent of c, in terms of a, b and c?
(A) 10^4*a/bc
(B) abc
(C) bc*10^4
(D) 1/abc
(E) abc/1000
Rationale: Algebraically, b% of c is just (b/100)*c, or bc/100. So we want to answer the question: a is what percent of bc/100? Say a is equal to m% of bc/100; then we have:
a = (m/100)*(bc/100)
10,000a/bc = m
A
Answer: (A) 10^4*a/bc
Question: A 20 kg metal bar made of alloy of tin and silver lost 2 kg of its weight in the water. 10 kg of tin loses 1.375 kg in the water; 5 kg of silver loses 0.375 kg. What is the ratio of tin to silver in the bar?
(A) 1/4
(B) 2/5
(C) 1/2
(D) 3/5
(E) 2/3
Rationale: The bar lost certain percentage of its weight. We don't know how much tin was lost and how much silver was lost but in all 2 kg was lost with is 10% of its overall weight.
Tin loses 1.375 kg in 10 kg so 13.75% of its weight when it is put in water.
Silver loses .375 kg in 5 kg so .375/5 * 100 = 7.5% of its weight in water.
Now, we just need to use weighted averages:
Wt/Ws = (7.5 - 10)/(10 - 13.75) = 2.5/3.75 = 2/3
Answer (E)
Answer: (E) 2/3
Question: A and B together invested Rs. 10,000 in a business. At the end of the year, out of total profit is Rs. 2,000 B's share was Rs. 800. A's investment was
(A) s. 4,000
(B) s. 6,000
(C) s. 10,500
(D) s. 11,250
(E) s. 12,250
Rationale: A+B=10000
total profit=2000
2000-800=1200
1200;800=3:2
then 3*10000/5=6000
ANSWER:B
Answer: (B) s. 6,000
Question: Mrs. Peter got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
(A) $145
(B) $231
(C) $112
(D) $214
(E) $321
Rationale: A
$145
Let the 1st paycheck be x (integer).
Mrs. Peter got a weekly raise of $ 145.
So after completing the 1st week she will get $ (x+145).
Similarly after completing the 2nd week she will get $ (x + 145) + $ 145.
= $ (x + 145 + 145)
= $ (x + 290)
So in this way end of every week her salary will increase by $ 145.
Answer: (A) $145
Question: In a box there are 5 red balls and 6 blue balls. What is the probability of drawing at least one red ball when drawing 3 consecutive balls randomly?
(A) 201/202
(B) 164/165
(C) 256/259
(D) 98/103
(E) 115/217
Rationale: P(at least one red) = 1 - P(no red, so 3 blue) = 1- 3/11*2/10*1/9 = 164/165.
Answer is B
Answer: (B) 164/165
Question: if 28 is divided into two parts such that one fourth of the greater part is equal to one third of the lesser part,then the greater part is
(A) 16
(B) 18
(C) 20
(D) 22
(E) 24
Rationale: 28 divided as (16 + 12).
one fourth of 16(greater part) = 4
one third of 12(lesser part) = 4
ANSWER:A
Answer: (A) 16
Question: The sum of seven numbers is 235. The average of the first three is 23 and that of the last three is 42. The fourth number is
(A) 40
(B) 126
(C) 69
(D) 195
(E) None
Rationale: Explanation:
Average of the first three is 23. Therefore their sum = 23 x 3
Average of the last three is 42. Therefore their sum = 42 x 3
Sum of all number = Sum of first three + Fourth number + Sum of last three
(23×3+a+42×3)=235⇒a=40
Correct Option: A
Answer: (A) 40
Question: How many multiples of 5 are there between 5 to 90?
(A) 9
(B) 16
(C) 17
(D) none of these
(E) Cannot be determined
Rationale: Explanation :
As you know, multiples of 5 are integers having 0 or 5 in the digit to the extreme right (i.e. the units place).
So the numbers are 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85.
Answer : B
Answer: (B) 16
Question: A store has 10 bottles of juice, including 6 bottles of apple juice. In the evening, 6 bottles of juice are sold one by one. What is the probability of selling 4 bottles of apple juice among the 6 bottles? Assume that every bottle has an equal chance of being bought.
(A) 2/5
(B) 3/5
(C) 2/3
(D) 1/2
(E) 3/7
Rationale: The total number of ways to sell 6 bottles from 10 is 10C6 = 210.
The number of ways to sell 4 bottles of apple juice is 6C4*4C2 = 15*6 = 90
P(selling 4 bottles of apple juice) = 90/210 = 9/21 = 3/7
The answer is E.
Answer: (E) 3/7
Question: At Company K, 15 percent of the employees are secretaries and 60 percent are salespeople. If there are 65 other employees of Company K, how many employees does Company K have?
(A)  260
(B)  180
(C)  190
(D)  200
(E)  400
Rationale: Let the total number of employees in the company be x
% of secretaries = 15%
% of salespeople = 60%
% of of employees other than secretaries and salespeople = 100 - 75 = 25%
But this number is given as 65
so 25% of x = 65
x = 260
Therefore there a total of 260 employees in the company K
Correct answer - A
Answer: (A)  260
Question: What is the minimum percentage increase in the mean of set G {-4, -1, 0, 6, 9} if its two smallest elements are replaced with two different primes?
(A)  25%
(B)  50%
(C)  75%
(D)  100%
(E)  200%
Rationale: Mean of G is (-4-1+0+6+9)/5=2;
In order the increase to be minimal we should replace two smallest elements of G, which are -4 and -1, with two smallest primes, which are 2 and 3. Hence our new set will be {2, 3, 0, 6, 9} --> new mean is (2+3+0+6+9)/5=4.
Percent increase=(4-2)/2*100=100%.
Answer: D.
Answer: (D)  100%
Question: Which of the following CANNOT be a product of two distinct positive integers a and b?
(A) a
(B) b
(C) 3b + 2a
(D) b - a
(E) ba
Rationale: we can eliminate answer choices A, B, and E right away. There is no reason to distinguish between aa and bb, so if aa cannot be a product, then bb cannot be either and since we cannot have two correct answers in PS problems, then neither A nor B can be correct. As for E it's clearly cannot be correct answer.
So, we are left with options C and D.
For C, can ab=3b+2aab=3b+2a? --> ab−2a=3bab−2a=3b --> a(b−2)=3ba(b−2)=3b --> a=3bb−2a=3bb−2. Now, if b=3b=3, then a=9a=9, so in this case ab=3b+2aab=3b+2a is possible.
Only option left is D.
Answer: D.
Answer: (D) b - a
Question: How many paying stones, each measuring 2 m * 1 m are required to pave a rectangular court yard 30 m long and 16 m board?
(A) 240
(B) 18
(C) 26
(D) 17
(E) 12
Rationale: 30 * 16 = 2 * 1 * x => x
= 240
Answer: A
Answer: (A) 240
Question: The length of a rectangular floor is more than its breadth by 200%. If Rs.150 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) 65
(B) 15
(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 = 150/2= 75 sq m
l b = 75 i.e., l * l/3 = 75
l2 = 225 => l = 15
Answer:B
Answer: (B) 15
Question: A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is:
(A) 7
(B) 9
(C) 8
(D) 65
(E) 4
Rationale: Explanation:
Let the required number of revolutions made by larger wheel be x.
Then, More cogs, Less revolutions (Indirect Proportion)
{\color{Black} \therefore } 14 : 6 :: 21 : x {\color{Black} \Rightarrow } 14 x x = 6 x 21
x={\color{Black} \frac{6\times 21}{14} } {\color{Black} \Rightarrow } x=9
Answer: B
Answer: (B) 9
Question: The successive discounts 20% and 15% are equal to a single discount of?
(A) 35%
(B) 38%
(C) 32%
(D) 29%
(E) None of these
Rationale: Let the CP of an article be Rs. 100
Given that successive discounts are 20% and 15%.
SP = 85% of 80% of 100 = (85/100)(80/100)(100)
=> SP = Rs. 68
Clearly, single discount is 32%.
ANSWER:C
Answer: (C) 32%
Question: Of the employees in a company, 30 % are female who have a master degree. If 20 % of the female employees do not have a master degree, what percent of the employees in the company are female?
(A) 25%
(B) 32.5%
(C) 30%
(D) 45%
(E) 37.5%
Rationale: No. of female employees with Masters = 0.3 x E
No. of female employees without masters = 0.2 x F
Therefore No. of female employees with masters = F - 0.2 F = 0.8 F
The 2 expressions equal each other therefore 0.8F = 0.3E; F/E = 0.3/0.8 = 37.5%
Answer: E
Answer: (E) 37.5%
Question: A board 7ft. 9 inches long is divided into 3 equal parts . What is the length of each part?
(A) 5ft. 7 inches
(B) 3ft. 7 inches
(C) 4ft. 7 inches
(D) 2ft. 7 inches
(E) 1ft. 7 inches
Rationale: Length of board=7ft. 9 inches=(7*12+9)inches=93 inches.
Therefore, Length of each part = (93/3) inches = 31 inches = 2ft. 7 inches
Answer is D.
Answer: (D) 2ft. 7 inches
Question: Tickets numbered 1 to 50 are mixed and one ticket is drawn at random. Find the probability that the ticket drawn has a number which is a multiple of 4 or 7?
(A) 9/25
(B) 9/29
(C) 9/26
(D) 9/24
(E) 9/21
Rationale: Explanation:
S = {1, 2, 3, … , 49, 50}
E = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 7, 14, 21, 35, 42, 49}
n(S) = 50
n(E) = 18
P(E) = n(E)/n(S) = 18/50
= 9/25
ANSWER: A
Answer: (A) 9/25
Question: The average mark of 10 students is 80%. Later it was found that for one student, instead of 60%, the recorded 90%, by mistake. Now the corrected new percentage?
(A) 55
(B) 66
(C) 77
(D) 88
(E) 99
Rationale: lets assume the total marks in the exam per student is 100.
and given that avg mark of 10 student is 80%
so, total mark=80*10=800 ;
but instead of 60 mark they take wrong as 90 mark;
so,800-90 + 60=770
this is correct mark of 10 student
and then average of 10 student is =770/10=77
ANSWER:C
Answer: (C) 77
Question: A box contains ELEVEN bulbs out of which 5 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good
(A) 65/66
(B) 67/66
(C) 69/66
(D) 64/66
(E) 61/66
Rationale: Required probability = 1-5C4/11C4 = 1 - 1/66 = 65/166.Answer:A
Answer: (A) 65/66
Question: In a renowned city, the average birth rate is 6 people every two seconds and the death rate is 2 people every two seconds. Estimate the size of the population net increase that occurs in one day.
(A) 32,300
(B) 172,800
(C) 468,830
(D) 338,200
(E) 259,200
Rationale: Every 2 seconds, 4 persons are added (6-2). Every second 2 persons are added.
In a day 24hrs = 24 * 60 Minutes = 24 * 60 * 60 = 86400 seconds.
86400 * 2 = 172800
Option B is the answer.
Answer: (B) 172,800
Question: If the sales tax reduced from 3 1/2 % to 3 1/3%, then what difference does it make to a person who purchases an article with market price of Rs. 9600 ?
(A) 11
(B) 13
(C) 14
(D) 18
(E) 16
Rationale: Required difference = [3 ½ % of Rs.9600] – [3 1/3 % of Rs.9600]
= [(7/20-(10/3)]% of Rs.9600 =1/6 % of Rs.9600
= Rs. [(1/6)8(1/100)*9600] = Rs. 16.
Answer is E.
Answer: (E) 16
Question: The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?
(A) 198
(B) 243
(C) 270
(D) 290
(E) 292
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 15
5x = 1350
x = 270
Smaller number = 270.
C
Answer: (C) 270
Question: From the given equation find the value of x: xÂ²-18x+45
(A) 5
(B) -15
(C) -3
(D) 14
(E) 15
Rationale: (X - 15)X - 3
X = 15 or 3
Answer is E
Answer: (E) 15
Question: The equation x = 2y^2 + 5y - 19, describes a parabola in the xy coordinate plane. If line l, with slope of 3, intersects the parabola in the upper-left quadrant at x = -5, the equation for l is
(A) 3x + y + 15 = 0
(B) y - 3x - 11 = 0
(C) -3x + y - 20 = 0
(D) -2x - y - 7 = 0
(E) -3x + y + 13.5 = 0
Rationale: The question is made to look difficult though it is pretty simple if you focus on just the line and use process of elimination. (Remember that GMAT does not focus on parabolas so basically, the question should be quite do-able even if someone doesn't know how to handle parabolas.)
We need equation of l. Its slope must be 3.
Slope in option A and D is not 3 so we are left with B, C and E
The line has a point (-5, y) on it where y is positive (since the point lies in upper left quadrant).
In options B and E, if you put x = -5, you get -ve value for y co-ordinate. So ignore them.
Answer must be (C)
Answer: (C) -3x + y - 20 = 0
Question: An article is bought for Rs.600 and sold for Rs.900, find the gain percent?
(A) 50%
(B) 63 1/3%
(C) 33 1/3%
(D) 93 1/3%
(E) 33 1/3%
Rationale: Explanation:
600 ---- 300
100 ---- ? => 50%
Answer:A
Answer: (A) 50%
Question: How many integers between 50 and 100 can be evenly divided by neither 3 nor 5?
(A) 24
(B) 25
(C) 26
(D) 27
(E) 28
Rationale: divisible by 3 between 50 and 100 = 17 (51,54,57,60,63,66,69,72,75,78,81,84,87,90,93,96,99)
divisible by 5 between 50 and 100 = 9 (55,60,65,70,75,80,85,90,95)
Common divisible for 5 and 3 = 3 (60, 75, 90)
Total divisible by 5 and 3 between 50 and 100 = 17+9-3 => 23
There are 49 numbers between 50 to 100 i.e 51 to 99
so the integers that are not divisible by 3 and 5 => 49 - 23 => 26
ANSWER:C
Answer: (C) 26
Question: If e<0, which of the following must be true?
(A) –100 < e < 100
(B) e ≤ –1
(C) e ≤ 1
(D) e^2 ≥ 1/4
(E) –100 < e < 0
Rationale: e is a negative number.
A. –100 < e < 100e can be a negative number less than -100
B. e ≤ –1e can be a fraction, in which case it would be greater than -1
C. e ≤ 1must be true since 1 is positive and e is negative
D. e^2 ≥ 1/4not true if e is a negative fraction like -1/5
E. –100 < e < 0e can be a negative number less than -100=C
Answer: (C) e ≤ 1
Question: A train 200 m long running at 72 kmph crosses a platform in 25 sec. What is the length of the platform?
(A) 443 m
(B) 354 m
(C) 450 m
(D) 350 m
(E) 300 m
Rationale: E
300
E = 72 * 5/18 = 25 = 500 â€“ 200 = 300
Answer: (E) 300 m
Question: A salesman’s terms were changed from a flat commission of 5% on all his sales to a fixed salary of Rs.900 plus 2.5% commission on all sales exceeding Rs. 4,000. If his remuneration as per new scheme was Rs. 600 more than that by the previous schema, his sales were worth?
(A) 10000
(B) 12000
(C) 12019
(D) 12197
(E) 12012
Rationale: [900 + (X-4000) * (2.5/100)] - X * (5/100)
= 600
X = 10000
Answer: A
Answer: (A) 10000
Question: A vessel of capacity 90 litres is fully filled with pure milk. Nine litres of milk is removed from the vessel and replaced with water. Nine litres of the solution thus formed is removed and replaced with water. Find the quantity of pure milk in the final milk solution?
(A) 72.7 litres
(B) 73.9 litres
(C) 63.0 litres
(D) 93.7 litres
(E) 23.8 litres
Rationale: Let the initial quantity of milk in vessel be T litres.
Let us say y litres of the mixture is taken out and replaced by water for n times, alternatively.
Quantity of milk finally in the vessel is then given by [(T - y)/T]n * T
For the given problem, T = 90, y = 9 and n = 2.
Hence, quantity of milk finally in the vessel
= [(90 - 9)/90]2 (90) =72.9 litres.
Answer: B
Answer: (B) 73.9 litres
Question: The price of commodity X increases by 30 cents every year, while the price of commodity Y increases by 20 cents every year. If in 2001, the price of commodity X was $4.20 and the price of commodity Y was $4.40, in which year will commodity X cost 80 cents more than the commodity Y?
(A) 2010.
(B) 2011.
(C) 2012.
(D) 2013.
(E) 2014.
Rationale: The cost of commodity X increases by 10 cents per year relative to commodity Y.
The price of X must gain 20 + 80 = $1.00 cents on commodity Y, which will take 10 years.
The answer is B.
Answer: (B) 2011.
Question: Machine M, N, O working simultaneously Machine M can produce x units in 3/4 of the time it takes machine N to produce the same amount of units. Machine N can produce x units in 2/9 the time it takes machine O to produce that amount of units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N?
(A) 1/2
(B) 3/5
(C) 4/13
(D) 8/29
(E) 6/33
Rationale: Now ultimately the speed of every machine is given with respect to Mach O.
So lets assume the speed of O, say 12 hrs to make x units (assuming 6 because we can see we will need to divide by 3 and 4
Mach O makes x units in 12 hrs
So, Mach N = 2/9 of O = 2/9*12 = 8/3 hrs to make x units
and Mach M = 3/4 of N = 3/4*8/3 = 6 hrs to make x units
No they are running simultaneously. Lets see how much each mach makes in 1 hr
Mach O = x/12 units
Mach N = 3x/8 units
Mach M = x/6 units
In 1 hr, together they make - x/12+3x/8+x/6 = 5x/8
So what ratio of this has Mach N made?
(3x/8) / (5x/8) =3/5
Ans:B=3/5
Answer: (B) 3/5
Question: A license plate in the country Kerrania consists of four digits followed by two letters. The letters A, B, and C are used only by government vehicles while the letters D through Z are used by non-government vehicles. Kerrania's intelligence agency has recently captured a message from the country Gonzalia indicating that an electronic transmitter has been installed in a Kerrania government vehicle with a license plate starting with 79. If it takes the police 50 minutes to inspect each vehicle, what is the probability that the police will find the transmitter within three hours?
(A) 18/79
(B) 1/6
(C) 1/25
(D) 1/250
(E) 1/900
Rationale: So there are 900 cars that they have to search.. Each takes 50mins, total of 45000 mins.. Have to find in 180 mins.. Prob180/45000 = 1/250 (ANSWER D)
Answer: (D) 1/250
Question: The largest two digit number which is a perfect cube, is:
(A) 25
(B) 36
(C) 49
(D) 64
(E) 81
Rationale: Explanation:
4*4*4 = 64
Answer: D
Answer: (D) 64
Question: A certain candy store sold lollipops for $0.90 each and pieces of individually wrapped saltwater taffy for $0.20 each. If a customer purchased both lollipops and taffy from the store, and spent a total of $3.90, what total number of lollipops and saltwater taffy did the customer purchase?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: we can take numbers, as price of lollipop 9, 2 for taffy and 39 total for ease.
Now we can determine quickly that total number should range between 39/9 <= N <=39/2, so ans should be between 4 and 20.
Now solving the expression 9A+2B =39
first possibility with 1 lollipop, 15 taffy we get $3.90 total amount, but 1+15=16, and 16 is not an option.
So next choice, for 9A+2B =39 would come by decreasing 39 in multiple of 9 and checking divisibility of that number by 2. this way we get
3 lollipop, 6 taffy would be $3.90 total, 3*0.90 + 6*0.20= 3.90
Hence total number is 3 + 6 = 9
Ans D
Answer: (D) 9
Question: A train takes 10 sec to pass a signal post and covers a distance of 10 km in 15 min. Find the length of train?
(A) 100.1 m
(B) 223.1 m
(C) 111.1 m
(D) 120.3 m
(E) 133.4 m
Rationale: EXPLANATION:
We know,
Speed =	Distance / Time
Speed =	10/50	x 60 = 40 x 5/18 m/sec = 11.1 m/sec
Length of train = (Speed x Time)
= (11.11 x 10)
= 111.1 m
ANSWER IS C
Answer: (C) 111.1 m
Question: In N is a positive integer less than 200, and 2N/108 is an integer, then N has how many different positive prime factors?
(A) 2
(B) 3
(C) 5
(D) 6
(E) 8
Rationale: (B).
2n/108 must be an integer. => n/54 must be an integer. Hence n must be a multiple of 2*3*9.
=> n has 3 different prime integers.
Answer: (B) 3
Question: A salt manufacturing company produced a total of 100 tonnes of salt in January of a particular year. Starting from February its production increased by 100 tonnes every month over the previous months until the end of the year. Find its average monthly production for that year?
(A) 700
(B) 650
(C) 750
(D) 800
(E) 725
Rationale: Total production of salt by the company in that year = 100 + 200 + 300 + .... + 1200 = 7800.
Average monthly production of salt for that year = 7800/12 = 650.
Answer: B
Answer: (B) 650