divelab/Sys2Bench huggingface dataset:
Question: Let x and y be positive integers, and r and s be single-digit positive integers. If x/y = r.sss, where the bar below the s indicates that the decimal repeats infinitely, which of the following CANNOT be true?=
Options:
A) y = 1.2 × 10^a, where a is a positive integer.
B) y = 1.5 × 10^b, where b is a positive integer.
C) y = 1.8 × 10^c, where c is a positive integer.
D) y = 2.5 × 10^d, where d is a positive integer.
E) y = 2.7 × 10^e, where e is a positive integer.
Rationale: Concentrating only on the answer choices, only option D is not a multiple of 3. The rest of them are multiples of 3, thats a common trend in other answer choices. With this logic can we say that Option A is correct answer?
Answer: A
Question: A cycle is bought for Rs.900 and sold for Rs.1170, find the gain percent?
Options:
A)27%
B)20%
C)80%
D)30%
E)24%
Rationale: 900 ---- 270
100 ---- ? => 30%
Answer: D
Answer: D
Question: A person has three children with at least one boy. Find the probability of having at least two boys among the children.
Options:
A)3/4
B)1/3
C)2/3
D)1/4
E)1/5
Rationale: Explanation :
The event is occuring under the following situations:
Second is a boy and third is a girl OR
Second is a girl and third is a boy OR
Second is a boy and third is a boy
This will be represented by: (1/2) x (1/2) + (1/2) x (1/2) + (1/2) x (1/2) = 3/4
Answer : A
Answer: A
Question: 39 persons can repair a road in 24 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?
Options:
A)10
B)13
C)14
D)15
E)26
Rationale: Let the required number of days be x.
Less persons, More days (Indirect Proportion)
More working hours per day, Less days (Indirect Proportion)
Persons	30	:	39	:: 12 : x
Working hours/day	6	:	5
30 x 6 x x = 39 x 5 x 24
x =	(39 x 5 x 24)/(30 x 6)
x = 26.
ANSWER:E
Answer: E
Question: P software has coding line 5% more than N, N software has coding line 4/20 more than M. M software has 80 lines of coding. find P lines.
Options:
A)101
B)107
C)108
D)109
E)110
Rationale: M s/w has 80 line of code
N s/w has = 80+80*4/20= 96 line of code
P s/w 5% more N' code 96+4.8=100.8
or
101 line of code
ANSWER:A
Answer: A
Question: Rs.8000 become Rs.9261 in a certain interval of time at the rate of 5% per annum of C.I. Find the time?
Options:
A)2 years
B)6 years
C)8 years
D)3 years
E)9 years
Rationale: 9261 = 8000(21/20)N
(21/20)3
= (21/20)N
=> N = 3
Answer:D
Answer: D
Question: The ratio of the incomes of Uma and Bala is 4:3 and the ratio of their expenditure is 3:2. If at the end of the year, each saves $5000 then the income of Uma is?
Options:
A)$24000
B)$23000
C)$22000
D)$21000
E)$20000
Rationale: Let the income of Uma and Bala be $4x and $3x
Let their expenditures be $3y and $2y
4x-3y = 5000-------1)
3x-2y = 5000-------2)
From 1) and 2)
x = 5000
Uma's income = 4x = 4*5000 = $20000
Answer is E
Answer: E
Question: A and B can together finish a work in 40days. They worked together for 10days and then B left. After another 15days, A finished the remaining work. In how many days A alone can finish the job?
Options:
A)10
B)25
C)60
D)30
E)20
Rationale: A+B 10days work = 10*1/40 = 1/4
Remaining work = 1-1/4 = 3/4
3/4 work is done by A in 15days
whole work will be done by A in 15*4/3 = 20days
Answer is E
Answer: E
Question: The number of years of service of the eight employees in a production department are 15, 10, 9, 19, 6, 4, 14 and 16. What is the range in the number of years of service of the eight employees?
Options:
A)10
B)11
C)12
D)13
E)15
Rationale: = 19-4
= 15
Answer E
Answer: E
Question: From the set of numbers {p, t, u, v, w, x, y, z}, how many different combinations can we have without the t or the u in them? Ex:. (x,y), (x), (w,z,y,x), etc... and note that (x,y)=(y,x)
Options:
A)16
B)31
C)32
D)63
E)64
Rationale: Any letter (p, v, w, x, y, z) can be included or not.
Thus there are 2^6 combinations - 1 empty combination = 63 combinations
The answer is D.
Answer: D
Question: 650 students took the test on English and Maths. 35% students failed in english and 45% failed in maths. 40% of those who passed in maths also passed in english, then how many students failed in both ?
Options:
A)a) 162
B)b) 138
C)c) 60
D)d) 38
E)e) 13
Rationale: Passed in english = 65%
Passed in maths = 55%
Passed in both = 40% of 55% = 2/5 * (55%) = 22%
Passed in (English + Maths - Both + Neither) = 100%
65 + 55 - 22 + Neither = 100
Neither = 100 - 98 = 2% = 0.02 * 650 = 13
Answer: E
Answer: E
Question: Which of the following is always true for any real number 'a' and 'b'?
Options:
A)|ab| = |a||b|
B)|a/b| = |a|/|b|
C)|-ab| < |a||b|
D)|ab| > |a/b|
E)|ab| = -|ab|
Rationale: This one is obvious if you know how absolute value works. One of the fundamental principles of absolute value is multiplicativeness, which holds that for absolute values, f(ab) = f(a) f(b). Thus the answer is A.
Answer: A
Question: The simple interest on a sum of money will be Rs.600 after 10 years. If the principal is trebled after 5 years what will be the total interest at the end of the tenth year?
Options:
A)8981
B)3799
C)1200
D)2693
E)1732
Rationale: P --- 10 ---- 600
P --- 5 ----- 300
3P --- 5 ----- 900
------
=> 1200
Answer: C
Answer: C
Question: How many ounces of a 60% salt solution must be added to 70 ounces of a 20 percent salt solution so that the resulting mixture is 40% salt?
Options:
A)16.67
B)30
C)50
D)60.33
E)70
Rationale: let x=ounces of 60% salt solution to be added
.2*70+.6x=.4(70+x)
x=70
Answer E
Answer: E
Question: A field is 90 metre long and 50 metre broad. A 25 metre long, 20 metre broad and 4 metre deep tank dug in the field and the earth taken out is spread evenly over the remaining field. How much the level of field will rise?
Options:
A)0.5 metre
B)0.3 metre
C)0.8 metre
D)0.6 metre
E)0.7 metre
Rationale: Area of field = 90 x 50 = 4500 m2
Area of field dug out = 25 x 20 = 500 m2
Therefore, Area of remaining field = 4500 m2 - 500 m2 = 4000 m2
Volume of the earth dug out = 25 x 20 x 4 = 2000 m3
Therefore, Field will rise by 2000/4000 = 0.5 metre
Answer A
Answer: A
Question: A shopkeeper purchased 70 kg of potatoes for Rs.420 and sold the whole lot at the rate of Rs 6.50 per kg .What will be his gain percent?
Options:
A)8 1/9
B)8 1/1
C)8 1/3
D)8 1/7
E)8 1/4
Rationale: Explanation:
Price per 1 kg = 4207042070 = Rs.6.
Profit per 1 kg = Rs.6.5 – Rs.6 = Rs.0.5
Profit for 70 kg = 0.5 × 70 = Rs.35
Gain % = 3542035420 × 100= 8.33% = 8 1/3
Answer: C
Answer: C
Question: Perimeter of rhombus is equal to perimeter of circle. Longest distance between two points in rhombus is 80. Area of rhombus is 2400 cm^2. Find area of circle.
Options: 10000, 62500, 2500, one more I don't Remember.
Options:
A)3284.28678
B)3184.28678
C)3084.28678
D)4184.28678
E)2184.28678
Rationale: Let Diagonals of Rhombus are p,q and side is a .
Let Longest side is one of the p and q, let its p=80;
Area of a Rhombus is A =p*q/2
A=2400
2400=80 *q /2
4800=80q=> q=60
4a^2 =60^2 + 80^2
4a^2=10,000=> a=>50
Given: Perimeter of R = Perimeter of Circle
4a = 2*3.14* r=> r=31.84
Area of circle = 3.14* r^2 = 3184.28678
ANSWER:B
Answer: B
Question: The simple interest at y% for y years will be $y on a sum of
Options:
A)$ (1000)/x
B)$(100)x^2
C)$ x
D)$ (100)/y
E)$ 100x
Rationale: Principal =$(100*y)/(y*y)=$(100/y).
Answer is D
Answer: D
Question: The simple interest on a sum of money is 4/9 of the principal and the number of years is equal to the rate percent. Find the rate and the time?
Options:
A)6 2/3%
B)6 2/8%
C)6 7/3%
D)9 2/3%
E)6 2/5%
Rationale: 4/9 P = (P*R*R)/100
R = 20/3
= 6 2/3%
Answer:A
Answer: A
Question: If 20 men take 15 days to to complete a job, in how many days can 20 men finish that work?
Options:
A)15
B)16
C)17
D)18
E)19
Rationale: Ans. 15 days
Answer: A
Question: When a number is divided by 3 &then multiply by 12 the answer is 9 what is the no.?
Options:
A)4.5
B)5
C)2.25
D)5.7
E)6.5
Rationale: if $x$ is the number, x/3 * 12 = 9
=> 4x = 9
=> x = 2.25
C
Answer: C
Question: Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is:
Options:
A)17523
B)2788
C)1750
D)2787
E)29899
Rationale: Explanation:
C.I.= Rs.[4000*(1+10/100)^2-4000]
=Rs.840
sum=Rs.(420 * 100)/3*8=Rs.1750\
Answer: C) Rs,1750
Answer: C
Question: A certain research group plans to create computer models of x% of a list of 10,000 bacterial species known to inhabit the human body. After a budget cut, the group finds it must reduce this selection by (x − 5)%. In terms of x, how many species of bacteria will the group be able to model?
Options:
A)x*x – 5x
B)(x)(105 – x)
C)(100)(105 – x)
D)(100)(95 – x)
E)(x-5)/100
Rationale: Let's say that x = 10
So 10% of 10,000 = 1,000 types of bacteria
After the budget cuts, this 1,000 is reduced by (10-5)% = 5%
5% of 1,000 = 50
1,000 - 50 = 950
Plug x=10 into the answers and find 950.
Answer:B
Answer: B
Question: 5, -28, 2, -31....
Options:
A)1
B)3
C)2
D)4
E)5
Rationale: 5 - 33 = -28
-28 +30 = 2
2 - 33 =31
31 + 30 = 1
ANSWER:A
Answer: A
Question: A certain telephone company offers two plans, A and B. Under plan A, the company charges a total of $0.60 for the first 5 minutes of each call and $0.06 per minute thereafter. Under plan B, the company charges $0.08 per minute of each call. What is the duration of a call, in minutes, for which the company charges the same amount under plan A and under plan B?
Options:
A)2
B)9
C)15
D)21
E)30
Rationale: Let the duration, in minutes, for which the company charges the same under plan A and plan B be t minutes.
Then under plan A the cost would be $0.6+0.06(t-5) and under plan B the cost would be $0.08t. We want these amount to be equal: 0.6+0.06(t-5)=0.08t --> 60+6(t-5)=8t --> t=15.
Answer: C.
Answer: C
Question: Two trains one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 4 hours and 9 hours respectively. The ratio of their speeds is
Options:
A)3 : 2
B)4 : 3
C)4 : 7
D)8 : 5
E)None
Rationale: Sol.
Let us name the trains as A and B. Then,
(A's speed) : (B's speed) = √b : √a
= √9 : √4
= 3 : 2.
Answer A
Answer: A
Question: father is aged three times more than his son ronit. after 8 years, he would be two and half times if ronit's age. after further 8 years , how many times would he be of ronit's age?
Options:
A)2 times
B)2.5 times
C)3 times
D)3.8 times
E)4 times
Rationale: ronit's present age be x years . then, father's present age= (x+3x)years= 4x years
therefore (4x + 8) = 5/2 (x + 8)
8x + 16 = 5x + 40
3x = 24 , x= 8, ratio = (4x + 16)/(x + 16)= 48/24=2,
correct answer (A)
Answer: A
Question: What is the perimeter, in meters, of a rectangular garden 16 meters wide that has the same area as a rectangular playground 16 meters long and 12 meters wide?
Options:
A)48
B)56
C)60
D)56
E)192
Rationale: Say Length of garden is L meters.
Then (L*16) = 16 * 12 [Given area is same. Area= L * B]
Therefore L works out to 12 meters.
Perimeter of Garden = 2* (12+16) = 56 meter.
Answer is D
Answer: D
Question: To deliver an order on time, a company has to make 25 parts a day. After making 25 parts per day for 3 days, the company started to produce 5 more parts per day, and by the last day of work 100 more parts than planned were produced. Find how many parts the company made and how many days this took.
Options:
A)600
B)500
C)575
D)655
E)675
Rationale: Let x be the number of days the company worked. Then 25x is the number of parts they planned to make. At the new production rate they made:
3⋅25+(x−3)⋅30=75+30(x−3)
Therefore: 25x=75+30(x−3)−100
25x=75+30x−90−100
190−75=30x−25
115=5x
x=23
So the company worked 23 days and they made 23⋅25+100=675 pieces.
So answer is E.
Answer: E
Question: In how many ways, a committee of 5 members can be selected from 6 men and 5 ladies, consisting of 3 men and 2 ladies?
Options:
A)451
B)124
C)531
D)145
E)200
Rationale: (3 men out 6) and (2 ladies out of 5) are to be chosen.
Required number of ways = (6c3x5c2)
= [6x5x4/3x2x1] x [5x4/2x1] = 200.
Ans: E
Answer: E
Question: For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when m is even. What is [9]*[4] equivalent to?
Options:
A)[108]
B)[54]
C)[36]
D)[27]
E)[18]
Rationale: [9]*[4] = 27*2 = 54 = (1/2)(108) =[108]
The answer is A.
Answer: A
Question: A sum of money invested at C.I. amounts to Rs. 800 in 3 years to Rs. 890 in 4 years. The rate of interest per annum is?
Options:
A)2 1/2 %
B)4%
C)5%
D)6 2/3 %
E)11 1/4%
Rationale: S.I. on Rs. 800 for 1 year = (890 - 800) = Rs.90 Rate = (100 * 90)/(800 * 1) = 11 1/4%
ANSWER:E
Answer: E
Question: X Y
+Y X
________
The sum of the two digit numbers above is a three digit number PQ1, where each letter X, Y, P, and Q represents a different non zero digit. Which of the following can be the value of X?
I)	7
II)	8
III)	9
Options:
A)I only
B)II only
C)III only
D)I and II only
E)all I , II and III
Rationale: it can be a combination of 9,2 or 8,3 or 7,4
I choose E as an answer.
Answer: E
Question: What is the probability that a leap year has 53 Sundays and 52 Mondays?
Options:
A)1/9
B)1/8
C)1/3
D)1/7
E)1/2
Rationale: A leap year has 52 weeks and two days
Total number of cases = 7
Number of favourable cases = 1
i.e., {Saturday, Sunday}
Required Probability = 1/7
Answer:D
Answer: D
Question: Machine Z can produce x units in 3/4 of the time it takes machine N to produce x units. Machine N can produce x units in 2/3 the time it takes machine O to produce x units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N?
Options:
A) 1/2
B) 1/3
C) 4/13
D) 8/29
E) 6/33
Rationale: Let the following be true:
Z makes x in time t
Then the following follows:
N makes x in 4t/3
O makes x in 3/2(4t/3) = 2t
M:N:O = 1:4/3:2=3:4:6
So N=4/(3+4+6)=4/13=C
Answer: C
Question: If cement, gravel and sand are to be mixed in 7:10:13 and 7 tons of cement is available how many tons of mixture can be produced assuming that sufficient gravel and sand is readily available.
Options:
A)35 7/8
B)30
C)34 2/7
D)34 5/7
E)34 6/7
Rationale: Cement:Gravel:Sand = 7:10:13 --> total of 7+10+13 = 30 parts.
If we use 7 tons of cement, then we'll get 7/7*30 = 30 tons of mixture.
Answer: B.
Answer: B
Question: If the cost price is 90% of the selling price, then what is the profit percent?
Options:
A)5%
B)11%
C)13%
D)21%
E)19%
Rationale: Let S.P. = $100
C.P. = $90
Profit = $10
Profit% = 10/90 * 100 = 25/6 = 11% approximately
Answer is B
Answer: B
Question: If w and y are positive integer and w/y is an even integer, which of the following can be an odd integer?
Options:
A)x
B)xy
C)x−y
D)x+2y
E)w/3
Rationale: C w-Y
Let says w =12 Y=3 iT BECOMES w-Y =9 This is odd True
w = 12 Y = 6 THEN w-Y = 2, Which is even hence this is False.
so both Yes and NO situations are exists for this Option. C can't be the correct answer same logic goes for E. I believe this question is incomplete b'coz of Irrelevant Options.
Answer: E
Question: Which of the following is equal to 3.14 x 10^6) ?
Options:
A)3.14
B)3140000
C)31400
D)314
E)314000
Rationale: = 3.14 x 10^6
= 3.14 x 1000000
= 3140000.
Answer is B.
Answer: B
Question: 9 men and 12 boys finish a job in 12 days, 12 men and 12 boys finish it in 10 days. 10 men and 10 boys shall finish it in how many days?
Options:
A)19 days
B)18 days
C)12 days
D)27 days
E)26 days
Rationale: 9M + 12B ----- 12 days
12M + 12B ------- 10 days
10M + 10B -------?
108M + 144B = 120M +120B
24B = 12M => 1M = 2B
18B + 12B = 30B ---- 12 days
20B + 10B = 30B -----? => 12 days
Answer: C
Answer: C
Question: A box contains 10 tablets of medicine A and 17 tablets of medicine B. What is the least number of tablets that should be taken from the box to ensure that at least two tablets of each kind are among the extracted.
Options:
A)12
B)15
C)17
D)19
E)21
Rationale: The worst case scenario will be if we remove all 17 tablets of medicine B first. The next 2 tablets we remove have to be of medicine A, so to guarantee that at least two tablets of each kind will be taken we should remove minimum of 17+2=19 tablets.
Answer:D.
Answer: D
Question: Which is better investment 11% stock at 143 or 9 Â¾% stock at 117
Options:
A)11 % stock at 143
B)9 3/4 stock at 117
C)both
D)cannot be compared
E)none of these
Rationale: Let the investment in each (143*117)
Income in first case = (11/143*143*117)=1287
Income in second case=((39/117*4)*143*117)=1394.25
Clearly, 9 Â¾% stock at 117
ANSWER B
Answer: B
Question: 96% of the population of a village is 23040. The total population of the village is?
Options:
A)26799
B)24000
C)26682
D)29973
E)12312
Rationale: X * (96/100) = 23040
X = 240 * 100
X = 24000
Answer: B
Answer: B
Question: Simplify:935421 x 625
Options:
A)594983125
B)584932715
C)584938125
D)584638125
E)584641258
Rationale: 935421 x 625 = 935421 x 54 = 935421 x (10/2)^ 4
935421 x 10^4/2^4=9354210000/16
= 584638125
Answer is D
Answer: D
Question: 1. Internet: $80, with no sales tax, plus $10 shipping fee
2. Store X: $90, a 10% discount, plus 10% tax on discounted price
3. Store Y: $90, no tax
4. Store Z: $90, a 10% sales tax, and $10 rebate after tax
Isaac can purchase a certain item in four different ways, as shown in the table. What is the lowest price for which he can purchase this item?
Options:
A)88.1
B)89.0
C)89.1
D)89.50
E)90.0
Rationale: 1. Internet: $80, with no sales tax, plus $10 shipping fee --> 80+10=90;
2. Store X: $90, a 10% discount, plus 10% tax on discounted price --> 90*0.9*1.1=89.1
3. Store Y: $90, no tax --> 90;
4. Store Z: $90, a 10% sales tax, and $10 rebate after tax --> 90*1.1-10=89.
So the lowest price is $89.
Answer: B.
Answer: B
Question: 3 men and 8 women complete a task in same time as 6 men and 2 women do. How much fraction of work will be finished in same time if 2 men and 3 women will do that task.
Options:
A)1/2
B)1/10
C)1/18
D)1/16
E)1/11
Rationale: 3 m + 8 w = 6 m + 2 w
3 m = 6 w
1 m = 2 w
Therefore 3 m + 8 w = 14 w
2 m + 3 w =7 w
Answer is 7/14 =1/2
Answer: A
Answer: A
Question: There are 10 cans in the refrigerator. 5 of them are red and 5 of them are blue. In how many ways we can remove 8 cans so that at least one red and at least one blue cans to remain the refrigerator.
Options:
A)410
B)490
C)493
D)455
E)445
Rationale: Answer: A.
Answer: A
Question: If W is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of W?
Options:
A)10
B)12
C)14
D)16
E)18
Rationale: W = 30!
8
W = 30 x 29 x 28 x 27 x 26 x 25 x 24 x 24 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 09 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
Out of these 30 , 27 , 24 , 21 , 18, 15 , 12 , 09 , 06 , 3 are factors of 3
3 x 10 , 3 x 3 x 3 , 3 x 8 , 3 x 3 x 2, 3 x 5 , 3 x 4 , 3 x 3 x 3 , 3 x 2 , 3
So we have a total of 14 three's ...
Therefore the maximum value of K can be 14 (C)
Answer: C
Question: At what rate percent per annum will a sum of money double in 6 years.
Options:
A)12.5%
B)13.5%
C)11.5%
D)14.5%
E)16.6%
Rationale: Let principal = P, Then, S.I.=P and Time=8 years
Rate = [(100 x P)/ (P x 6)]% = 16.6% per annum. Answer: E
Answer: E
Question: What decimal fraction is 70 ml of a litre ?
Options:
A).7
B).07
C).05
D)0.07
E)None of these
Rationale: Answer
Required fraction = 70/1000
= 7/100
= .07
Correct Option: B
Answer: B
Question: There are 8 baskets numbered from 1 to 8 and filled with apples. 10 children are asked to pick apples one by one from each basket such that the number of apples picked by each child from each basket is equal to the number marked on the basket. If there were 1000 apples in total and the baskets were filled in such a way that none of the basket became empty in the process, how many apples were left in the end?
Options:
A)640
B)680
C)720
D)760
E)800
Rationale: Each child takes a total of 1+2+3+4+5+6+7+8 = 8*9/2 = 36 apples.
The total number of apples taken by 10 children is 10*36 = 360
The number of apples left in the end is 1000 - 360 = 640 apples.
The answer is A.
Answer: A
Question: If two numbers x, a perfect square and y, a perfect cube are added results a two digit number, whose digits if reversed, difference is 9, Find x and y ?
Options:
A)x=4,y=8
B)x=4,y=9
C)x=4,y=7
D)x=4,y=9
E)x=5,y=8
Rationale: 4+8=12
when reversed 21
21-12=9
x=4,y=8
ANSWER:A
Answer: A
Question: The food in a camp lasts for 40 men for 35 days. If ten more men join, how many days will the food last?
Options:
A)34days
B)32days
C)30days
D)28days
E)26days
Rationale: one man can consume the same food in 40*35 = 1400 days.
10 more men join, the total number of men = 50
The number of days the food will last = 1400/50 = 28 days.
Answer: D
Answer: D
Question: The total of the ages of Amar, Akbar and Anthony is 80 years. What was the total of their ages three years ago ?
Options:
A)71 years
B)72 years
C)73 years
D)74 years
E)75 years
Rationale: Answer : A.
Required sum = (80 - 3 x 3) years = (80 - 9) years = 71 years.
Answer: A
Question: If (x+4)^2/(x+10)=8, then the difference between the two possible values of x is:
Options:
A)2
B)6
C)12
D)16
E)24
Rationale: (x+4)^2/(x+10)=8
(x+4)^2=8(x+10)
x^2+8x+16=8x+80
x^2-64=0
(x-8)(x+8)=0
x=8 or x=-8
The answer is D.
Answer: D
Question: If m and n are nonzero integers and 390m = 150n, then mn must be divisible by
Options:
A)10
B)45
C)50
D)65
E)75
Rationale: 390m = 150n;
m/n = 5/13.
m is a multiple of 5 and n is a multiple of 13, therefore mn must be a multiple of 5*13 = 65.
Answer: D.
Answer: D
Question: A is the average (arithmetic mean) of the first 7 positive multiples of 6 and B is the median of the first 3 positive multiples of positive integer n. If the value of A^2 – B^2 is zero, what is the value of n?
Options:
A)8
B)10
C)12
D)16
E)24
Rationale: If A^2 - B^2 = 0, then let's assume that A = B.
A must equal the 4th positive multiple of 4, thus A = 24, which also equals B.
B is the second positive multiple of n, thus n = 24/2 = 12.
The answer is C.
Answer: C
Question: Two pipes P and Q can fill a cistern in 10 and 25 minutes respectively. Both are opened together, but at the end of 5 minutes the first is turned off. How much longer will the cistern take to fill?
Options:
A)12 1/7
B)12 1/4
C)12 1/3
D)12 1/2
E)12 1/5
Rationale: 5/10+ x/25 = 1
x= 12 1/2 Answer: D
Answer: D
Question: 4 litres of water is mixed in certain amount of pure milk whose cost is Rs. 3 per litre. If the dishonest milkman earns a profit of 20% by selling the mixture at initial price then what is the quantity of pure milk obtained by the customer?
Options:
A)24
B)20
C)18
D)25
E)None of these
Rationale: cost given = Rs 3/ltr.
i.e cost earned through water mixture= 4*3 = 12 rs
therefore earned 20%, that is on water .. therefore total earned = 12*100/20 = 60 rs.
hence 60/3 = 20 ltr overall mixture!
ANSWER:B
Answer: B
Question: When two coins are tossed,Find the probability of getting all tails?
Options:
A)1/3
B)3/4
C)1/8
D)3/8
E)1/4
Rationale: When two coins are tossed,
S = {HH, HT, TH, TT} where H = Head and T = Tail
Let E = event of getting all tails
Then E = {TT}
so, P(E) = n(E)/n(S) =1/4
Answer: E
Question: Ravi purchased 20 dozens of toys at the rate of Rs. 340 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit?
Options:
A)16.4%
B)1.2%
C)5.6%
D)34.1%
E)12.2%
Rationale: A
C.P. of 1 toy = 340/12 = Rs. 28.3
S.P of 1 toy = Rs. 33
Profit = 4.6/31.25 * 100 = 16.4%
Answer is A
Answer: A
Question: Let x, y and z be distinct integers, x and y are odd and positive, and z is even and
positive. Which one of the following statements cannot be true?
Options:
A)(x – z)^2 * y is even
B)(x – z)*y^2 is odd
C)(x – z)*y is odd
D)(x – y)^2 * z is even
E)none
Rationale: Explanation :
Let x = 5, y= 3, z = 2 (according to the given condition)
(x – z)2 * y :- ( 5 - 2)2 * 3 = 27
(x – z) * y2 :- (5 - 2) * 32 = 27
(x – z) * y :- (5 - 2) * 3 = 9.
(x – y)2 * z :- (5 - 3)2 * 2 = 8.
Answer : A
Answer: A
Question: Boy sells a book for Rs. 450 he gets a loss of 10%, find CP of the book?
Options:
A)Rs.300
B)Rs.400
C)Rs.500
D)Rs.550
E)Rs.600
Rationale: Find cost price
Let C.P. of book = x and S.P. = Rs. 450
S.P. of book = C.P. – (10% of C.P.)
S.P. = x – (0.10x)
450 = 0.9 x
x i.e cost price = Rs.500
C
Answer: C