divelab/Sys2Bench huggingface dataset:
Question: Four friends (A, B, C and D) started a business in partnership by investing capitals in the proportion 3 : 5 : 4 : 6. During the period of one-year, these capitals were utilized in the proportion of 6 : 4 : 5 : 3 respectively. If, at the end of the year, a profit of Rs. 15,550 was made, what will be the share of D?
Options:
A)3682.89
B)3682.87
C)3682.81
D)3682.82
E)6222.33
Rationale: Explanation:
A = (Investment * capital utilized) = (3 * 6) = 18
B = (5 * 4) = 20
C = (4 * 5) = 20
D = (6 * 3) = 18
Thus, out of Rs. 76 (18 +20 + 20 + 18), D's share is Rs. 18. Hence, out of Rs. 15,500 the share of D would be given as (18/76) * 15550 = Rs. 3682.89
ANSWER: A
Answer: A
Question: In each term of a sequence, 15 is added to get the next term. If the first term is 10, what is the eighty-first term?
Options:
A) 1630
B) 1210
C) 1110
D) 1720
E) 1750
Rationale: 1rst term + 80 terms = 10 + 15+15+15+15+15+15+15+...+15 (80 times)
10 + (15 x 80) = 10 + 1200 = 1210
Answer B
Answer: B
Question: Set #1 = {A, B, C, D, E}
Set #2 = {K, L, M, N, O, P}
There are these two sets of letters, and you are going to pick exactly one letter from each set. What is the probability of picking at least one vowel?
Options:
A)1/6
B)1/3
C)1/2
D)2/3
E)5/6
Rationale: So Not a vowel in Set-1 : 3/5
And not a vowel in Ser-2:5/6
Now,
3/5∗5/6=12
This is for not a vowel.
Then for at least one vowel will be = 1−1/2=1/2
Answer will be C.
Answer: C
Question: find out the wrong number in the given sequence of numbers
15,16,34,105,424,2124,12756
Options:
A)105
B)424
C)2124
D)15
E)34
Rationale: 15*1+1=16
16*2+2=34
34*3+3=105
105*4+4=424
424*5+5=2125
2125*6+6=12756
wrong number is 2124
ANSWER:C
Answer: C
Question: Lloyd normally works 7.5 hours per day and earns $4.00 per hour. For each hour he works in excess of 7.5 hours on a given day, he is paid 1.5 times his regular rate. If Lloyd works 10.5 hours on a given day, how much does he earn for that day?
Options:
A)$33.75
B)$48.00
C)$51.75
D)$54.00
E)$70.00
Rationale: Daily working hour*Regular Rate + Overtime*Increased Rate
7.5*4.0+ 3*4.0*1.5=48
Answer B
Answer: B
Question: If x is an integer, and 225 < x^2 <= 361, which of the following is the sum of all possible values of x?
Options:
A) None of the above
B) 124
C) 116
D) 105
E)135
Rationale: The range of x is from 16 .. to 19 and -16 to -19 so the sum is 0 hence ans A, I guess, unless I am missing something!
Answer: A
Question: Which of the following is closer to √0.1+√0.05?
Options:
A)0.5
B)0.7
C)0.9
D)1.1
E)1.2
Rationale: √0.1+√0.05=approximately √0.09+√0.04=0.3+0.2=0.5. Hence, the correct answer is A.
Answer: A
Question: If A is 25% greater than B then how much percentage is B smaller than A?
Options:
A)10%
B)20%
C)30%
D)40%
E)45%
Rationale: A = 125
B = 100
A-B/A × 100 = 25/125 × 100 = 20 % smaller smaller than A
B)
Answer: B
Question: A train 120 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
Options:
A)22
B)48.2
C)99
D)288
E)12
Rationale: Speed of the train relative to man = (120/10) m/sec = (12) m/sec. [(12) * (18/5)] km/hr = 43.2 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 43.2 ==> x = 48.2 km/hr.Answer: B
Answer: B
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
Options:
A)5 kmph
B)10 kmph
C)15 kmph
D)20 kmph
E)12 kmph
Rationale: Explanation:
M = 15
S = 5
DS = 15 + 5 = 20kmph
Answer: D
Answer: D
Question: 5356 x 51 = ?
Options:
A)273156
B)273243
C)273247
D)273250
E)273258
Rationale: 5356 x 51	= 5356 x (50 + 1)
= 5356 x 50 + 5356 x 1
= 267800 + 5356
= 273156.
A
Answer: A
Question: If the cost price of 140 pencils is equal to the selling price of 100 pencils, the gain percent is
Options:
A)36
B)37
C)38
D)39
E)40
Rationale: Let C.P. of each pencil be Re. 1.
Then, C.P. of 100 pencils = Rs. 100; S.P. of 100 pencils = Rs. 140.
Gain % = 40/100 * 100 = 40%
Answer:E
Answer: E
Question: (12345679 x 72) = ?
Options:
A)88888888
B)888888888
C)898989898
D)9999999998
E)None
Rationale: Explanation: 12345679 x 72 = 12345679 x (70 +2)
= 12345679 x 70 + 12345679 x 2
= 864197530 + 24691358
= 888888888
Answer: Option B
Answer: B
Question: A cistern is normally filled in 6 hrs,but takes 2 hrs longer to fill because of a leak on its bottom,if Cistern is full ,how much time citern would empty?
Options:
A)24 hours
B)20 hours
C)30 hours
D)40 hours
E)50 hours
Rationale: If leakage/hour=1/x, then 1/6 -1/x= 1/8, solving 1/x=1/24
So in 24 hours full cistern will be empty.
ANSWER:A
Answer: A
Question: The pages of a report are numbered consecutively from 1 to 11. If the sum of the page numbers up to and including page number x of the report is equal to six more than the sum of the page numbers following page number x, then x =
Options:
A)5
B)6
C)7
D)8
E)4
Rationale: sum of the first few numbers =1+2+3+4+5+6+7+8 =36
sum of the last few = 9 +10+11 =30 page no.8 answer .D
Answer: D
Question: What is the average (arithmetic mean) of the numbers 100, 150, 200, 200, 250, and 300?
Options:
A) 100
B) 150
C) 140
D) 200
E) 250
Rationale: {100, 150, 200, 200, 250, 300}={200-100,200-50, 200, 200,200+50,200+100} --> the average = 200.
Answer: D.
Answer: D
Question: Ajay can walk 3km in 1 hour. In how many hours he can walk 50km?
Options:
A)5hrs
B)16.6 hrs
C)15.6 hrs
D)20.4 hrs
E)30hrs
Rationale: 1 hour he walk 3km
he walk 50km in = 50/3 * 1 = 16.6hours
Answer is B
Answer: B
Question: an unbaised coin is tossed until it shows up the same face in 2 consicative throws wat is the probability that the no of tosses is not more than 4.
Options:
A)3/4
B)1/4
C)7/8
D)1/8
E)6/8
Rationale: using 0 and 1 for head and tail respectively and considering binary system , we find that
Out of 16 possibilities, 14 are desired options.
Then probability = 14/16=7/8
ANSWER:C
Answer: C
Question: A tap can fill a tank in 16 minutes and another can empty it in 8 minutes. If the tank is already 1/2 full and both the taps are opened together, will the tank be filled or emptied? How long will it take before the tank is either filled or emptied completely as the case may be ?
Options:
A)Emptied; 16 min
B)Filled; 8 min
C)Emptied; 8 min
D)Filled; 12 min
E)None of these
Rationale: If both the pumps are opened together, then the tank will be emptied because the working efficiency of pump empting is more than that of the pump filling it. Thus in 1 min net proportion of the volume of tank filled
= (1⁄8 - 1⁄16) = 1⁄16
or the tank will be emptied in 16 min
⇒ 1⁄2 tank will be emptied in 8 min.
Answer C
Answer: C
Question: A, B and C enter into a partnership. They invest Rs. 60,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. In what ratio will the profit be shared at the end of 3 years?
Options:
A)9 : 3 : 4
B)9 : 2 : 4
C)9: 2 : 1
D)9: 8: 14
E)none
Rationale: Sol.
A : B : C = (60000 * 36) : (80000 * 12 + 40000 * 24)
: (120000 * 24 + 40000 * 12) =216 : 192 : 336 = 9: 8: 14
Answer D
Answer: D
Question: A wheel of a car of radius 21 cms is rotating at 900 RPM. What is the speed of the car in km/hr?
Options:
A)71.28 km/hr
B)47.52 km/hr
C)7.92 km/hr
D)39.6 km/hr
E)3.96 km/hr
Rationale: Explanatory Answer
The radius of the wheel measures 21 cm.
In one rotation, the wheel will cover a distance which is equal to the circumference of the wheel.
∴ in one rotation this wheel will cover 2 * π * 21 = 132 cm.
In a minute, the distance covered by the wheel = circumference of the wheel * rpm
∴ this wheel will cover a distance of 132 * 900 = 118800 cm in a minute.
In an hour, the wheel will cover a distance of 118800 * 60 = 7128000 cm.
Therefore, the speed of the car = 7128000 cm/hr = 71.28 km/hr
Choice A is the correct answer.
Answer: A
Question: If n is a positive integer and (n+1)(n+3)(n+1)(n+3) is odd, then (n+2)(n+4)(n+2)(n+4) must be a multiple of which one of the following?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: (n+1)(n+3)(n+1)(n+3) is odd only when both (n+1)(n+1) and (n+3)(n+3) are odd. This is possible only when nn is even.
Hence, n=2mn=2m, where mm is a positive integer. Then,
(n+2)(n+4)=(2m+2)(2m+4)=2(m+1)2(m+2)=4(m+1)(m+2)(n+2)(n+4)=(2m+2)(2m+4)=2(m+1)2(m+2)=4(m+1)(m+2)
=4 * (product of two consecutive positive integers, one which must be even)=4 * (product of two consecutive positive integers, one which must be even) =4 * (an even number), and this equals a number that is at least a multiple of 8=4 * (an even number), and this equals a number that is at least a multiple of 8
Hence, the answer is (D).
Answer: D
Question: A man, a woman and a boy can complete a job in 3, 4 and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in 1/4 of a day?
Options:
A)22
B)77
C)12
D)41
E)76
Rationale: (1 man + 1 woman)'s 1 day work = (1/3 + 1/4) = 7/12 Work done by 1 man and 1 woman in 1/4 day = (7/12 * 1/4) = 7/48
Remaining work = (1 - 7/48) = 41/48
Work done by 1 boy in 1/4 day = ( 1/12 * 1/4) = 1/48
Number of boys required = 41/48 * 41 = 41.
Answer: D
Answer: D
Question: A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 160 meter length?
Options:
A)11 seconds
B)41.6 seconds
C)40 seconds
D)88 seconds
E)19 seconds
Rationale: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec
Total distance = 360+160 = 520 meter
Time = Distance/speed
= 520 * (2/25) = 41.6 seconds
Answer: B
Answer: B
Question: Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit?
Options:
A)Rs.10595
B)Rs.10529
C)Rs.10598
D)Rs.10508
E)Rs.10500
Rationale: Simran : Nanda = (50000 * 36) : (80000 * 30) = 3:4
Simran's share = 24500 * 3/7
= Rs.10500
Answer:E
Answer: E
Question: What is the sum of the digits of integer k, if k = (10^40- 79)
Options:
A)345
B)340
C)343
D)349
E)338
Rationale: There are 41 digits in 10^40
When we subtract 79 from it, there will be 40 digits left.
10^40 can be written as 9999999....(40 times) + 1
So,
10^40 - 79 = 9999999....(40 times) + 1 - 79 = 9999999....(40 times) -78
Consider the last 2 digits,
99-78 = 21
The last 2 digits will be 21.
And our number would be 99999......99921 with 2 less 9s after subtraction.
Number of 9s left are 38 and the last two digits are 21
The sum of the digits will be
(38*9) + 2 + 1 =345
Answer:- A
Answer: A
Question: A 600 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 3 kilometer long bridge, at the same speed?
Options:
A)4 min
B)8 min
C)9 min
D)6 min
E)1 min
Rationale: S = 600/40 = 15 mps
S = 3600/15 = 240 sec = 4 min
Answer:A
Answer: A
Question: Simplify: 256 x 256 - 144 x 144
Options:
A)761200
B)44800
C)761800
D)761500
E)None of them
Rationale: (256)^2 - (144)^2 = (256 + 144) (256 - 144) = 400 x 112 = 44800
Answer is B
Answer: B
Question: If the integer c is rounded to the nearest hundred, the result represents a 66 2/3 % increase over the value obtained when c is rounded to the nearest ten. which of the following is a possible value of c?
Options:
A)64
B)67
C)99
D)133
E)147
Rationale: We have to check options 1 by 1.
64 rounded to nearest hundred = 100
64 rounded to nearest ten = 60
now difference = 40
the result represents a 66 2/3 % increase over the value obtained when x is rounded to the nearest ten.
therefore 40/60)*100 = 66 2/3 ==>this is the answer.
99 rounded to nearest ten = 100
133 rounded to nearest ten = 130
133 rounded to nearest hundred c= 100=A
Answer: A
Question: 20-3*4^2+20 = ?
Options:
A)287
B)-13
C)-73
D)13
E)None
Rationale: 20-3*4^2+20
= 20-3*16+20
=20-48+20=-8..
E
Answer: E
Question: At a certain food stand, the price of each apple is 40¢ and the price of each orange is 60¢. Mary selects a total of 10 apples and oranges from the food stand, and the average (arithmetic mean) price of the 10 pieces of fruit is 56¢. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is 50¢?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: If the average price is 56, then Mary has 8 oranges and 2 apples (a ratio of 4:1).
For the average price to be 50, the ratio should be 1:1.
Mary must put back 6 oranges.
The answer is E.
Answer: E
Question: At a meeting of the 6 Chiefs of Staff, the Chief of Naval Operations does not want to sit next to the Chief of the National Guard Bureau. How many ways can the Chiefs of Staff be seated around a circular table?
Options:
A)56
B)64
C)72
D)80
E)88
Rationale: 6 people can be arranged around a table in 5! ways.
Consider the two chiefs who will not sit together as a single unit.
The number of ways to arrange 5 units around a table is 4!
We need to multiply this by 2 as the two people can be switched in each arrangement.
The total number of ways to arrange the chiefs is 5! - 2*4! = 3*4! = 72
The answer is C.
Answer: C
Question: If a - b = 3 and
a2+b2=29
, then find the value of ab
Options:
A)7
B)8.5
C)10
D)12
E)14
Rationale: Explanation:
2ab=(a2+b2)−(a−b)2
=> 2ab = 29 - 9 = 20
=> ab = 10
Option C
Answer: C
Question: A, B and C enter into a partnership. A initially invests Rs. 25 lakhs and adds another Rs. 10 lakhs after one year. B initially invests Rs. 35 lakhs and withdraws Rs. 10 lakhs after 2 years and C invests Rs. 30 lakhs. In what ratio should the profits be divided at the end of 3 years ?
Options:
A)11:10:15
B)20:17:23
C)19:19:18
D)5:4:9
E)1:3:6
Rationale: Explanation:
A:B:C =(25 lakhsÃ—Ã—1)+(35 lakhsÃ—Ã—2) :(35 lakhsÃ—Ã—2+25 lakhsÃ—Ã—1) :(30 lakhsÃ—Ã—3)
= 95 lakhs : 95 lakhs : 90 lakhs =19:19:18.
Answer IS C
Answer: C
Question: The average age of 12 men in a group is increased by 2 years when two men whose ages are 20 years and 22 years, are replaced by new members. What is the average age of the new men included?
Options:
A)22
B)767
C)77
D)33
E)99
Rationale: Explanation:
Total age of two men replaced = 20 + 22 = 42 years
Total increase in age on replacement = 2 × 12 = 24 years
Total age two new persons included = 42 + 24 = 66 years
Therefore, Average age of new persons = 66/2 = 33 years
Answer:D
Answer: D
Question: Three years ago the average age of a class of six members was 24 years. A boy have been added, the average age of the class is the same today. What is the age of the boy?
Options:
A)A)1
B)B)2
C)C)3
D)D)4
E)E)6
Rationale: 6 * 27 = 162
7 * 24 = 168
`6
E
Answer: E
Question: Last week David spent 20 percent of his wages on recreation. This week, his wages are 30 percent less than last weekʼs wages and he spent 20 percent of his wages on recreation. The amount he spends on recreation this week is what percent of the amount he spent on recreation last week
Options:
A)75%
B)72%
C)70%
D)73%
E)74%
Rationale: Say David's wages last week were $100, so he spent 0.20*100=$20 on recreation;
This week's wages is 0.70*100=$70, so he spends 0.2*70=$14 on recreation;
14/20=0.70, hence the amount he spends on recreation this week is 70% of the amount he spent on recreation last week: 20*0.7=14
Answer: C
Answer: C
Question: A can do a work in 12 days. B can do the same work in 24 days. If both A & B are working together in how many days they will finish the work?
Options:
A)3
B)5
C)8
D)2
E)6
Rationale: A rate = 1/12
B rate = 1/24
(A+B) rate = (1/12)+(1/24) = 1/8
A & B finish the work in 8 days
correct option is C
Answer: C
Question: If x and y are even integers, which of the following is an odd integer?
Options:
A)xy
B)y^2
C)x+y+3
D)x^2
E)None of these
Rationale: even * even = even
even + odd = odd
Answer : C
Answer: C
Question: A baker filled with a measuring cup with 3/4 cup water. He poured 1/2 of the water into the batter, and then spilled 3/8 of the water on the floor. How much water will the baker needed to add what is left in the cup to have 50% more than what he started with?
Options:
A)1/8 cup
B)3/8 cup
C)1/4 cup
D)1/2 cup
E)9/8 cup
Rationale: 3/4 is the original water in cup .half in batter.So left is 3/8 out which 3/8 is spilled out.So again left with 0/8.
so 50% more than what he started was = 3/4+1/2*(3/4)=9/8
Amount of water needed to add = 9/8 - 0/8=9/8
ANSWER:E
Answer: E
Question: The measures of the 2 acute angles of a triangle are in the ratio of 2 : 7. What arethe measures of the 2 angles?
Options:
A)20°
B)70°
C)110°
D)120°
E)140°
Rationale: If the ratio of the two angles is 2:7, then the measures of two angles can be written as 2x and 7x. Also the two acute angles of a triangle is equal to 90°. Hence
2x + 7x = 90
9x = 90
x = 10
Measures of the two acute angles are
2x = 2 × 10 = 20°
7x = 7 × 10 = 70°
B
Answer: B
Question: If y is the smallest positive integer such that 11,025 multiplied by y is the square of an integer, then y must be
Options:
A)2
B)4
C)6
D)7
E)14
Rationale: i just tried plugging in the numbers and found out that
4*11025 = 44, 100, which is a square of 210
B
Answer: B
Question: #p is defined as 2p+20 for any number p. What is p, if #(#(#p))=4?
Options:
A)–108
B)–44
C)10
D)-17
E)18
Rationale: #p = 2p+20 --->#(#p) = 2(2p+20)+20 = 4p+60 and thus #(4p+60) = 2(4p+60)+20 = 8p+140 = 4 ---> 8p= -136 ---> p = -17, D is the correct answer.
Answer: D
Question: If Tim had lunch at $60.50 and he gave 20% tip, how much did he spend?
Options:
A)$30.60
B)$72.60
C)$70.60
D)$40.60
E)$50.60
Rationale: The tip is 20% of what he paid for lunch. Hence
tip = 20% of 60.50 = (20/100)*60.50 = $12.1
Total spent
60.50 + 12.1 = $72.6
correct answer B
Answer: B
Question: Solve the equation:
(2x - 1)2 – x(10x + 1) = x(1 – x)(1 + x) – (2 – x)3
Options:
A)1
B)1/2
C)2
D)2/1
E)None
Rationale: Solution:
(2x - 1)2 – x(10x + 1) = x(1 – x)(1 + x) – (2 – x)3 <=>
4x2 - 4x + 1 -10x2 – x = x – x3 - 8 + 12x - 6x2 + x3 <=>
18x = 9 <=> x = 1/2
Answer B
Answer: B
Question: If a , b, and c are integers and a∗b2/ca∗b2/cis a positive even integer, which of the following must
be true?
I. ab is even
II. ab > 0
III. c is even
Options:
A)l
B)ll only
C)l and ll
D)l and lll
E)l,ll,and lll
Rationale: Given: a∗b2c=even>0a∗b2c=even>0 --> ab2=c∗even=evenab2=c∗even=even --> either aa is even or bb or both.
I. abab is even --> according to the above this must be true;
II. ab>0ab>0 --> not necessarily true, bb could be positive as well as negative (for example a=1a=1, c=1c=1 and b=−2b=−2);
III. cc is even --> not necessarily true, see above example.
Answer: A (I only).
Answer: A
Question: Of the 40 electronics components that a factory must manufacture, 30 percent would be most e¢ ciently manufactured by Machine A and the remaining 70 percent would be most efficiently manufactured by Machine B, though either machine could manufacture any of the 40 components. If 70 percent of the components were manufactured by Machine A and the remainder were manufactured by Machine B, what is thehighest possible number of components that were manufactured by the machine that would manufacture them the most efficiently?
Options:
A) 30
B) 32
C) 60
D) 35
E) 36
Rationale: A can manufacture 30 % of 40 efficiently, which is 12.
B can manufacure 70 % of 40 efficiently, which is 28.
Now 80 % of 40 are produced by A. This means 32 parts. Since A can produce 12 efficiently, all 32 are produced efficiently. Rest (8) is produced by B, which can produce max. 28 parts efficiently.
Hence parts that were produced efficiently = 32+28 = 60. (C).
Answer: C
Question: What is the 36th digit to the right of the decimal point in the decimal expansion of 1/37?
Options:
A) 0
B) 2
C) 4
D) 7
E) 9
Rationale: 1/37=0.027027... So, we have a repeating cycle of 027. Every third digit (3rd, 6th, 9th, ...) to the right of the decimal point is 7, thus 36th digit to the right of the decimal point is also 7.
Answer: D.
Answer: D
Question: The simple interest and the true discount on a certain sum for a given time and at a given rate are Rs. 85 and Rs. 78 respectively. The sum is:
Options:
A)1360
B)1450
C)1600
D)947
E)None
Rationale: Sol.
Sum = S.I. * T.D. / (S.I)-(T.D.) = 85 * 78 / (85 - 78) = Rs.947.
Answer D
Answer: D
Question: A person distributed 20% of his income to his 3 children each. He deposited 30% of his income to his wife's account. He donated 5% of remaining amount to an orphan house.Finally he has $60000. Find his total income?
Options:
A)A)1200000
B)B)562000
C)C)800000
D)D)500000
E)E)652000
Rationale: 3 children got = 3*20% = 60%
wife got = 30%
orphan house = 5%
total = 60+30+5 = 95%
remaining = 100-95 = 5%
5% = 60000
100% = 60000*100/5 = $1200000
Answer is A
Answer: A
Question: In particular old age home, 60% are suffering from diabetic and at the same time 80% are suffering from blood pressure.If suppose 75% are suffering from diabetic,what percentage of old people suffering from blood pressure at the same old age home?
Options:
A)23
B)16
C)26
D)36
E)20
Rationale: given : % of people suffering from diabetics = 60%; % of people suffering from blood pressure = 80% (ie ) 0.8
total =75*100; Those who are suffering from diabetics= 75 - 60 = 15; Those who are suffering from blood pressure =
100 - 80=20; so those who are suffering from blood pressure =0.8*20=16; Total number of people suffering from blood pressure = 20+16 = 36. Answer: D
Answer: D
Question: If P/6 = Q/7 = R/8 then find P:R:Q
Options:
A)1:2:3
B)6:8:7
C)2:4:9
D)4:9:7
E)3:5:7
Rationale: Let P/6 = Q/7 = R/8 = K
P = 6K
Q = 7K
R = 8K
P:R:Q = 6:8:7
Answer is B
Answer: B
Question: ABCD is a square. E and F are the midpoints of sides CD and BC, respectively. What is the ratio of the shaded region area to the unshaded region?
Options:
A)1:1
B)2:1
C)3:1
D)5:3
E)8:3
Rationale: Let's join the midpoints as shown in the figure then we'll get four small squares...
AODX be 1 and similarly all squares..and we can split the unit 1 into half and half as per the mid points...
Then shaded will be 1+1/2+1/2+1/2 = 5/2
and unshaded is 1/2+1/2+1/2 = 3/2..
shaded : unshaded is 5:3..
ANS option D.
Answer: D
Question: The average of five consecutive odd numbers is 51. What is the difference between the highest and lowest number?
Options:
A)3
B)7
C)8
D)11
E)None of these
Rationale: Explanation:
Let the numbers be x, x + 2, x + 4, x + 6 and x + 8.
Then, [x + (x + 2) + (x + 4) + (x + 6) + (x + 8)] / 5 = 51
5x + 20 = 255
x = 47
So, required difference = (47 + 8) – 47 = 8
ANSWER C
Answer: C
Question: In a city, the streets are aligned in a grid, where the east-west roads are called 1st Rd, 2nd Rd, 3rd Rd, etc, increasing in number as one moves northward. The north-south roads are called 1st Ave, 2nd Ave, 3rd Ave, etc, increasing in number as one moves eastward. If Bill needs to walk from the corner of 2nd Rd and 3rd Ave to the corner of 10th Rd and 5th Ave in the shortest possible time, how many different routes could he take?
Options:
A)45
B)60
C)75
D)90
E)105
Rationale: Bills needs to walk 8 blocks north and 2 blocks east.
One possible solution is NNNNNNNNEE.
There are 10C8 = 45 possible solutions.
The answer is A.
Answer: A
Question: If two of the four expressions x+y, x+5y, x-y, and 5x-y are chosen at random, what is the probability W that their product will be of the form of x^2-(by)^2, where b is an integer?
Options:
A)1/2
B)1/3
C)1/4
D)1/5
E)W=1/6
Rationale: Only (X+y)(x-y) pair will give the form x^2-(by)^2
The probability of selecting these two pairs are 1/4 * 1/3 = 1/12, assuming x+y is picked first, then x-y, but x-y can be picked first followed by x+y. So the probability W= 1/12 * 2 = 1/6
Ans E
Answer: E
Question: How many numbers between 11 and 90 are divisible by 7?
Options:
A)7
B)9
C)11
D)8
E)10
Rationale: The required numbers are 14, 21, 28, 35, .... 77, 84.
This is an A.P. with a = 14 and d = (21 - 14) = 7.
Let it contain n terms.
Then, T^n = 84 => a + (n - 1) d = 84
=> 14 + (n - 1) x 7 = 84 or n = 11.
Answer is C.
Answer: C
Question: HCF of 2472,1284 and a third number 'n'is 12.If their LCM is 8*9*5*103*107.then the number 'n'is.
Options:
A)160
B)170
C)180
D)190
E)200
Rationale: 2472=8*3*103
1284=4*3*107
so n = 4*3*x
dividing by hcf
2472/12=2*103
1284/12=107
lcm/12=2*3*5*103*107
x=lcm/first*second
x=2*3*5*103*107/2*103*107=3*5=15
number is = 15*12=180
ANSWER:C
Answer: C