mathewhe/aqua_rat huggingface dataset:
Question: If a and b are positive integers such that a/b = 5.75, which of the following must be a divisor of a
(A) 6
(B) 5
(C) 4
(D) 1
(E) 7
Rationale: a/b = 5.75
a/b = 575/100
a/b = 23/4
a = 23/4*b
We require to find from the available 5 options that must be a divisor of a"
This also means which of the following 5 options can divide 23 evenly
(Ignore b as its value unknown; Ignore 4 as in denominator)
Only option D = 1 best fits in
Answer = 1
ANSWER:D
Answer: (D) 1
Question: If 213 × 16 = 3408, then 1.6 × 2.13 is equal to :
(A) 0.3408
(B) 3.408
(C) 34.08
(D) 340.8
(E) None of these
Rationale: Solution
1.6 × 2.13 = (16/10x 213/100)= (16x 213/1000) = 3408/100 = 3.408. Answer B
Answer: (B) 3.408
Question: Mahesh marks an article 15% above the cost price of Rs. 540. What must be his discount percentage if he sells it at Rs. 457?
(A) 26.4%
(B) 21%
(C) 20%
(D) 19%
(E) None of these
Rationale: CP = Rs. 540, MP = 540 + 15% of 540 = Rs. 621
SP = Rs. 457, Discount = 621 - 457 = 164
Discount % = 164/621 * 100 = 26.4%
ANSWER:A
Answer: (A) 26.4%
Question: Which of the numbers below is the odd one out
1,4,10,19,21,31,46.
(A) 4
(B) 21
(C) 10
(D) 19
(E) 31
Rationale: 21 is the odd man.. diff between sucessive no.s are multiples of 3
ANSWER:B
Answer: (B) 21
Question: The average (arithmetic mean) of a normal distribution of a school's test scores is 62, and standard deviation of the distribution is 6.5. A student scoring a 78 on the exam is in what percentile of the school?
Choices
(A) 63rd percentile
(B) 68th percentile
(C) 84th percentile
(D) 96th percentile
(E) 98th percentile
Rationale: (78-65)/6.5 = 2 sigmas or 95.5th percentile for +-2 sigma but in our case we need only upper tail, so it's 100 - (100 - 95.5)/2 = 84th percentile
C
Answer: (C) 84th percentile
Question: A part-time employee whose hourly wage was decreased by 20 percent decided to increase the number of hours worked per week so that the employee's total income did not change. By what percent E should the number of hours worked be increased?
(A) 12.5%
(B) 20%
(C) 25%
(D) 50%
(E) 100%
Rationale: Correct Answer: C
Solution: C. We can set up equations for income before and after the wage reduction. Initially, the employee earns W wage and works H hours per week. After the reduction, the employee earns .8W wage and works X hours. By setting these equations equal to each other, we can determine the increase in hours worked: WH = .8WX (divide both sides by .8W) 1.25H = X We know that the new number of hours worked E will be 25% greater than the original number. The answer is C.
Answer: (C) 25%
Question: If A lends Rs.3500 to B at 10% per annum and B lends the same sum to C at 11.5% per annum then the gain of B in a period of 3 years is?
(A) 157.55
(B) 157.76
(C) 157.5
(D) 157.57
(E) 157.87
Rationale: (3500*1.5*3)/100
=> 157.50
Answer: C
Answer: (C) 157.5
Question: Four dice are thrown simultaneously. Find the probability that all of them show the same face.
(A) 1/215
(B) 1/216
(C) 1/217
(D) 2
(E) 2/215
Rationale: The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:
=6×6×6×6=64
n(S)=64
Let X
be the event that all dice show the same face.
X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}
n(X)=6
Hence required probability,
=n(X)n(S)=664
=1/216
Answer is B
Answer: (B) 1/216
Question: If x^4 + y^4 = 650, then the greatest possible value of x is between:
(A) 1 to 2
(B) 2 to 3
(C) 3 to 4
(D) 5 to 6
(E) 7 to 8
Rationale: The answers to this question provide a great 'hint' as to how to go about solving it; since they're all essentially 'ranges', you can use them to figure out which solution contains the maximum value of X.
We're told that X^4 + Y^4 = 100. To maximize the value of X, we need to minimize the value of Y^4. The smallest that Y^4 could be is 0 (when Y = 0), so we'll have....
X^4 = 650
Looking at the answers, it makes sense to see what 5^4 equals....
5^4 = 625
Since that is BELOW 650, and 6^4 will clearly be MORE than 650, we have the correct answer.
Final Answer:
D
Answer: (D) 5 to 6
Question: If * stands for /, / stands for -, + stands for * and - stands for +, then
9/8*7+5-10 = ?
(A) 13.3
(B) 10.8
(C) 10.7
(D) 11.4
(E) 12.5
Rationale: 9/8*7+5-10 this expression becomes 9-8/7*5+10 after exchanging the symbols then the values for it would be 9-1.142*5+10=13.290(app)=13.3
ANSWER:A
Answer: (A) 13.3
Question: Sixty five percent of a number is 21 less than four fifth of that number. What is the number ?
(A) 120
(B) 150
(C) 190
(D) 110
(E) 140
Rationale: Let the number be x.
Then, 4*x/5 –(65% of x) = 21
4x/5 –65x/100 = 21
5 x = 2100
x = 140.
Answer is E.
Answer: (E) 140
Question: If a and b are nonzero integers such that 2a/5 = b, then each of the following must be true EXCEPT
(A) 0 < b/a < 1
(B) ab is positive.
(C) On the number line, b lies between 0 and a.
(D) The ratio of a to b is equivalent to 10/4.
(E) a – b is positive.
Rationale: This question can be solved by TESTing VALUES. Based on its wording, you would likely need to do 2 TESTs to get to the correct answer though.
We're told that A and B are NONZERO INTEGERS and that 2a/5 = b or 2a = 5b. We're told that each of the answer is always true EXCEPT for one of them...
Before we get to the actual work, it's important to note a few details:
1) We are NOT told that A and B are positive - we're just told that they're NONZERO - that's interesting - it means that we have to consider the possibility that they're both NEGATIVE...
2) 4 of the answers will always be true, while one of them will EITHER be sometimes true OR never true. We'll have to keep working until we find 1 answer that is not true (for whatever reason) - that will be the solution to this question.
Since 2A = 5B, I'm going to run 2 pairs of TESTs at the same time...
A = 5
B = 2
AND
A = -5
B = -2
Answer A: 0 < B/A < 1
2/5 and -2/-5 both = 2/5. Answer A appears true.
Answer B: AB is positive
(2)(5) and (-2)(-5) both = +10. Answer B appears true.
Answer C: B is between 0 and A on the number line
0....2....5
-5....-2....0
Answer C appears true.
Answer D: A/B = 10/4
5/2 = -5/-2
10/4 = 5/2
Answer D appears true.
Answer E: A - B is positive
5 - 2 = 3
-5 - (-2) = -3 *****This is NOT always true.
Final Answer:
E
Answer: (E) a – b is positive.
Question: If log10 2 = 0.3010, then log2 10 is equal to:
(A) 0.699
(B) 0.301
(C) 699/301
(D) none of these
(E) 1000/301
Rationale: log2 10 =	1/log10 (2)
=	1/0.3010
= 10000/3010
= 1000/301	.
Answer is E.
Answer: (E) 1000/301
Question: A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is?
(A) Rs.340
(B) Rs.282
(C) Rs.739
(D) Rs.400
(E) Rs.538
Rationale: 2*12 : 3*12 : 4*24
1: 3: 4
1/8 * 3200 = 400
Answer:D
Answer: (D) Rs.400
Question: A 2-digit number is such that the product of the digits plus the sum of the digits
is equal to the number. What is the units digit of the number?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: Assume the 2 digit number is of the form xy, with x 6= 0. The statement indicates
that these two digits satisfy the equation xy + x + y = 10x + y. A quick simplication gives
y = 9.
correct answer E
Answer: (E) 9
Question: What are the number of ways to select 3 men and 2 women such that one man and one woman are always selected?
(A) 76 ways
(B) 66 ways
(C) 30 ways
(D) 56 ways
(E) 43 ways
Rationale: The number of ways to select three men and two women such that one man and one woman are always selected = Number of ways selecting two men and one woman from men and five women
= ⁴C₂ * ⁵C₁ = (4 * 3)/(2 * 1) * 5
= 30 ways.
Answer: C
Answer: (C) 30 ways
Question: (935421 x 625) = ?
(A) 575648125
(B) 584638125
(C) 584649125
(D) 585628125
(E) None of these
Rationale: Explanation:
935421 x 625 = 935421 x 54 = 935421 x(10/2)4
= 584638125
ANSWER IS B
Answer: (B) 584638125
Question: 2,3,5,8,13,21,34,?
(A) 57
(B) 58
(C) 55
(D) 54
(E) 56
Rationale: Each number is the sum of the previous two numbers, ie 18 + 29 = 55.
Answer : C
Answer: (C) 55
Question: one person Tharak speed with the current is 10 km/hr and the speed of the current is 3 km/hr. Tharak's speed against the current is:
(A) 0 km/hr
(B) 1 km/hr
(C) 2 km/hr
(D) 3 km/hr
(E) 4 km/hr
Rationale: Man's speed with the current = 10 km/hr
=> speed of the man + speed of the current = 10 km/hr
speed of the current is 3 km/hr
Hence, speed of the man = 10-3 = 7 km/hr
man's speed against the current = speed of the man - speed of the current
= 7-3 = 4 km/hr
ANSWER:E
Answer: (E) 4 km/hr
Question: The price of electricity in the area where the Smith family lives is scheduled to increase by 20% next year. Since the Smith family cannot afford an increase in their electric bill, how much will they have to reduce consumption to keep their cost the same?
(A) 30%
(B) 25%
(C) 16.7%
(D) 20%
(E) None
Rationale: Solution: Let the current year's electrical expense be represented by Rs. 100.
The price of electricity rises 20%. So, to buy same amount of electricity, they need to increase their expense,
= (100 + 20% of 100) = Rs. 120.
But, they want to keep electricity expense the same, so they have to cut Rs. by 20 to keep it to Rs. =100.
The % decrease in consumption is,
(20/120)*100 = 20%.
Mental Calculation Method;
100-----20%↑---→120------X%↓---→100.
Here, X = (20/120)*100 = 16.7%.
Answer: Option C
Answer: (C) 16.7%
Question: A computer program generates a single digit by a random process, according to which the probability of generating any digit is directly proportional to the reciprocal of one more than that digit. If all digits are possible to generate, then the probability T of generating an odd prime digit is between
(A) 0 and 1/6
(B) 1/6 and 1/3
(C) 1/3 and 1/2
(D) 1/2 and 2/3
(E) 2/3 and 5/6
Rationale: K (1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9+ 1/10) =1
Note that 1/10 is least value and is equal to 0.1 so we can write above series as
K (1+0.5+0.3+0.25+0.2+0.16+0.5+residual) = 1
K=1/3+
P (3 or 5 or 7) =K*13/24
Required probability T= 13/24 × 1/3+ = 4+/24 > 1/6
Answer should be B
P.s. 3+ denotes a value little greater than 3 .
Same for 4+.
Answer: (B) 1/6 and 1/3
Question: When integer Q is divided by 15, the remainder is 5. Which of the following has a remainder of 10 when divided by 15 ?
I. 3l
II. 4l+10
III. 5l
IV. 2l
V .6l
(A) I
(B) II
(C) IV
(D) V
(E) III
Rationale: E
Answer: (E) III
Question: Life expectancy is defined by the formula 2SB/G, where S = shoe size, B = average monthly electric bill in dollars, and G = GMAT score. If Melvin's GMAT score is twice his monthly electric bill, and his life expectancy is 80, what is his shoe size?
(A) 80
(B) 70
(C) 75
(D) 40
(E) 50
Rationale: Solution -
Given that, G = 2B and Life expectancy(L) = 80
L=2SB/G -> 80 = 2SB/2B --> S=80.
ANS A
Answer: (A) 80
Question: The sum of the first k positive integers is equal to k(k+1)/2. What is the sum of the integers from c to d, inclusive, where 0<c<d?
(A) d(d+1)/2 - (c+1)(c+2)/2
(B) d(d+1)/2 - c(c+1)/2
(C) d(d+1)/2 - (c-1)c/2
(D) (d-1)d/2 - (c+1)(c+2)/2
(E) (d-1)d/2 - c(c+1)/2
Rationale: Or try plug-in method: let d=4 and c=3 --> then d+c=7. Let see which option yields 7.
A. d(d+1)/2 - (c+1)(c+2)/2 = 10-10=0;
B. d(d+1)/2 - c(c+1)/2 = 10-6=4;
C. d(d+1)/2 - (c-1)c/2 = 10-3=7 --> OK;
D. (d-1)d/2 - (c+1)(c+2)/2 = 6-10=-4;
E. (d-1)d/2 - c(c+1)/2 = 6-6=0.
Answer: C.
Answer: (C) d(d+1)/2 - (c-1)c/2
Question: P can lay railway track between two stations in 16 days. Q can do the same job in 12 days. With the help of R, they completes the job in 4 days. How much days does it take for R alone to complete the work?
(A) 2/7
(B) 4/9
(C) 6/7
(D) 1/2
(E) 9 3/5
Rationale: Explanation :
Amount of work P can do in 1 day = 1/16
Amount of work Q can do in 1 day = 1/12
Amount of work P, Q and R can together do in 1 day = 1/4
Amount of work R can do in 1 day = 1/4 - (1/16 + 1/12) = 3/16 – 1/12 = 5/48
=> Hence R can do the job on 48/5 days = 9 (3/5) days
ANSWER:E
Answer: (E) 9 3/5
Question: Calculate how many men are needed to finish a specific task in 15 days if it will take 60 men to complete the same task in 80 days. ?
(A) 325
(B) 323
(C) 310
(D) 320
(E) 221
Rationale: men required to finish the work in 15 days = 60*80/15 = 320
Answer is D
Answer: (D) 320
Question: A certain country is divided into 8 provinces. Each province consists entirely of Progressives and Traditionalists. If each province contains the same number of Traditionalists and the number of Traditionalists in any given province is 1/12 the total number of Progressives in the entire country, what fraction of the country is Traditionalist?
(A) 1/5
(B) 1/3
(C) 1/2
(D) 2/3
(E) 3/5
Rationale: Let P be the number of Progressives in the country as a whole.
In each province, the number of traditionalists is P/12
The total number of traditionalists is 8P/12 = 2P/3.
The total population is P + 2P/3 = 5P/3
P / (5P/3) = 3/5
The answer is E.
Answer: (E) 3/5
Question: Solve the equation for x : 6x - 47 + 3x = 4 + 9 - x
(A) 4
(B) 5
(C) 7
(D) 9
(E) 6
Rationale: E
6
9 x + x = 13 + 47
10 x = 60 => x = 6
Answer: (E) 6
Question: If 1/8 of a pencil is black, 1/2 of the remaining is white and the remaining 3 1/2 cm is blue, find the total length of the pencil.
(A) 12
(B) 9
(C) 8
(D) 6
(E) 5
Rationale: Let the total length of the pencil be x cm.
Black part is 1/8 of the length so x/8.
so the Remaining part is x - x/8 ==> 8x/8 - x/8 ==> 7x/8 cm.
white part = 1/2 * 7x/8 = 7x/16 cm.
so the remaining part is 7x/8 - 7x/16 ==> 14x/16 - 7x/16 = 7x/16
which is equal to 3 1/2.
7x/16 = 7/2 cross multiply and we get x = 16/2 = 8 cm.
so the total length of the pencil is 8 cm. The correct answer is option C) 8.
Answer: (C) 8
Question: There are 100 freshmen at a particular college, all of whom must take at least one of the three core classes: Art, Biology, and Calculus. Of these freshmen, 17 take only Biology, 10 take only Calculus, 9 take all three classes, and 20 take Art and exactly one of the other two core classes. If the number of freshmen who take only Art is 3 times the number of freshmen who take every core class except Art, how many freshmen take Art?
(A) 25
(B) 32
(C) 36
(D) 48
(E) 62
Rationale: Make a venn diagram to get a clear picture. Look at the diagram:
Each letter represents only one color. b represents the people who take only Art. d represents people who take only Art and Bio etc.
d + f = 20 (People who take Art and one other class)
b = 3e (people who take only Art is 3 times the people who take Bio and Calculus)
17 + 10 + 9 + b + d + e + f = 100 (Total people)
b + b/3 = 44
b = 33
Number of freshmen who take Art = 33 + 20 + 9 = 62
Answer E
Answer: (E) 62
Question: 65% of a number is 21 less than 4/5th of that number. What is the number?
(A) 100
(B) 120
(C) 140
(D) 130
(E) 115
Rationale: Let the number be x
Then, 4x/5 - (65% of x) = 21
4x/5-65x/100 = 21
x = 140
Answer is C
Answer: (C) 140
Question: A train crosses a platform of 350 m in 15 sec, same train crosses another platform of length 500m in 20 sec. then find the length of the train?
(A) 100m
(B) 180m
(C) 159m
(D) 250m
(E) 152m
Rationale: Length of the train be ‘X’
X + 350/15 = X + 500/20
4X + 1400 = 3X + 1500
X = 100m
Answer:A
Answer: (A) 100m
Question: P has $63 more than what Q and R together would have had if both B and C had 1/9 of what P has. How much does P have?
(A) $69
(B) $72
(C) $75
(D) $78
(E) $81
Rationale: P = (2/9)*P+63
(7/9)*P=63
P=81
The answer is E.
Answer: (E) $81
Question: A can do a piece of work in 12 days. When he had worked for 2 days B joins him. If the complete work was finished in 8 days. In how many days B alone can finish the work?
(A) 17 days
(B) 19 days
(C) 22 days
(D) 20 days
(E) 18 days
Rationale: E
18 days
8/12 + 6/x = 1
X = 18 days
Answer: (E) 18 days
Question: In the next Cricket World Cup T-20, Team R has decided to score 200 runs only through 4s and 6s. In how many ways can the Team R score these 200 runs?
(A) 13
(B) 15
(C) 16
(D) 17
(E) 18
Rationale: Team R can score a maximum of 50 fours and a minimum of 2 fours with an interval or spacing of 3 units to accommodate the 6's.
So the number of fours scored forms an AP 2, 5, 8, ... 50 with a common difference of 3.
Number of ways of scoring 200 only through 4's and 6's = (50 - 2)/3 + 1 = 17
Answer: D
Alternate solution: 4x + 6y = 200 --> 2x + 3y = 100
x = (100 - 3y)/2 --> 100 - 3y should be even. This is possible when 3y is even.
There are 17 even multiples of 3 between 0 and 100.
Answer: D
Answer: (D) 17
Question: As a treat for her two children, a mother runs to the freezer in which she has three cherry ice pops, four orange ice pops, and five lemon ice pops. She chooses two at random to bring outside to the children, but realizes as she runs out the door that she cannot bring them different flavors without one being jealous of the other and getting even more upset. What is the probability that she has to return to the freezer to make sure that they each receive the same flavor?
(A) 7/22
(B) 17/33
(C) 27/44
(D) 37/55
(E) 47/66
Rationale: P(2 cherry) = 3/12 * 2/11 = 6/132
P(2 orange) = 4/12 * 3/11 = 12/132
P(2 lemon) = 5/12 * 4/11 = 20/132
P(2 of the same flavor) = 38/132
P(2 different flavors) = 1 - 38/132 = 94/132 = 47/66
The answer is E.
Answer: (E) 47/66
Question: The sum of all consecutive odd integers from −19 to 29, inclusive, is
(A) 125
(B) 135
(C) 150
(D) 175
(E) 235
Rationale: The sum of the odd numbers from -19 to +19 is 0.
Let's add the remaining numbers.
21+23+25+27+29 = 5(25) = 125
The answer is A.
Answer: (A) 125
Question: In how many ways Chief Minister and Minister be elected from a team of 8 members?
(A) 65
(B) 56
(C) 50
(D) 58
(E) 60
Rationale: To do this, if captain is elected first, then we have 8 ways of doing this.
For election of vice-captain, we have only 7 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)
So, the ans is 8*7 = 56 ways.
B
Answer: (B) 56
Question: What is the place value of 8 in the numeral 8729
(A) 8000
(B) 3400
(C) 3500
(D) 3000
(E) 4000
Rationale: Option 'A'
8 * 1000 = 8000
Answer: (A) 8000
Question: Claire has a total of 80 pets consisting of gerbils and hamsters only. One-quarter of the gerbils are male, and one-third of the hamsters are male. If there are 25 males altogether, how many gerbils does Claire have?
(A) 39
(B) 50
(C) 54
(D) 57
(E) 36
Rationale: G+H =80 ...1 ; G/4 +H/3 =25 ....2 OR 3G +4H =25*12 =300
G =80-H OR 3(80-H) +4H =300 H = 300-240 =60 THEN G= 96-60 =36
E
Answer: (E) 36
Question: Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is?
(A) 33
(B) 16
(C) 77
(D) 88
(E) 11
Rationale: Ratio of times taken by Sakshi and Tanys = 125:100 = 5:4
Suppose Tanya takes x days to do the work.
5:4 :: 20:x => x= 16 days.
Hence, Tanya takes 16 days to complete the work.
Answer: B
Answer: (B) 16
Question: Victor's job requires him to complete a series of identical jobs. If Victor is supervised at work, he finishes each job three days faster than if he is unsupervised. If Victor works for 144 days and is supervised for half the time, he will finish a total of 36 jobs. How long E would it take Victor to complete 10 jobs without any supervision?
(A) 34
(B) 52
(C) 60
(D) 70
(E) 92
Rationale: Rate when supervised = (job)/(time) = 1/t.
Rate when unsupervised = (job)/(time) = 1/(t+3).
For 144/2=72 days he is supervised and for 144/2=72 days he is unsupervised and does 36 jobs:
72/t + 72/(t+3) = 36 --> t=3 days --> t+3 = 6 days.
Victor to complete 10 jobs without any supervision will need E 10(t + 3) = 60 days.
Answer: C.
Answer: (C) 60
Question: A monkey start climbing up a tree 18 ft tall.Each hour it hops 3 ft and slips back 2 ft. How much time would it take the monkey to reach the top.
(A) 15 hrs
(B) 18 hrs
(C) 19 hrs
(D) 17 hrs
(E) 16 hrs
Rationale: if monkey hops 3ft and slips back 2ft in a hour, it means the monkey hops (3ft-2ft)= 1ft/hr.
similarly in 15hrs it wil be 15ft.
Bt since the height of the tree is 18ft, so if the monkey hops up the tree in the next hr i.e 16th hr then it reaches at the top of the tree.
hence it takes 16 hrs for monkey to reach at the top
ANSWER:E
Answer: (E) 16 hrs
Question: If each participant of a chess tournament plays exactly one game with each of the remaining participants, then 120 games will be played during the tournament. Find the number of participants.
(A) 15
(B) 16
(C) 17
(D) 18
(E) 19
Rationale: Let P be the number of participants.
PC2 = 120
(P)(P-1) = 240 = 16*15
P = 16
The answer is B.
Answer: (B) 16
Question: A wolf eats 5.5 Kg of meat in 2 days. A baby tiger eats 3 Kg of meat in 4 days. How much meat can the two combined eat in two days?
(A) 10.
(B) 9.
(C) 8.
(D) 7.
(E) 6.
Rationale: 2/2*5.5+2/4*3=7 kg
D
Answer: (D) 7.
Question: A sum of money when distributed among friends is in the ratio of 3:4:5, if the amount is the larger 3digit number divisible by 24, what is the share of 3rd person?
(A) 400
(B) 410
(C) 420
(D) 430
(E) 440
Rationale: Largest 3 digit number divisible by 24= 984
So their shares are (984*3/12=246) , (984*4/12=328) , (984*5/12=410)
ANSWER:B
Answer: (B) 410
Question: The measure of the side of a square is multiplied by 5. If x represents the perimeter of the original square, what is the value of the new perimeter?
(A) 3x
(B) 4x
(C) 5x
(D) 12x
(E) 27x
Rationale: Original perimeter = x
Hence original side = x/4
New side = 5x/4
New perimeter = 4*5x/4 = 5x
Correct Option: C
Answer: (C) 5x
Question: A computer factory produces 4032 computers per month at a constant rate, how many computers are built every 30 minutes assuming that there are 28 days in one month?
(A) 2.25.
(B) 3.00.
(C) 4.5.
(D) 5.225.
(E) 6.25.
Rationale: Number of hours in 28 days = 28*24
Number of 30 mins in 28 days = 28*24*2
Number of computers built every 30 mins = 4032/( 28*24*2) = 3
Answer B
Answer: (B) 3.00.
Question: S(n) is sum of first n natural numbers, Z(n) = 2S(n)+41, lowest value of n such that Z(n) is NOT a prime.
(A) 7
(B) 6
(C) 40
(D) always a prime
(E) none
Rationale: as the sum of first N natural numbers is
S(n)=n/2(1+n)
so z(n)=2(s(n))+41=2*n/2(1+n)+41=n(1+n)+41
Now put all the given options one by one
take n=7
z(7)=7(7+1)+41=56+41=97 a prime number
take n=6
z(6)=6(6+1)+41=41+41=83 again a prime number
now take n=40
z(40)=40(40+1)+41=40*41+41=41(40+1)=41*41=1681 not a prime number
ANSWER:C
Answer: (C) 40
Question: A boat can travel with a speed of 14 km/hr in still water. If the speed of the stream is 6 km/hr, find the time taken by the boat to go 72 km downstream.
(A) 4.25 hr
(B) 3.6 hr
(C) 8.25 hr
(D) 2.25 hr
(E) 2.50 hr
Rationale: speed of boat in still water = 14 km/hr
speed of the stream = 6 km/hr
Speed downstream = (14+6) = 20 km/hr
Time taken to travel 72 km downstream = 72â„20 =3.6 hours
Answer is B
Answer: (B) 3.6 hr
Question: A and B starts a business with Rs.8000 each, and after 5 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months?
(A) 36:23
(B) 18:23
(C) 18:10
(D) 18:14
(E) 14:11
Rationale: A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 5 months and then withdraws Rs.4000. So, the investment of B for remaining 13 months is Rs.4000 only.
A : B
8000*18 : (8000*5) + (4000*13)
14400 : 92000
A:B = 36:23
Answer: A
Answer: (A) 36:23
Question: Two persons A and B can complete a piece of work in 30 days and 45 days respectively. If they work together, what part of the work will be completed in 4 days?
(A) 2/5
(B) 1/6
(C) 1/4
(D) 1/9
(E) 2/9
Rationale: A's one day's work = 1/30
B's one day's work = 1/45
(A + B)'s one day's work = 1/30 + 1/45 = 1/18
The part of the work completed in 4 days = 4 (1/18) = 2/9.
ANSWER E
Answer: (E) 2/9
Question: 1,5,6 ,25, 26,30,31, 125,126,130,131,150,151,155,156,……… What is the value of 33rd term in the
given series
(A) 3124
(B) 3125
(C) 3126
(D) 3127
(E) 3128
Rationale: 1st terms gives 2nd and 3rd terms
1st term is 1
2nd term 1*5=5 3rd term= 5+1=6
similarly,
4th term =5*5=25 5th term=25+1=26
1st term gives 2nd and 3rd values
2nd term gives 4th and 5th values
lke wise
16th term gives 32nd and 33rd values
16 th term is 125*5=625
32nd term is 625*5=3125 and 33rd value is 3126
ANSWER:C
Answer: (C) 3126