divelab/Sys2Bench huggingface dataset:
Question: Ages of two persons differ by 16 years. If 6 year ago, the elder one be 3 times as old the younger one, find their present age
Options:
A)12,28
B)14,30
C)16,32
D)18,34
E)19,34
Rationale: Explanation:
Let the age of younger person is x,
Then elder person age is (x+16)
=> 3(x-6) = (x+16-6) [6 years before]
=> 3x-18 = x+10
=> x = 14.
So other person age is x + 16 = 30
Answer: Option B
Answer: B
Question: On simplification, 3500 – (1000 ÷ 20.50) is equal to :
Options:
A)3451.21
B)3029.0
C)2993.03
D)2984.36
E)None of these
Rationale: Explanation:
Given exp. = 3500 - ((1000 ÷ 2050) * 100)
= 3451.21
ANSWER A
Answer: A
Question: An alloy weighing 16 ounces is 50% gold. How many ounces of pure gold must be added to create an alloy that is 80% gold?
Options:
A)24
B)18
C)9
D)27
E)18
Rationale: An alloy of 16oz which is 50% gold means there is 8 oz of gold. To get to an alloy that is 80% gold, let's use this expression: (8 + x)/(16 + x) = 0.8 with x representing the amount of pure gold that must be added to get to 80%. The expression we are using represents the new total weight of pure gold over the new total new weight of the alloy and this fraction should represent 80% or 0.8. you will see that 24 is the correct answer, as 32/40=0.8
Choose A
Answer: A
Question: Ben and King are partners in a business. Ben is a working partner and King is a sleeping partner in the business. Ben invested Rs.3500 and King invested Rs.7000. Ben receives 7% of the profit for managing the business the rest is divided in proportion of their capitals. Out of a total profit of Rs.9600, how much did Ben receive?
Options:
A)2648
B)3648
C)3548
D)4648
E)3628
Rationale: ratio of their investments Rs.3500:Rs.7000=1:2
7% of the profit for managing the business =7/100*9600=672
remaining profit=9600-672=8928
share profit in ratio of investment 8928/3 =2976
Ben ratio share=1*2976=2976
total money Ben collects=2976+672=3648
Answer: B
Answer: B
Question: Which of the following is the lowest positive integer that is divisible by the first 7 positive integer multiples of 3?
Options:
A)600
B)820
C)1040
D)1260
E)1480
Rationale: The number must be divisible by 3, 2*3, 3^2, 2^2*3, 5*3, 2*3^2, and 7*3.
The lowest such number is 2^2*3^2*5*7 = 1260.
The answer is D.
Answer: D
Question: The average age of three boys is 10 years and their ages are in proportion 2:4:4. What is the age in years of the youngest boy?
Options:
A)6
B)9
C)8
D)4
E)2
Rationale: 2x + 4x + 4x = 30
x =3
2x = 6
Answer: A
Answer: A
Question: Of the 200 employees in a certain company, 25 percent will be relocated to City X and the remaining 75 percent will be relocated to City Y. However, 30 percent of the employees prefer City Y and 70 percent prefer City X. What is the highest possible number of employees who will be relocated to the city they prefer?
Options:
A) 65
B) 110
C) 115
D) 130
E) 135
Rationale: 140 prefer X (Group 1);
60 prefer Y (Group 2).
City Y needs 150 people: letall 60 who prefer Y (entire Group 2) be relocated there, the rest 90 will be those who prefer X from Group 1;
City X needs 50 people: 140-90=50 from Group 1 will be relocated to X, which they prefer.
So, the highest possible number of employees who will be relocated to the city they prefer is 60+50=110.
Answer: B.
Answer: B
Question: How many zeros are the end of 380! ?
Options:
A)90
B)91
C)94
D)None
E)95
Rationale: 380! has 380/5+380/5^2+380/5^3=76+15+3=94 trailing zeros ( take only the quotient into account).
Answer: C.
Answer: C
Question: (0.0077)(3.6) / (0.04)(0.1)(0.007)=
Options:
A)0.099
B)0.0099
C)9.9
D)990
E)99
Rationale: (0.0077)(3.6) / (0.04)(0.1)(0.007)=0.0077 * 360/4 * (0.1)(0.007)
= 0.077*90/1 * 0.007 = 77*90/7 = 11*90
=990
Answer : D
Answer: D
Question: A factory that employs 1000 assembly line workers pays each of these workers $5 per hour for the first 40 hours worked during a week and 1½ times that rate for hours worked in excess of 40. What was the total payroll for the assembly-line workers for a week in which 30 percent of them worked 35 hours, 50 percent worked 40 hours, and the rest worked 50 hours?
Options:
A) $180,000
B) $185,000
C) $190,000
D) $207,500
E) $205,000
Rationale: 30% of 1000 = 300 worked for 20 hours
Payment @ 5/hr
Total Payment = 300*35*5 = 52500
50 % of 1000 = 500 worked for 40 hours
Payment @ 5/hr
Total payment = 500*40*5 = 100000
Remaining 200 worked for 50 Hours
Payment for first 40 Hours @ 5 /hr
Payment = 200*40*5 = 40000
Payment for next 10 hr @ 7.5/hr
Payment = 200 * 10 * 7.5 = 15000
Total Payment = 52500+100000 + 40000 +15000 = 207500
Hence , answer is D
Answer: D
Question: In a 100 m race, A can beat B by 25 m and B can beat C by 4 m. In the same race, A can beat C by:
Options:
A)21 m
B)26 m
C)28m
D)29m
E)30m
Rationale: Explanation:
A : B = 100 : 75
B : C = 100 : 96.
A : C =A/BXB/C=100/75 X100/96=100:72
A beats C by (100 - 72) m = 28 m.
ANSWER IS C
Answer: C
Question: The radius of the two circular fields is in the ratio 3: 7 the area of the first field is what percent less than the area of the second?
Options:
A)82.9%
B)84.2%
C)81.0%
D)80.6%
E)81.6%
Rationale: r = 3 Ï€r2 = 9
r = 7 Ï€r2 =49
49Ï€ â€“ 40 Ï€
100 ---- ? => 81.6%.Answer:E
Answer: E
Question: If the perimeter of a rectangular playground is 1200 m, its length when its breadth is 500 m is?
Options:
A)300
B)200
C)100
D)400
E)500
Rationale: 2(l + 500) = 1200 => l = 100 m Answer: C
Answer: C
Question: Ashok and Pyarelal invested money together in a business and share a capital of Ashok is 1/9 of that of Pyarelal.if the incur a loss of Rs 1600 then loss of Pyarelal?
Options:
A)600
B)700
C)840
D)940
E)1440
Rationale: Let the capital of Pyarelal be x, then capital of Ashok=x/9
So ratio of investment of Pyarelal and Ashok = x : x/9 =9x : x
Hence out of the total loss of 1600, loss of Pyarelal= 1600*9x/10x=1440
ANSWER:E
Answer: E
Question: A tradesman by means of his false balance defrauds to the extent of 14%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
Options:
A)54.6%
B)29.96%
C)24.45%
D)24%
E)45%
Rationale: g% = 14 + 14 + (14*14)/100
= 29.96%
Answer: B
Answer: B
Question: Richard has to paint a mural with seven horizontal stripes. He only has enough paint for four blue stripes, four white stripes, four black stripes, and four yellow stripes. If his patron wants at most two different colors in the mural, how many different ways can he paint the wall?
Options:
A)420
B)350
C)700
D)2,520
E)5,040
Rationale: Number of ways to choose 2 colors among 4 - 4c2
Number of ways that the chosen colors can be painted for 7 horizontal stripes - 2 (either (4,3) or (3,4))
Now the order,
the number of ways in which a particular color among the 2 chosen colors can be painted for 4 stripes is - 7c4
[Note: We don't need to calculate the ways for the remaining 3 stripes as they are obvious and already counted under this]
Total number of combinations - 4c2 * 2* 7c4 = 420
A
Answer: A
Question: The parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)
Options:
A)28.99
B)23.52
C)23.51
D)23.56
E)23.57
Rationale: Let the side of the square be a cm.
Parameter of the rectangle = 2(16 + 14) = 60 cm Parameter of the square = 60 cm
i.e. 4a = 60
A = 15
Diameter of the semicircle = 15 cm
Circimference of the semicircle
= 1/2(∏)(15)
= 1/2(22/7)(15) = 330/14 = 23.57 cm to two decimal places.Answer:E
Answer: E
Question: The C.I. on a certain sum for 2 years at 10% per annum is Rs. 525. The S.I. on the same sum for double the time at half the rate percent per annum is?
Options:
A)Rs.502
B)Rs.500
C)Rs.520
D)Rs.512
E)Rs.132
Rationale: Let the sum be Rs. P. Then,
[P(1 + 10/100)2 - p] = 525
P[(11/10)2 - 1] = 525
P = (525 * 100) / 21 = 2500
Sum = Rs. 2500
So, S.I. = (2500 * 5 * 4)/100
= Rs.500
Answer: B
Answer: B
Question: 1000 men have provisions for 18 days. If 400 more men join them, for how many days will the provisions last now?
Options:
A)12.9
B)12.8
C)12.6
D)12.2
E)12.1
Rationale: 1000*18 = 1400*x
x = 12.8
Answer: B
Answer: B
Question: A certain college's enrollment at the beginning of 1992 was 20 percent greater than it was at the beginning of 1991, and its enrollment at the beginning of 1993 was 25 percent greater than it was at the beginning of 1992. The college's enrollment at the beginning of 1993 was what percent greater than its enrollment at the beginning of 1991 ?
Options:
A)47.5%
B)44%
C)50%
D)35%
E)38%
Rationale: Suppose enrollment in 1991 was 100
Then enrollment in 1992 will be 120
And enrollment in 1993 will be 120*1.25=150
Increase in 1993 from 1991 = 150-100= 50
Answer : C
Answer: C
Question: In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected, is:
Options:
A)21
B)21/41
C)21/47
D)21/45
E)21/46
Rationale: Let S be the sample space and E be the event of selecting 1 girl and 2 boys.
Then, n(S) = Number ways of selecting 3 students out of 25
= 25C3 `
= (25 x 24 x 23)
(3 x 2 x 1)
= 2300.
n(E) = (10C1 x 15C2)
= 10 x (15 x 14)
(2 x 1)
= 1050.
P(E) = n(E) = 1050 = 21 .
n(S) 2300 46
Answer: E
Question: A circular ground whose diameter is 35 metres, has a 1.4 metre-broad garden around it. What is the area of the garden in square metres?
Options:
A)160.16
B)6.16
C)122.66
D)Data inadequate
E)None of these
Rationale: Req. area = π[(17.5 + 1.4)2 – (17.5)2]
= 22⁄7 × (36.4 × 1.4)[since a2 - b2 = (a + b)(a - b)]
= 22 × 36.4 × 0.2 = 160.16 sq m
Answer A
Answer: A
Question: Last year a certain bond yielded 5 percent of its face value in interest. If that interest was approximately 4 percent of the bonds selling price of $8,000, what is the bonds face value?
Options:
A) $6,000
B) $6,750
C) $6,400
D) $7,500
E) $9,375
Rationale: Interest = 0.05*face value = 0.04*8,000 --> face value = 0.04*8,000/0.05 = 6,400.
Answer: C.
Answer: C
Question: If 100 microns = 1 decimeter, and 10,000 angstroms = 1 decimeter, how many angstroms equal 1 micron?
Options:
A)100
B)10
C)0.01
D)0.0001
E)0.0001
Rationale: Given that 100 microns = 1 decimeter =10,000 angstroms
So, 1 micron = 10,000/100
=100
Answer : A
Answer: A
Question: The product of all the prime numbers less than 15 is closest to which of the following powers of 10 ?
Options:
A)10^9
B)10^8
C)10^5
D)10^6
E)10^7
Rationale: Product of Prime numbers less than 15 is 2*3*5*7*11*13
2*5=10 .
10*11*3*7*13 = 10*10*3*10*10 (approximately) ~ Product will be >10^4 <10^6 i.e. 10^5
C is the answer
Answer: C
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If four marbles are picked at random, what is the probability that none is blue?
Options:
A)33/998
B)33/91
C)33/99
D)33/95
E)33/92
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. When four marbles are picked at random, then the probability that none is blue is = ¹²C₄/¹⁵C₄ = (12 * 11 * 10 * 9)/(15 * 14 * 13 * 12) =33/91.Answer: B
Answer: B
Question: If the sum of the first n positive integers is S, what is the sum of the first n negative even integers, in terms of S ?
Options:
A) S/2
B) S
C) 2S
D) 2S + 2
E) 4S
Rationale: Answer is C
Given sum of -1 -2 -3.....-n = S
sum of -2 , -4 , -6 ....-2n = 2[sum(-1 -2 -3....n) ] = 2S
Answer: C
Question: A solution contains 8 parts of water for every 7 parts of Lemonade syrup. How many parts of the solution should be removed and replaced with water so that the solution will now contain 10% lemonade syrup?
Options:
A)1.5
B)1.75
C)2.14
D)2.34
E)2.64
Rationale: Let the total solution is 150 L with 80 L water70 L syrup.
To make 10% syrup solution, the result solution must have 135 L syrup and 15 L syrup.
Therefore we are taking 55 L of syrup from initial solution and replacing with water.
using urinary method:
70 L syrup in 150 L solution
55 L syrup in 117.9 L solution
We started by multiplying 10
Now to get to the result we need to divide by 55 => amount of solution to be replaced with water = (117.9/55) = 2.14.
Correct option : C
Answer: C
Question: 12 men take 18 days to complete a job whereas 12 women in 18 days can complete 3â„5 of the same job. How many days will 10 men and 8 women together take to complete the same job?
Options:
A)6
B)13 1â„2
C)14 3/5
D)Data inadequate
E)None of these
Rationale: 12 M Ã— 18 = 12 W Ã— 18 Ã— 5/3
\ w = 3/5 M
10M + 8W = 10M + 8 Ã— 3â„5M = 14 4/5 M
\14 4/5 men can complete the same work
in 12Ã—18/14 4/5=14 3/5days
Answer C
Answer: C
Question: Yearly subscription to professional magazines cost a company $940.00. To Make a 35% cut in the magazine budget, how much less must be spent?
Options:
A)654
B)655
C)611
D)657
E)658
Rationale: total cost 940
940*35/100=329
so the cut in amount is 329
the less amount to be spend is 940-329=611
ANSWER:C
Answer: C
Question: The entire contents of a full sack of flour can be used to make 15 cupcakes and 8 pizzas. The same full sack of flour can be used to make 9 cupcakes and 14 pizzas. If a full sack of flour is used to make only pizzas, how many pizzas can be made?
Options:
A)18 1/4
B)18 1/2
C)18 3/4
D)19
E)23
Rationale: 15x+8y=9x+14y
x=y. Answer E
Answer: E
Question: How many two-digit numbers are there whose remainder when divided by 13 is 1, and whose remainder when divided by 6 is 5?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: 2 digit numbers whose remainder when divided by 10 is 1 are
11 , 21 , 31 , 41 , 51 , 61 , 71 , 81 , 91
Out of above , numbers whose remainder when divided by 6 is 5 are
11 , 41 and 71
Answer D
Answer: D
Question: A boat can travel with a speed of 16 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 60 km downstream.
Options:
A)2 hours.
B)3 hours.
C)4 hours.
D)5 hours.
E)6 hours.
Rationale: Speed downstream = (16 + 4) km/hr = 20 km/hr.
Time taken to travel 60 km downstream = 60/20 = 3 hours.
Answer :B
Answer: B
Question: The average age of 8 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men. The average age of the two new men is
Options:
A)22
B)30
C)99
D)38
E)27
Rationale: total age increased = (8 * 2) years = 16 years.
Sum of ages of two new men = (21 + 23 + 16) years = 60 years
Average age of two new men = (60/2) years = 30 years.
Answer: B
Answer: B
Question: Look at this series: XXIV, XX, __, XII, VIII, ... What number should fill the blank?
Options:
A)XV
B)XVI
C)XII
D)VII
E)VI
Rationale: B
XVI
This is a simple subtraction series; each number is 4 less than the previous number.
Answer: B
Question: Rs.160 contained in a box consists of one rupee, 50 paisa and 25 paisa coins in the ratio 4:5:6. What is the number of 25 paisa coins?
Options:
A)197
B)219
C)120
D)165
E)287
Rationale: 4x 5x 6x
100 50 25
400x + 350x + 150x = 16000
x = 20
6x =120
Answer: C
Answer: C
Question: A cricketer whose bowling average is 12.4 runs per wicket takes 5 wickets for 26 runs and there by decreases his average by 0.4. The number age of the family now is?
Options:
A)65
B)67
C)87
D)85
E)65
Rationale: Let the number of wickets taken till the last match be x. Then,
(12.4x + 26)/(x + 5) = 12
= 12.4x + 26 = 12x + 60
= 0.4x = 34
= x = 340/4 =85
Answer: D
Answer: D
Question: How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
Options:
A)11 sec
B)30 sec
C)77 sec
D)14 sec
E)12
Rationale: Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 500 * 3/50
= 30 sec.
Answer: B
Answer: B
Question: A woman has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
Options:
A)80
B)90
C)100
D)110
E)None
Rationale: Explanation:
Let number of notes of each denomination be x.
Then x + 5x + 10x = 480
16x = 480
x = 30.
Hence, total number of notes = 3x = 90.
B)
Answer: B
Question: At a reception, one-third of the guests departed at a certain time. Later two-fifths of the guests departed. Even later two-thirds of the remaining guests departed. If six people were left, how many were originally present at the party?
Options:
A)28
B)37
C)20
D)45 people
E)27
Rationale: Explanation:
Let Original members be x
First One third guest departed i.e x/3
Remaining guests = x – (x/3) = 2x/3
Now from the remaining (2x/3) two-fifths departed = 2/5(2x/3) = 4x/15
i.e. Now remaining guests will be (2x/3 – 4x/15) = 2x/5
Now from remaining (2x/5) two-thirds departed = 2/3(2x/5) = 4x/15
Now remaining guests = (2x/5 – 4x/15) = 2x/15
Given 2x/15 = 6 ⇒ x = 45
Answer: D
Answer: D
Question: Three students appear at an examination of Mathematics. The probability of their success are 1/3, 3/4, 1/5 respectively. Find the probability of success of at least two.
Options:
A)11/30
B)12/50
C)13/30
D)3/50
E)4/50
Rationale: The probability of success of at least two students will involve the following possibilities.
The first two students are successful, the last two students are successful, the first and third students are successful and all the three students are successful.
Therefore, the required probability = 1/3 x 3/4 x 4/5 + 3/4 x 1/5 x 2/3 + 1/3 x 1/5 x 1/4 + 1/3 x 3/4 x 1/5 = 11/30
ANSWER:A
Answer: A
Question: Find the value of 4 x [(3.6 x 0.48 x 2.50) / (0.12 x 0.09 x 0.5)]
Options:
A)800
B)3200
C)900
D)1600
E)None
Rationale: Answer
4 x [(3.6 x 0.48 x 2.50) / (0.12 x 0.09 x 0.5)]
= 4 x [(36 x 48 x 250) / (12 x 9 x 5)]
= 4 x 4 x 4 x 50 = 3200
Correct Option: B
Answer: B
Question: A drink vendor has 20 liters of Maaza, 144 liters of Pepsi and 368 liters of Sprite. He wants to pack them in cans, so that each can contains the same number of liters of a drink, and doesn't want to mix any two drinks in a can. What is the least number of cans required?
Options:
A)135
B)137
C)142
D)130
E)133
Rationale: The number of liters in each can = HCF of 20, 144 and 368 = 4 liters.
Number of cans of Maaza = 20/4 = 5
Number of cans of Pepsi = 144/4 = 36
Number of cans of Sprite = 368/4 = 92
The total number of cans required = 5 + 36 + 92 = 133 cans.
ANSWER:E
Answer: E
Question: The ratio of the number of boys and girls in a college is 7:8. If the percentage increase in the number of boys and girls be 20% and 10% respectively. What will be the new ratio?
Options:
A)29:32
B)21:34
C)21:22
D)31:20
E)21:39
Rationale: Originally, let the number of boys and girls in the college be 7x and 8x respectively.
Their increased number is (120% of 7x) and (110% of 8x).
i.e., (120/100 * 7x) and (110/100 * 8x)
i.e., 42x/5 and 44x/5
Required ratio = 42x/5 : 44x/5 = 21:22
Answer: C
Answer: C
Question: nine persons went to a hotel for taking their meals 8 of them spent Rs.12 each on their meals and the ninth spent Rs.8 more than the average expenditure of all the nine.What was the total money spent by them?
Options:
A)132
B)451
C)175
D)145
E)117
Rationale: Sol: Let the average expenditure of all nine be Rs.x
Then 12*8+(x+8)=9x or 8x=104 or x=13.
Total money spent = 9x=Rs.(9*13)=Rs.117.
Ans: E
Answer: E
Question: (a-b)/(c/2)
In the expression above, a, b, and c are different numbers and each is one of the numbers 1, 2, or 4. What is the least possible value of the expression?
Options:
A)1/4`
B)2/4
C)4/2
D)1/2
E)3/4
Rationale: (a-b)/(c/2)
= 2(a-b)/c
The expression will have the least value when numerator 2(a-b) is the smallest.
= 2(2-1)/4
=2/4
Answer B
Answer: B
Question: Sum of the squares of three numbers is 138 and the sum of their products taken two at a time is 131. Find the sum?
Options:
A)20
B)25
C)26
D)28
E)29
Rationale: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 138 + 2* 131
a + b + c = √400 = 20
A
Answer: A
Question: A certain manufacturer produces items for which the production costs consist of annual fixed costs totaling $130,000 and variables costs averaging $10 per item. If the manufacturer’s selling price per item is $15, how many items the manufacturer produce and sell to earn an annual profit of $150,000?
Options:
A)2,858
B)18,667
C)21,429
D)35,000
E)56,000
Rationale: Let the items manufactured or sold bex
130000+10x = 15x-150000
5x = 280000
x =56000
Ans:E
Answer: E
Question: The HCF of two numbers is 40 and the other two factors of their LCM are 11 and 12. What is the largest number.
Options:
A)462
B)450
C)488
D)480
E)555
Rationale: Explanation:
HCF of the two numbers = 40
HCF will be always a factor of LCM
40 is factor of LCM
other two factors are 11 & 12
Then the numbers are (40 *11) and (40 x 12)
= 440 and 480
Answer: Option D
Answer: D
Question: The speed at which a man can row a boat in still water is 10 kmph. If he rows downstream, where the speed of current is 2 kmph, what time will he take to cover 60 metres?
Options:
A)18 seconds
B)34 seconds
C)14 seconds
D)12 seconds
E)15 seconds
Rationale: Speed of the boat downstream = 10 + 2 = 12 kmph
= 12 * 5/18 = 10/3 m/s
Hence time taken to cover 60 m = 60*3/10
= 18 seconds.
Answer: A
Answer: A
Question: Maxwell leaves his home and walks toward Brad's house at the same time that Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 80 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 6 km/h, what is the distance traveled by Brad?
Options:
A) 16
B) 48
C) 20
D) 24
E) 30
Rationale: Time taken = Total Distance / Relative Speed
Total Distance = 80 kms
Relative Speed (Opposite side) (As they are moving towards each other speed would be added ) = 6+ 4 = 10 kms/hr
Time taken = 80 / 10 = 8 hrs
Distance traveled by Brad = Brad's speed * time taken = 6 * 8 = 48 kms... Answer - B
Answer: B
Question: Find the number of factors of 180 that are in the form (4*k + 2), where k is a non-negative integer?
Options:
A)1
B)2
C)3
D)4
E)6
Rationale: Make sure to follow posting guidelines (link in my signatures). Title of the thread must mention the first few words of the question itself.
As for the question, the most straightforward way is to list out the factors (this is fine for this question as 180 is a relatively small number). Number of factors of 180 (=2^2*3^2*5) = 18. So listing the factors gives us:
1, 180
2, 90
3, 60
4, 45
5, 36
6, 30
9, 20
10, 18
12, 15
As the question asks us about the factors of the form 4k+2 ---> eliminate all ODD factors. You are now left with
2,4,6,10,12,18,20,30,36,60,90,180
For the form 4k+2, the first few values are 2, 6, 10, 14, 18, 22, 26, 30 ... already giving you 5 factors (=2,6,10,18,30). You can stop here and mark 6 (6th one = 90) as the correct answer as 5 is not given.
For checking any particular factor whether they conform to the form 4k+2---> do the following
4k+2 = 36 ---> 4k = 34 --> this will NOT give you an integer value for k ---> reject. Proceed with others until you find all the values asked.
E is thus the correct answer.
Answer: E
Question: What is the greatest number which divides 29, 32, 38 and leaves same remainder in each case?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: Explanation:
HCF of differences between given numbers is the required answer
32 - 29 = 3
38 - 32 = 6
38 - 29 = 9
HCF of 3, 6, 9 is 3
Answer: Option B
Answer: B
Question: How many positive integers will divide evenly into 420?
Options:
A)8
B)12
C)16
D)18
E)20
Rationale: 520 = 10*13*4 = 8*5*13 = 2^3*5*13
We need to positive integers will divide evenly into 520 or simply the factors of 520
If a number is of the form 2^a*3^b*5^c,
Total factors = (a+1)(b+1)(c+1)
Therefore, number of factors of 520 = (3+1)*(1+1)*(1+1) = 4*2*2 = 12
Option CB
Answer: B
Question: A student chose a number, multiplied it by 3, then subtracted 138 from the result and got 102. What was the number he chose?
Options:
A)80
B)120
C)130
D)140
E)150
Rationale: Solution:
Let xx be the number he chose, then
3⋅x−138=102
3x=240
x=80
Answer A
Answer: A
Question: Ajay spends 25 per cent of his salary on house rent, 5 percent on food, 10 percent travel, 10 percent on clothes and the remaining amount of Rs.20000 is saved. What is Ajayâ€™s income?
Options:
A)Rs.40000
B)Rs.80500
C)Rs.60700
D)Rs.70500
E)None of these
Rationale: Explanation:
Savings = Income â€“ expenditure
100 â€“ (25+5+10+10) = 50%
50% of income = Rs.20000
:. Income = 20000 x 100/50 = Rs. 40000.
Answer: Option A
Answer: A