divelab/Sys2Bench huggingface dataset:
Question: S1 = 3 S2 = 6 ... Sn = 3n + 4 For the sequence above, in which any term n is defined as 3n + 4, what is the value of n for the first term in the sequence to exceed 50?
Options:
A)13
B)16
C)12
D)9
E)8
Rationale: term 16 = 3*16+4 = 52
Answer : B
Answer: B
Question: The smallest 3 digit prime number is?
Options:
A)101
B)102
C)110
D)112
E)113
Rationale: The smallest 3-digit number is 100, which is divisible by 2.
100 is not a prime number.
101 < 11 and 101 is not divisible by any of the prime numbers 2, 3, 5, 7, 11.
101 is a prime number.
Hence 101 is the smallest 3-digit prime number.
A)
Answer: A
Question: If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is?
Options:
A)4/16
B)4/10
C)4/11
D)4/13
E)4/12
Rationale: P(SᴜK) = P(S) + P(K) - P(S∩K), where S denotes spade and K denotes king.
P(SᴜK) = 13/52 + 4/52 - 1/52 = 4/13
Answer: D
Answer: D
Question: Four of the five parts numbered (a), (b), (c), (d) and (e) in the following equation are exactly equal. Which part is not equal to the other four? The number of that part is the answer
Options:
A)x(x + y)2 – 2x2y
B)x(x + y)2 + 2x2y
C)x(x2 – y2)
D)x[(x + y)2 – 2xy]
E)x[(x + y)2 – 2xy2]
Rationale: Others are x3 + xy2
Answer E
Answer: E
Question: The average of 17 numbers is 10.9. If the average of first nine numbers is 10.5 and that of the last nine numbers is 11.4, the middle number is
Options:
A)11.8
B)11.4
C)10.9
D)11.7
E)11.9
Rationale: Sum of first nine numbers (N1 to N9) + Sum of last nine numbers (N9 to N17) = 10.5 x 9 + 11.4 x 9 = 21.9 x 9 = 197.1
Hence, the middle number
= 197.1 - 17 x 10.9
= 197.1 - 185.3 = 11.8
ANSWER:A
Answer: A
Question: Envelopes can be purchased for $1.50 per pack of 100, $1.00 per pack of 50, or $0.03 each. What is the greatest number of envelopes that can be purchased for $7.60?
Options:
A)426
B)430
C)443
D)470
E)486
Rationale: I think first we should see in what group envelopes value less, so that we can buy as many as we can with a specific amount of money:
-the 100 pack costs 1.5$, meaning 0.015$ per envelope
-the 50 pack costs 1$, meaning 0.02$ per envelope
-the single envelope costs 0.03$ per envelope
Thus, we have to buy as many 100 packs as we can, then as meny of 50 packs as we can and the remaining envelopes are single ones.
Having 7.6$, we can buy as many as 4 packs of 100 (4 x 1.5$ = 6$). We then have 1.6 $ left. so we buy 1 pack of 50 for 1$. We now have 0.6$ left, so we buy 20 individual envelopes. If we add up the numbers, we get 400+50+20=470 envelopes. Answer D
Answer: D
Question: If 3a + 1 < 2a < 9 - a, which of the following must be true?
I. -1 < a < 3
II. a < -1
III. a < 3
Options:
A) II only
B) III only
C) I and II only
D) II and III only
E) I, II and III
Rationale: Just try plugging a in a number like 0 or 1, and you'll quickly find that the inequality doesn't hold.
So you can immediately cross out any answers with I or III, leaving just (A) II only.
Answer: A
Question: In the rectangular coordinate system Point O has coordinates (0,0) and Point B has coordinates (4,3) and if point A is equidistant from points O and B and the area of the triangle OAB is 16, which of the following are the possible coordinates of point A.
Options:
A)(-2,6)
B)(0,4)
C)(2,-6)
D)(2,6)
E)(4,0)
Rationale: Area.pngSince A is equidistant from points O and B, then it must be somewhere on the green line (perpendicular bisector of OB).
(2,-6) and (2,6) are not on that line. If A is at (0,4) or (3,0), then the area is 1/2*4*3=6. Thus A must be at (2,-6).
Answer: C.
Answer: C
Question: A firm has 5 senior partners and 4 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is a senior partner. (2 groups are considered different if at least one group member is different)
Options:
A)70
B)75
C)80
D)85
E)90
Rationale: The total number of ways to form a group of 3 is 9C3 = 84
The number of groups without a senior partner is 4C3 = 4
The number of groups which include a senior partner is 84-4 = 80
The answer is C.
Answer: C
Question: A car is running at a speed of 110kmph. What distance will it cover in 9sec?
Options:
A)100m
B)279m
C)180m
D)200m
E)250m
Rationale: Speed = 110kmph = 110*5/18 = 31 m/s
Distance covered in 9sec = 31*9 = 279m
Answer is B
Answer: B
Question: If 34 men do a work in 40 days, in how many days will 20 men do it?
Options:
A)65
B)68
C)61
D)55
E)74
Rationale: 34 * 40 = 20 * x
x = 68 days
Answer: B
Answer: B
Question: A grocer is storing soap boxes in cartons that measure 25 inches by 42 inches by 60 inches. If the measurement of each soap box is 7 inches by 6 inches by 5 inches, then what is the maximum number of soap boxes that can be placed in each carton?
Options:
A)210
B)252
C)280
D)300
E)420
Rationale: Maximum number of soap boxes that can be placed in each carton = Volume of each carton/ volume of each box
= (25*42*60)/(7*6*5)= 300
ANSWER:D
Answer: D
Question: Vijay went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
Options:
A)19.7
B)20.1
C)21.4
D)21.7
E)21.8
Rationale: Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25−30/100−x)6/100 = 30/100
⇒ 6(25 −0.3 −x) = 30
⇒ (25 − 0.3 − x) = 5
⇒ x = 25 − 0.3 − 5 = 19.7
A)
Answer: A
Question: A pharmaceutical company made 3000 strips of tablets at a cost of Rs. 4800. The company gave away 1000 strips of tablets to doctors as free samples. A discount of 25% was allowed on the printed price. Find the ratio profit if the price is raised from Rs. 3.25 to Rs. 4.25 per strip and if at the latter price, samples to doctors were done away with. (New profit / Old profit).
Options:
A)55.5
B)63.5
C)75
D)99.25
E)80
Rationale: Solution: Total sales revenue (Old) = 2000*3.25*0.75 = 4875[0.75 as 25% discount was allowed]
ProfitOld = Total sales revenue - 4800
= 4875-4800 = 75
Total sales revenue (New) = 3000*4.25*0.75 = 9562.5[New price is calculated on doctors samples as well.]
ProfitNew = 9562.5 - 4800 = 4762.5
Ratio,
ProfitNew / ProfitOld = 4762.5/75 = 63.5.
Answer: Option B
Answer: B
Question: In shop contains 500 articles each of a cost of $10. He sold them at a price of $20. If the shop keeper has a order of 200 articles, how much profit he will get?
Options:
A)A)200
B)B)4000
C)C)1500
D)D)2000
E)E)600
Rationale: Total money after selling articles = 200*20 = 4000
cost price = 200*10 = 2000
profit = 2000
correct option is D
Answer: D
Question: 7 points are marked on a straight line and another 8 points are marked on a second straight line with no points in common. How many triangles can be constructed with vertices from among the above points?
Options:
A)21
B)91
C)168
D)196
E)364
Rationale: select 2 points from one line and one from another.
7C2 * 8C1 [ 2 points from the line containing 7 points and 1 from the line containing 8 points]
+
8C2 * 7C1 [ 2 points from the line containing 8 points and 1 from the line containing 7 points]
=364
ANSWER: [E]
Answer: E
Question: During a sale, the price of a pair of shoes is marked down 13% from the regular price. After the sale ends, the price goes back to the original price. What is the percent of increase to the nearest percent from the sale price back to the regular price for the shoes?
Options:
A)9%
B)10%
C)11%
D)15%
E)90%
Rationale: Assume the price = 100
Price during sale = 87
Price after sale = 100
Percent increase = 13/87*100 = 15% approx.
Correct Option: D
Answer: D
Question: Working alone, A can complete a certain kind of job in 3 hours. A and D, working together at their respective rates, can complete one of these jobs in 2 hours. In how many hours can D, working alone, complete one of these jobs?
Options:
A) 2
B) 4
C) 6
D) 8
E) 10
Rationale: Let total time taken by D to complete the job = D
total time taken by A to complete the job = 3
Work done by A in an hour
1/A = 1/3
Working together A and D can complete the job in 2 hours
1/A + 1/D = 1/2
=>1/D = 1/2 - 1/A
= 1/2- 1/3
= 1/6
=> D = 6 hours
Answer C
Answer: C
Question: There are 8 students. 4 of them are men and 4 of them are women. If 4 students are selected from the 8 students. What is the probability that the number of men is equal to that of women?
Options:
A)18/35
B)16/35
C)14/35
D)13/35
E)12/35
Rationale: men= women means 2 men 2 women
total such combinations = 4c2 * 4c2 = 4!/2!.2! * 4!/2!.2! = 6*6
total combinations = 8c4 = 8*7*6*5/4*3*2*1 = 70
so probability = 36/70 = 18/35
hence A
Answer: A
Question: The diagonals of a rhombus are 15 cm and 12 cm. Find its area?
Options:
A)70
B)90
C)60
D)80
E)292
Rationale: 1/2 * 15 * 12
= 90
Answer:B
Answer: B
Question: The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is?
Options:
A)6
B)8
C)4
D)9
E)3
Rationale: S = 1
M = x
DS = x + 1
US = x - 1
35/(x + 1) + 35/(x - 1) = 12
x = 6
Answer: A
Answer: A
Question: If 45-[28-{37-(15-*)}]= 59, then * is equal to:
Options:
A)-29
B)-19
C)20
D)29
E)39
Rationale: 45-[28-{37-(15-*)}]= 59 => 45-[28-{37-15+*}]=59
45-[28-37+15-*]=59 => 45[43-37-*]=59
45-[6-*]=59 => 45-6+*=59
39+*=59 => *=59-39
= 20
ANSWER:C
Answer: C
Question: A sum of money lent out at S.I. amounts to Rs. 820 after 2 years and to Rs. 1020 after a further period of 5 years. The sum is?
Options:
A)Rs.440
B)Rs. 500
C)Rs. 540
D)Rs. 740
E)Rs. 840
Rationale: S.I for 5 years = (1020 - 820) = Rs. 200.
S.I. for 2 years = 200/5 * 2 = Rs. 80.
Principal = (820 - 80) = Rs. 740.
ANSWER:D
Answer: D
Question: At a contest with 2000 participants, 1/2 of the people are aged 16 to 18. Next year, the number of people aged 16 to 18 will increase by 1/4. After this change, what percentage of the total 2000 people will the 16- to 18- year-olds represent?
Options:
A)62.50%
B)60%
C)70%
D)65%
E)66/3%
Rationale: I just wanted to mention a couple of things here:
* this is a pure ratio question; the number 2000 is completely irrelevant, and you can ignore it if you like. When we increase something by 1/4, we are multiplying it by 1 + 1/4 = 5/4, so the answer here must be (1/2)*(5/4) = 5/8 = 62.50 %.
Answer : A
Answer: A
Question: Four milkmen rented a pasture. A grazed 24 cows for 3 months, B 10 cows for 5 months, C 35 cows for 4 months and D 21 cows for 3 months. If A’s share of rent is Rs.720, find the total rent of the field.
Options:
A)Rs.3250
B)Rs.3350
C)Rs.3450
D)Rs.3550
E)Rs.3650
Rationale: Ratio of shares of A, B, C, D = (24 * 3) : (10 * 5) : (35 * 4) : (21 * 3)
= 72 : 50 : 140 : 63
Let total rent be Rs.x. Then, A’s share = Rs. 72x/325.
Therefore, 72x/325 = 720 => x = 720 * 325/72 = 3250.
Hence, total rent of the field is Rs.3250.
ANSWER:A
Answer: A
Question: Sandy purchased 20 dozen toys at the rate of $144 per dozen. Sandy sold each toy at the rate of $15. What was the percentage profit?
Options:
A)15%
B)25%
C)35%
D)45%
E)55%
Rationale: A dozen toys cost $144, so each toy cost $12.
selling price / cost price = 15 / 12 = 1.25
The percentage profit is 25%.
The answer is B.
Answer: B
Question: The total number of digits used in numbering the pages of a book having 366 pages is
Options:
A)732
B)990
C)1098
D)1305
E)1605
Rationale: Explanation:
Total number of digits
= (No. of digits in 1- digit page nos. + No. of digits in 2-digit page nos. + No. of digits in 3- digit page nos.)
= (1 x 9 + 2 x 90 + 3 x 267) = (9 + 180 + 801) = 990.
Answer: B
Answer: B
Question: If x is odd and y is odd, then x + y is
Options:
A)Odd
B)Odd whenever xy is even
C)Even whenever xy is odd
D)Even
E)It cannot be determined
Rationale: x is odd and y is odd, then x + y is
Let's take x=9 and y=5.
x+y=9+5=14.
x+y=14=even.
Option: D
Answer: D
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow?
Options:
A)2/27
B)2/29
C)2/21
D)2/22
E)2/27
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = ³C₂/¹⁵C₂ = (3 * 2)/(15 * 14) = 1/35
Probability that both are yellow = ²C₂/¹⁵C₂ = (2 * 1)/(15 * 14) = 1/105
Probability that one blue and other is yellow = (³C₁ * ²C₁)/¹⁵C₂ = (2 * 3 * 2)/(15 * 14) = 2/35
Required probability = 1/35 + 1/105 + 2/35
= 3/35 + 1/105 = 1/35(3 + 1/3)
= 10/(3 * 35) = 2/21
Answer:C
Answer: C
Question: A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 55 hrs and a machine of type S does the same job in 22 hours. If the company used the same number of each type of machine to do the job in 5 hours, how many machines of type R were used?
Options:
A)22/7
B)28/7
C)23/7
D)25/7
E)22/7
Rationale: Rate of machine R =1/55
Rate of machine S =1/22
since same no of machines used for R and S to do the same work in 5 hrs
So collective rate needed to finish the work in 5 hrs= 1/5
Let the no of machine be x
So, x/55 +x/22 =1/5
7x=22
x=22/7
So no of machine R is 22/7
Answer E
Answer: E
Question: A highway is to be divided into four lanes. For this purpose, three yellow stripes are painted so that stripes divide the highway into four lanes. If 3 gallons of paint cover an area of 5P square feet of highway, how many gallons of paint are needed to paint two stripes x inches wide on a stretch of highway m miles long? (1 mile = 5280 feet and 1 feet = 12 inches)
Options:
A)792mx/P
B)264mx/P
C)792P/mx
D)264P/mx
E)880mx/P
Rationale: 1 square foot needs 3/5P gallons of paint.
The width of each stripe is x/12 feet.
The length of each stripe is 5280m feet.
The area of each stripe is (5280m)(x/12) = 440mx square feet.
For three stripes, the total area is 1320mx square feet.
The number of gallons needed is (1320mx)*(3/5P) = 792mx/P gallons.
The answer is A.
Answer: A
Question: In how many years, Rs. 75 will produce the same interest at 6% as Rs. 800 produce in 2 years at 4½% ?
Options:
A)4 years
B)16 years
C)8 years
D)9 years
E)12 years
Rationale: Explanation :
Let Simple Interest for Rs.75 at 6% for n years = Simple Interest for Rs.800 at 4½ % for 2 years
75×6×n/100=800×9/2×2/100
75×6×n=800×9/2×2
75×6×n=800×9
n=16 years
Answer : Option B
Answer: B
Question: Three 6 faced dice are thrown together. The probability that all the three show the same number on them is ?
Options:
A)1/38
B)1/36
C)1/39
D)1/31
E)1/29
Rationale: It all 3 numbers have to be same basically we want triplets. 111, 222, 333, 444, 555 and 666. Those are six in number. Further the three dice can fall in 6 * 6 * 6 = 216 ways.
Hence the probability is 6/216 = 1/36
Answer:B
Answer: B
Question: If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is ?
Options:
A)1/6
B)1/2
C)1/9
D)1/1
E)1/5
Rationale: The number of exhaustive outcomes is 36.
Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2
P(E) = 1 - 1/2
= 1/2.
Answer: B
Answer: B
Question: If S is a positive integer, which of the following must be odd?
Options:
A)S+1
B)S^2+S
C)S^2+S+1
D)x^2−1
E)3x^2−3
Rationale: A. S+1 = can be odd or even. Since O + O =E or E + O = O
B. S^2 + S = S(S+1). Since from the above derivation we already know the term S+1 can be Odd or Even, directly substitute here. S(ODD) = Even (When S is Even) or S(EVEN) = EVEN [When S is ODD]
C. Here's the answer. Since we know the term S^2 + S can always take a EVEN number, EVEN + 1 = ODD
Hence C.
Answer: C
Question: Present birth rate is 32 per thousand while death rate is 11 per thousand. What will be the percentage increase in the rate of population?
Options:
A)0.21%
B)21%
C)0.021%
D)2.1%
E)None of these
Rationale: birth rate=32/1000=0.032
death rate=11/1000=0.011
increase in population=0.032-0.011=0.021=2.1%
ANSWER:D
Answer: D
Question: What will be the output of the following code statements?
Integer a = 13, b = 39, c = 10 print (a × b / c) – c
Options:
A)65
B)26
C)29
D)26
E)41
Rationale: Explanation:
Apply BODMAS rule
13 × 39 = 507/10-10 =50.7 –10 =40.7
Answer:E
Answer: E
Question: The instructions state that Cheryl needs 2/9 square yards of one type of material and 1/8 square yards of another type of material for a project. She buys exactly that amount. After finishing the project, however, she has 4/18 square yards left that she did not use. What is the total amount of square yards of material Cheryl used?
Options:
A)1/12
B)1/9
C)1/8
D)1 1/9
E)2 1/9
Rationale: Total bought = 2/9+1/8
left part 4/18--->2/9
so used part 2/9+1/8-2/9=1/8
ANSWER:C
Answer: C
Question: The concentration of spirit in three different vessels A, B and C are 30%, 30% and 25% respectively. If 4 litres from vessel A, 5 litres from vessel B and 6 litres from vessel C are mixed, find the concentration of spirit in the resultant solution.
Options:
A)32%
B)33%
C)34%
D)35%
E)28%
Rationale: Quantity of spirit in new solution=(4*30/100)+(5*30/100)+(6*25/100)=1.2+1.5+1.5=4.2 liters
So % concentration of spirit=100*4.2/(4+5+6)=28%
ANSWER:E
Answer: E
Question: Arnold wanted to create a perfect shade of pink for his new canvas painting. He started out replacing 25% of a 100% red colored paint with white. He then further replaced 15% of this shade with white. Finally, he repeated the process by replacing 10% of the shade with white. What was the final percentage of red in Arnold's pink paint?
Options:
A)62.40%
B)51%
C)68.21%
D)57.37%
E)70%
Rationale: Quick answer: 100x0.75x0.85x0.9
We begin with 100% red paint. 25% of this is replaced with white paint which leaves us with a mixture of 75% red paint (as 25% is white)
Next, 15% of this mixture is further mixed with white paint. That implies that 85% of the previous red paint remains. Hence, the new percentage is 75x0.85% = 63.75%
Finally, 10% of the new paint mixture is again mixed with white. This leaves us with 90% of the previous red quantity. So the final percentage of red is 63.75x0.9% = 57.37%
Answer: D
Answer: D
Question: If an item costs Rs.3 in '99 and Rs.203 in '00.What is the % increase in price?
Options:
A)200/3 %
B)200/6 %
C)100%
D)200%
E)none of these
Rationale: increase is 203-3=200
%increase is 200*100/3=6666.667%
ANSWER:E
Answer: E
Question: In a certain random experiment, exactly one of the outcomes A, B, and M will occur. In each random experiment, the probability that outcome A will occur is 1/3 , and the probability that outcome B will occur is 1/3. What is the probability that when the random experiment is conducted 6 independent times, each of outcomes A, B, and M will occur twice?
Options:
A)5/243
B)1/12
C)10/81
D)1/6
E)16/81
Rationale: Number of ways in which a group of 2A,2B,2M can be formed in any order = 6!/(2!*2!*2!) [ formula for total of 6 items with 2 each of similar kind)
Total number of ways in which the die can be thrown independently = _ _ _ _ _ _ ; there are 6 places .First can be filled in 3 different ways A/B/M; Second in 3 diff ways again and so on.
So total number of ways = 3X3X3X3X3X3 = 3^6
There fore probability = 6!/(2!x2!x2!) by 3^6 = 90/3^6 = 10/81 Answer C
Answer: C
Question: A man buys a cycle for Rs. 1600 and sells it at a loss of 15%. What is the selling price of the cycle?
Options:
A)s. 1090
B)s. 1360
C)s. 1190
D)s. 1202
E)s. 1256
Rationale: S.P. = 85% of Rs. 1600 = Rs.85/100x 1600	= Rs. 1360
ANSWER :B
Answer: B
Question: Which of the following data sets has the largest standard deviation?
Options:
A) {1, 2, 3, 4, 5}
B) {2, 3, 3, 3, 4}
C) {2, 2, 2, 4, 5}
D) {0, 2, 3, 4, 6}
E) {-1, 1, 3, 5, 7}
Rationale: since we are asked to compare 'standard deviation', we should look out for similarity between all the sets..
The SIMILARITY is - the SUM of all sets is equal =15..
and hence average = 15/5 = 3...
Now we have 5 different sets which have AVG as 3, so we will look for the spread of the other elements of set around the AVERAGE..
clearly E has a range of 7-(-1) or 8, and has the highest standard deviation..
ans E
Answer: E
Question: At present, the ratio between the ages of Arun and Deepak is 5:4. After 5 years, Arun's age will be 40 years. What is the age of Deepak at present?
Options:
A)28
B)26
C)24
D)22
E)20
Rationale: Let the present ages of Arun and Deepak be 5x and 4x years respectively.
Then, 5x + 5 = 40 => x = 7
Deepak's age = 4x = 28 years.
Answer: A
Answer: A
Question: Twenty four men can do a work in 35 days. How many men are required to complete the work in 21 days?
Options:
A)11
B)40
C)99
D)77
E)21
Rationale: We have M1 D1 = M2 D2
So, 24 * 35 = M2 * 21 => M2
= 40.
Answer: B
Answer: B
Question: An express traveled at an average speed of 100 km/hr, stopping for 3 min after every 75 kn. How long did it take to reach its destination 600 km from the starting point?
Options:
A)5 hrs 21 min
B)4 hrs 21 min
C)6 hrs 41 min
D)6 hrs 21 min
E)4 hrs 34 min
Rationale: D
6 hrs 21 min
Time taken to cover 600 km = 600/100 = 6 hrs.
Number of stoppages = 600/75 - 1 = 7
Total time of stoppages = 3 * 7 = 21 min
Hence, total time taken = 6 hrs 21 min.
Answer: D
Question: In a kilometer race, A beats B by 20 meters or 10 seconds. What time does A take to complete the race?
Options:
A)490 sec
B)190 sec
C)176 sec
D)716 sec
E)123 sec
Rationale: Time taken by B run 1000 meters
= (1000 * 10)/20 = 500 sec.
Time taken by A = 500 - 10
= 490 sec.
Answer:A
Answer: A
Question: A group of 4 students bought movie tickets in one row next to each other. If Bob and Lisa are in this group, what is the probability that Bob and Lisa will each sit next to only one of the three other students from the group?
Options:
A)5.55%
B)16.67%
C)15.75%
D)20.45%
E)25%
Rationale: The question basically asks about the probability that Bob and Lisa sit at the ends.
The total # of sitting arrangements is 4!.
Desired arrangement is either BYZL or LYZB. Now, YZ can be arranged in 2! ways, therefore total # of favorable arrangements is 2*2!.
P=(favorable)/(total)=(2*2!)/4!=1/6.
Answer: B.
Answer: B
Question: AB
+BA
___
141
In the addition problem above, A and B represent digits in two different two-digit numbers. What is the sum of A and B?
Options:
A)6
B)8
C)9
D)11
E)12
Rationale: two ways to do it..
1) straight logic..
we can see that ones digit is 1 when units digit B and A are added..
only 12 fits in..
E
Answer: E
Question: If 6 (A's capital) = 8 (B's capital) = 10 (C's capital). Then the ratio of their capitals is:
Options:
A)20:15:16
B)20:15:11
C)20:15:12
D)20:15:18
E)20:19:19
Rationale: 6A = 8B = 10 C
A:B:C = 1/6:1/8:1/10
= 20:15:12
Answer:C
Answer: C
Question: Find the invalid no.from the following series 3, 7, 15, 27, 63, 127, 255
Options:
A)3
B)7
C)27
D)63
E)127
Rationale: Go on multiplying the number by 2 and adding 1 to it to get the next number.So, 27 is wrong.
C
Answer: C
Question: (1.00001)(0.99999) - (1.00006)(0.99994) =
Options:
A)35(10^-10)
B)10^-10
C)3(10^-10)
D)10^-5
E)3(10^-5)
Rationale: (1.00001*0.99999)-(1.00006*0.99994)
= (1+0.00001)(1-0.00001) - (1+0.00006)(1-0.00006)
= 1 - (0.00001)^2 - 1 + (0.00006)^2
= -(0.0000000001) + (0.0000000036)
= 0.0000000035=35(10^-10)
Answer A
Answer: A
Question: Find ? x 11 = 555555
Options:
A)505
B)5050
C)50505
D)5005
E)None of these
Rationale: Answer
Let N x 11 = 555555
Then N = 555555 / 11 = 50505.
Correct Option: C
Answer: C
Question: In 1982 and 1983, Company B’s operating expenses were $12.0 million and $13.0 million, respectively, and its revenues were $15.6 million and $18.8 million, respectively. What was the percent increase in Company B’s profit (revenues minus operating expenses) from 1982 to 1983 ?
Options:
A)3%
B)61 1/9%
C)25%
D)33 1/3%
E)60%
Rationale: Profit in 1982 = 15.6 - 12 = 3.6 million $
Profit in 1983 = 18.8 - 13 = 5.8 million $
Percentage increase in profit = (5.8-3.6)/3.6 * 100 %
= 61 1/9 %
Answer B
Answer: B