divelab/Sys2Bench huggingface dataset:
Question: P, Q, R subscribe Rs. 50,000 for a business. P subscribes Rs. 4000 more than Q and Q Rs. 5000 more than R. Out of a total profit of Rs. 25,000, what will be P's share?
Options:
A)10,509
B)10,502
C)10,500
D)10,501
E)10,506
Rationale: Explanation:
Let amount subscribed for R be x.
Therefore, Q = x + 5000 and P = x + 5000 + 4000 = x + 9000
So, x + x + 5000 + x + 9000 = 50000
3x = 36000
x = 12000
P : Q : R = 21000 : 17000 : 12000 = 21 : 17 : 12
ANSWER: Rs. 10,500
P’s share = 25000 X (21/50) = Rs. 10,500
ANSWER:C
Answer: C
Question: Sravan and Bhavan began business with Rs.16000 and Rs.20000 after 8 months, Sravan advances Rs.4000 more and Bhavan withdraws Rs.4000. At the end of two years, their profits amounted to Rs.5535 find the share of Sravan.
Options:
A)2850
B)2870
C)3000
D)2800
E)2825
Rationale: (16*8 + 20*16):(20*8 + 16*16)
14:13
14/27 * 5535 = 2870. Answer: B
Answer: B
Question: In a class, the average age of 30 boys is 13 years and the average of 20 girls is 12 years. what is the average age of the whole class?
Options:
A)10.6
B)11.6
C)12.6
D)13.6
E)14.6
Rationale: Explanation:
Total age of 50 students
(30X 13+20 X 12) = 630
Average = 630/50 = 12.6 Years
Answer C
Answer: C
Question: A certain school supplies store arranges pencils on display such that each of the six different colors of pencils, yellow, orange, green, red, blue, and purple are consecutive in a repeating pattern. If seven consecutively displayed pencils are purchased, what is the probability that two of the pencils
are purple?
Options:
A)1/6
B)1/36
C)1/20
D)2/3
E)2/5
Rationale: After yellow, orange, green, red, blue, and purple, the next pencil can be of any given six colours, therefore we have total six possibilites, out of which we need purple i.e. 1 therefore prob is 1/6.
Answer: A
Question: From the beginning to the end of 2007, the price of a stock rose 20 percent. In 2008, it dropped 25 percent. In 2009, it rose 20 percent. What percent of the stock’s 2007 starting price was the price of the stock at the end of 2009?
Options:
A)80
B)90
C)95
D)100
E)108
Rationale: Assume a value at the beginning of 2007. As this is a % question, assume P=100.
At the end of 2007 it becmae = 1.2*100=120
At the end of 2008 it decreased by 25% = 120*.75 = 90
At the end of 2009 it increased by 20% = 90*1.2 = 108
Thus ratio = 108/100 = 1.08 (in % terms = 108%). Thus E is the correct answer.
Answer: E
Question: At the wholesale store you can buy an 8-pack of hot dogs for $1.55, a 20-pack for $3.05, and a 250-pack for $20.95. What is the greatest number of hot dogs you can buy at this store with $300?
Options:
A) 3,108
B) 3,100
C) 3,108
D) 3,540
E) 3,256
Rationale: To maximize number of hot dogs with 300$
Total number of hot dogs bought in 250-pack = 20.95*14 =293.30$
Amount remaining = 300 - 293.30 = 6.7$
Total number of hot dogs bought in 20-pack = 3.05*2 =6.10$
Amount remaining = 6.70 - 6.10= 0.6$
This amount is too less to buy any 8- pack .
Greatest number of hot dogs one can buy with 300 $ = 250*14+20*2 = 3,540
Answer D
Answer: D
Question: if A and B both work for 6 hrs,B and C work for 7.5 hrs,C and A work for 10 hrs .
i dont remember but ......its arrange in increasing order by their work
Options:
A)cab
B)cba
C)abc
D)bac
E)none of these
Rationale: A and B both can finish the work in 6 days means
1/A+1/B=1/6 ................(i)
B and C both can finish the work in 7.5 days means
1/B+1/C=1/7.5 ...................(ii)
C and A both can finish the work in 10 days means
1/A+1/B=1/10 ........................(iii)
Adding (i),(ii) and (iii), we get
2(1/A+1/B+1/C)=2/5 ......................(iv)
from (i) we have 1/A+1/B=1/6 put in (iv) ,we wiil get
1/6+1/C=1/5
C=30
Similarly, we will get A=15 and B=10
so in increasing order it will be BAC
ANSWER:D
Answer: D
Question: A and B invests Rs.10000 each, A investing for 8 months and B investing for all the 12 months in the year. If the total profit at the end of the year is Rs.25000, find their shares?
Options:
A)Rs.1300
B)Rs.1599
C)Rs.7290
D)Rs.15000
E)Rs.72821
Rationale: The ratio of their profits A:B = 8:12 = 2:3
Share of A in the total profit = 2/5 * 25000 = Rs.10000 Share of A in the total profit = 3/5 * 25000 = Rs.15000
Answer:D
Answer: D
Question: If x is a positive integer with fewer than 3 digits, what is the probability Q that x*(x + 1) is a multiple of either 4 or 5?
Options:
A)4/99
B)2/25
C)8/99
D)49/100
E)86/99
Rationale: Interesting question! Also one that we should be able to answer very quickly be keeping an eye on our best friends, the answer choices.
We know that x belongs to the set {1, 2, 3, ... , 99}. We want to know the probability Q that x(x+1) is a multiple of either 4 or 5.
When will this happen? If either x OR (x+1) is a multiple of 4 or 5.
Since 4*5 is 20, let's look at the first 20 numbers to get a rough idea of how often this happens.
Out of the numbers from 1 to 20:
4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 16, 17, 20
So, 14 out of the first 20 numbers match our criteria. Since:
probability = (# of desired outcomes)/(total # of possibilities), we guesstimate the answer to be 14/20. Since (E) is the only answer greater than 1/2, we go with (E).
Answer: E
Question: A can do piece of work in 15 days and B in 20 days they finished the work with the assistance of c in 5 days and got Rs.45 as their wages find the share for each in wages?
Options:
A)11,12,13
B)15,11,13
C)15,11.25,18.75
D)11,15.25,18.75
E)None of these
Rationale: Explanation:
A’s 1 day work =1/3
B’s 1 day work =1/4
C’s 1 day work =1-1/4-1/3 =5/12
A’s share =45 *1/3 = 15
B’s share= 45*1/4 = 11.25
C’s share =45*5/12 = 18.75
Answer: Option C
Answer: C
Question: The rate of spin of a certain gyroscope doubled every 10 seconds from the moment a particular stopwatch started. If after a minute and a half the gyroscope reached a speed of 6400 meters per second, what was the speed, in meters per second, when the stopwatch was started?
Options:
A)25/2
B)25/4
C)25/8
D)25/16
E)25/32
Rationale: Let x be the original speed when the stopwatch was started.
In 90 seconds, the speed doubled 9 times.
2^9 * x = 6400
x = (2^8 * 25) / 2^9 = 25/2
The answer is A.
Answer: A
Question: If v and t are integers and v^2 – t^2 is an odd integer, which of the following must be an even integer?
I. v + t + 2
II. v^2 + 2vt + t^2
III. v^2 + t^2
Options:
A)None
B)I only
C)II only
D)III only
E)I, II, and III
Rationale: v^2–t^2 is an odd integer means that either v is even and t is odd or v is odd and t is even.
Check all options:
I. v + t + 2 --> even+odd+even=odd or odd+even+even=odd. Discard;
II. v^2 + 2vt + t^2 --> even+even+odd=odd or odd+even+even=odd. Discard;
III. v^2 + t^2 --> even+odd=odd or odd+even=odd. Discard.
Answer: A.
Answer: A
Question: If Jesse flips a coin seven times in a row, what is the probability that the result will be heads at all the times?
Options:
A)1/128
B)29/128
C)35/128
D)1/16
E)1/4
Rationale: In a flip of a coin seven times in a row, heads at all times means,
Heads = at least 7 heads
Atleast 7 heads in 7 flip.
The total outcome of flip is = 2^7 = 128
For any Coins problem write the ask in the shown format.
HHHHHHH
Once you have written in the above mentioned format the answer is pretty straight.
HHHHHHH = [7!]/[7!] = 1
Sum = 1 =
Answer = 1/128
Answer - A
Answer: A
Question: A girl was asked to multiply a certain number by 43. She multiplied it by 34 and got his answer less than the correct one by 1251. Find the number to be multiplied.
Options:
A)130
B)132
C)134
D)136
E)139
Rationale: Let the required number be x. Then,
43x – 34x = 1251 or 9x = 1251 or x = 139.
Required number = 139.
ANSWER:E
Answer: E
Question: The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?
Options:
A)7%
B)4%
C)5%
D)2%
E)1%
Rationale: 65*(90/100)*((100-x)/100)
= 56.16
x = 4%
Answer: B
Answer: B
Question: How many words can be formed from the letters of the word "SIGNATURE" so that vowels always come together.
Options:
A)17280
B)4320
C)720
D)80
E)None of thsee
Rationale: Explanation:
word SIGNATURE contains total 9 letters.
There are four vowels in this word, I, A, U and E
Make it as, SGNTR(IAUE), consider all vowels as 1 letter for now
So total letter are 6.
6 letters can be arranged in 6! ways = 720 ways
Vowels can be arranged in themselves in 4! ways = 24 ways
Required number of ways = 720*24 = 17280
Option A
Answer: A
Question: 15 + sqrt(- 6 + 8Ã—5Ã·4) =?
Options:
A)31
B)32
C)33
D)34
E)35
Rationale: According to order of operations, inner brackets first where 8x5Ã·4 is first calculated since it has a multiplication and a division.
8x5Ã·4 = 40Ã·4 = 10
Hence
15 + sqrt(- 6 + 8Ã—5Ã·4) = 15+ sqrt(- 6 + 10)
= 15 + sqrt(4) = 15 + 16 = 31
correct answer A)31
Answer: A
Question: How many of the positive factors of 63 , 84 and how many common factors are there in numbers?
Options:
A)2
B)4
C)3
D)5
E)1
Rationale: factors of 63 - 1,3,7,9,21,63
factors of 84 - 1,2,3,4,6,7,12,14,21,28,42,84
Comparing both, we have three common factors of 63 and 84- 1,3,7,21
Answer(B)
Answer: B
Question: A numberais squared and then multiplied by negative 3. The result of this operation R is equal to three times the sum of three timesaand two. What is one possible value ofa?
Options:
A)-3
B)-2
C)1
D)2
E)3
Rationale: R=-3*a^2=3(3a+2)
a= -2 or -1
a=-2=B
Answer: B
Question: Let the number which when multiplied by 13 is increased by 180.
Options:
A)14
B)20
C)15
D)28
E)30
Rationale: Solution
Let the number be x .
Then, 13x - x = 180
‹=›12x = 180
x ‹=› 15.
Answer C
Answer: C
Question: 5 persons a, b, c, d, e are to be lined up in a row. If a, b, and c adhere always together, how many possible cases are there?
Options:
A)24
B)36
C)48
D)72
E)144
Rationale: firstly it is not GEOMETRY but COMBINATIONS, so changing the TAG accordingly..
total 5 are there..
take a,b, and c as one,so total =3..
these 3 can be arranged in 3! ways..
a,b, and c can be arranged within themselves in 3! ways ..
TOTAL = 3!*3!=36
B
Answer: B
Question: A rower whose speed is 4 km/hr in still water rows to a certain point upstream and back to the starting point in a river which flows at 2 km/hr. What is the rower's average speed (in km/hr) for the total journey?
Options:
A)6
B)4
C)9
D)3
E)2
Rationale: time upstream = d / 2
time downstream = d / 6
total time = d/2 + d/6 = 2d/3
average speed = 2d / (2d/3) = 3 km/hr
The answer is D.
Answer: D
Question: What is the probability of getting exactly 2 heads in a single throw of four fair coins?
Options:
A)1/2
B)3/4
C)3/8
D)3/16
E)5/16
Rationale: One possible case is HHTT.
P(HHTT) = 1/2*1/2*1/2*1/2 = 1/16
There are 4C2 = 6 possible cases.
P(2 heads) = 6*1/16 = 3/8
The answer is C.
Answer: C
Question: The sale price sarees listed for Rs.750 after successive discount is 20% and 15% is?
Options:
A)227
B)570
C)342
D)680
E)230
Rationale: 750*(80/100)*(85/100)
= 570
Answer: B
Answer: B
Question: The average age of a class of 32 students is 16 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher
Options:
A)49
B)88
C)25
D)18
E)11
Rationale: Total age of students is 32X16 = 512 Years
Total age inclusive of teacher = 33X (16+1) = 561
So, Teacher's age is 561-512 = 49 Yrs
Answer: A
Answer: A
Question: How many odd factors does 520 have?
Options:
A) 3
B) 4
C) 5
D) 6
E) 8
Rationale: Start with the prime factorization: 520 = 2*5*13
For odd factors, we put aside the factor of two, and look at the other prime factors.
set of exponents = {1, 1}
plus 1 to each = {2, 2}
product = 2*2 = 4
Therefore, there are 4 odd factors of 520.
Answer: B.
Answer: B
Question: Population of a city in 20004 was 1300000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city at the end of the year 2007
Options:
A)354354
B)545454
C)465785
D)456573
E)2818075/2
Rationale: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)
= P (1 + 15/100)(1 - 35/100)(1 + 45/100)
= 2818075/2
E
Answer: E
Question: Find the area of a parallelogram with base 32 cm and height 14 cm?
Options:
A)498 cm2
B)384 cm2
C)430 cm2
D)128 cm2
E)448 cm2
Rationale: Area of a parallelogram
= base * height
= 32 * 14 = 448 cm2
Answer:E
Answer: E
Question: The probability of Sam passing the exam is 1/5. The probability of Sam passing the exam and Michael passing the driving test is 1/6. What is the probability of Michael passing his driving test?
Options:
A)1/24.
B)1/2.
C)5/6.
D)2/3.
E)2/5
Rationale: 1/5 *1/m= 1/6 , 1/m = 5/6
Answer C
Answer: C
Question: A shipment of 8 television sets contains 2 black-and-white sets and 4 color sets. If 2 television sets are to be chosen at random from this shipment, what is the probability that at least 1 of the 2 sets chosen will be a black-and-white set?
Options:
A)1/7
B)1/4
C)5/14
D)11/14
E)13/28
Rationale: I get 11/14, which is not in the answer choices.
the probability of getting at least one b/w TV is 1-(the probability of getting 2 color TVs)
1-C(4,2)/C(8/2)=22/28=11/14
D
Answer: D
Question: An office supply store stocks three sizes of notebooks, each in five colors: blue, green, yellow, red, or pink. The store packs the notebooks in packages that contain either 3 notebooks of the same size and the same color or 3 notebooks of the same size and of 3 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible?
Options:
A)24
B)30
C)42
D)45
E)60
Rationale: First let's consider the small notebooks.
There are 5 ways to choose 3 notebooks of the same color.
The number of ways to choose 3 notebooks with different colors is 5C3=10.
There are 15 different packages we can make with the small notebooks.
We can use the same process to find 15 different packages with medium and large notebooks.
The total number of different packages is 45.
The answer is D.
Answer: D
Question: A train 175 m long pass a telegraph pole in 5 seconds. Find the speed of the train
Options:
A)66 km/hr
B)68.4 km/hr
C)72 km/hr
D)126 km/hr
E)None
Rationale: Sol.
Speed = [175/6] m/sec = [352 * 18/5] km/hr = 126 km/hr.
Answer D
Answer: D
Question: A sum of money placed at C.I. interest doubles itself in 5 years. It will amount to eight times itself at the same rate of interest in?
Options:
A)20 years
B)1 years
C)15 years
D)39 years
E)39 years
Rationale: Explanation:
P(1 + R/100)5 = 2P => (1 + R/100)5 = 2
Let P(1 + R/100)n = 8P
=> (1 + R/100)n = 8 = 23 = {(1 + R/100)5}3
=> (1 + R/100)n = (1 + R/100)15 => n = 15 Required time = 15 years.
Answer: Option C
Answer: C
Question: Set F consists of all the prime numbers between 10 and 25. What is the range of set F?
Options:
A)12
B)13
C)16.6
D)17
E)23
Rationale: Answer of set F is 12=A
Answer: A
Question: If a mixture is 5⁄9 alcohol by volume and 4⁄9 water by volume, what is the ratio of the volume of alcohol to the volume of water in this mixture?
Options:
A)1/4
B)3/4
C)5/4
D)6/4
E)7/4
Rationale: Should be a sub-600 level Q..
volume= {5/9}/{4/9}=5/4
C
Answer: C
Question: when n divided by 3, the remainder is 2.
when n divided by 4, the remainder is 1
what is the the remainder when divided by 12
Options:
A)1
B)3
C)4
D)5
E)12
Rationale: when n divided by 3, the remainder is 2.
This statement can be written as
n=3k+2 (where k is the quotient) ----1
similarly
when n is divided by 4, the remainder is 1
can be written as
n=4p+1 (here p is the quotient) ------2
from eq 1 and 2
3k+2=4p+1
or,
k=(4p-1)/3
substitute p= 1 , the result will give ----> k=1
substitute back in the equations
in both the cases we have n=5
dividing n by 12 will give remainder 5 !!
ANSWER:D
Answer: D
Question: The mean of set L does not exceed mean of any subset of set L. Which of the following must be true about set L?
I. Set L contains only one element
II. All elements in set L are equal
III. The median of set L equals the mean of set L
Options:
A)of the three qualities is necessary
B)II only
C)III only
D)II and III only
E)I, II, and III
Rationale: The only necessary condition seems to be II.
If all nos are equal.... them mean of any subset is the same.
I is obviously ruled out ( e.g. L = {1,1,1} )
But III, what about 3?
It is not necessary in itself, rather, is automatically implied by II.
All sets that satsify II satisfy III=D
Answer: D
Question: The ratio of number of students studying Arts, Commerce and Science in a College is 7 : 5 :8. What is the new ratio of the number of students studying Arts, Commerce and Science respectively if there is an increase of 20%, 40% and 25% in the number of students studying Arts, Commerce and Science?
Options:
A)18 : 35 : 50
B)3 : 10 : 10
C)4 : 8 : 5
D)21 : 35 : 50
E)None of these
Rationale: Suppose the number of students studying Arts, Commerce and Science be 7x, 5x and 8x respectively.
When their numbers are increased by 20%, 40% and 25% respectively the new ratio becomes
7x × 120% : 5x × 140% :
8x × 125% = 42 : 70 : 100
= 21 : 35 : 50
Answer D
Answer: D
Question: xy=1 then what is (4^(x+y)^2) / (4^(x-y)^2)
Options:
A)2
B)4
C)8
D)256
E)32
Rationale: (x+y)^2 - (x-y)^2
(x+y+x-y)(x+y-x+y)
(2x)(2y)
4xy
4
4^4 = 256
Answer D
Answer: D
Question: A motorcyclist goes from Bombay to Pune, a distance of 192 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 ½ hours after the first, and reaches Pune ½ hour earlier. What is the ratio of the speed of the motorcycle and the car?
Options:
A)1:2
B)1:9
C)1:1
D)1:9
E)3:2
Rationale: T = 192/32 = 6 h
T = 6 - 3 = 3
Time Ratio = 6:3 = 2:1
Speed Ratio = 1:2
Answer: A
Answer: A
Question: A researcher computed the mean, the median, and the standard deviation Q for a set of performance scores. If 5 were to be added to each score, which of these three statistics would change?
Options:
A)The mean only
B)The median only
C)The standard deviation only
D)The mean and the median
E)The mean and the standard deviation
Rationale: If we add or subtract a constant to each term in a set the standard deviation Q will not change..
If we add (or subtract) a constant to each term in a set the mean and the median will increase (decrease) by the value of that constant.
Answer: D.
Answer: D
Question: If X = Y/Z+1, -1 < Z < 0 and 2 < Y, which of the following is correct?
Options:
A)1 < X <2
B)0 < X <-2.
C)-4 < X < 0
D)0 < X <-4
E)X < -20
Rationale: Y is +ve & Z is -ve
For min. value max. numerator and minimize denominator
take Y=2.1 & Z=-0.9
X=2.1/(-0.9+1) X=2.1/1.9
1 < X <2
Ans A
Answer: A
Question: If O is the center of the circle in the figure above and the area of the unshaded sector is 5, what is the area of the shaded region?
Options:
A)25/√π
B)30/√π
C)20
D)twenty five (25)
E)30
Rationale: 60/360 = 1/6
1/6 of total area = 5
5/6 of total area = 5*5 = 25
ANSWER:D
Answer: D
Question: Two assembly line inspectors, Lauren and Steven, inspect widgets as they come off the assembly line. If Lauren inspects every fourth widget, starting with the fourth, and Steven inspects every third, starting with the third, how many of the 98 widgets produced in the first hour of operation are not inspected by either inspector?
Options:
A)50
B)52
C)53
D)55
E)56
Rationale: Widgets inspected by Lauren: ((96-4)/4)+1=23+1=24
Widgets inspected by Steven: ((96-3)/3)+1 =31+1 =32
Widgets inspected by both: ((96/12)+1 =9
Total : 24+32 -9=45
hence, widgets not inspected: 98-45=53
Option C
Answer: C
Question: How many seconds will a 600 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)36 sec
B)30 sec
C)13 sec
D)19 sec
E)12 sec
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 = 600 * 3/50
= 36 sec.
Answer:A
Answer: A
Question: In a series of football matches, the probability that Team P wins a match against Team Q is 1/3 and the probability that the match ends in a draw is 1/5. If the two teams play five matches, what is the probability that all five matches end in a draw?
Options:
A)1/1625
B)1/2225
C)1/3125
D)1/4225
E)1/5425
Rationale: P(5 draws)=(1/5)^5=1/3125
The answer is C.
Answer: C
Question: A man gets a simple interest of Rs.600 on a certain principal at the rate of 5% p.a in two years. Find the compound interest the man will get on twice the principal in two years at the same rate.
Options:
A)Rs.500
B)Rs.250
C)Rs.307.5
D)Rs.5062.50
E)None of these.
Rationale: Let the principal be Rs.P
S.I at 5% p.a in 8 years on Rs.P = Rs.600
(P)(8)(5)/100 = 600
P = 1500
C.I on Rs.2P i.e., Rs.2500 at 5% p.a in two years
=3000{ [1 + 5/100]2 - 1} = 3000{ 212 - 202 /202}
= 3000/400(441 - 400)
= Rs.307.5
ANSWER:C
Answer: C
Question: A boy has nine trousers and 12 shirts. In how many different ways can he select a trouser and a shirt?
Options:
A)167 ways
B)828 ways
C)627 ways
D)108 ways
E)622 ways
Rationale: The boy can select one trouser in nine ways.
The boy can select one shirt in 12 ways.
The number of ways in which he can select one trouser and one shirt is 9 * 12 = 108 ways.
Answer:D
Answer: D
Question: A factory produces 5500 toys per week. If the workers at this factory work 4 days a week and if these workers make the same number of toys everyday, how many toys are produced each day?
Options:
A)1375 toys
B)2375 toys
C)3375 toys
D)4375 toys
E)5375 toys
Rationale: To find the number of toys produced every day, we divide the total number of toys produced in one week (of 4 days) by 4.
5500 ? 4 = 1375 toys
correct answer A
Answer: A
Question: The speed of a boat in still water is 60kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
Options:
A)20 kmph
B)40 kmph
C)27 kmph
D)28 kmph
E)22 kmph
Rationale: Speed downstream = 60 + 20
= 80 kmph
Speed upstream = 60 - 20
= 40 kmph
Answer:B
Answer: B
Question: There are two circles of different radii. The are of a square is 784 sq cm and its side is twice the radius of the larger circle. The radius of the larger circle is seven - third that of the smaller circle. Find the circumference of the smaller circle.?
Options:
A)87
B)98
C)12
D)27
E)28
Rationale: Let the radii of the larger and the smaller circles be l cm and s cm respectively. Let the side of the square be a cm.
a2 = 784 = (4)(196) = (22).(142)
a = (2)(14) = 28
a = 2l, l = a/2 = 14
l = (7/3)s
Therefore s = (3/7)(l) = 6 Circumference of the smaller circle
= 2∏s = 12∏ cm.
Answer:C
Answer: C
Question: The length and width of a rectangle are integer values. What is the area of the smallest such rectangle that can be inscribed in a circle whose radius is also an integer
Options:
A) 12
B) 24
C) 46
D) 48
E) 60
Rationale: If we consider all pythagorean triplets with integral values, we have the following results:-
(3,4,5),(6,8,10)........
The diameter of the circle is 5 in the 1st case and 10 in the 2nd.
But the question says that radius of the circle is also an integer hence the 1st triplet will be ruled out.
We are left with the 2nd triplet where radius of the circle=5,
Hence the sides of the rectangle are 6 and 8 making the area =46.
C
Answer: C
Question: Solving a linear equation with several occurrences of the variable, solve for w. Simplify answer as much as possible.
(7w + 6)/6 + (9w +8)/2 = 22
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: (7w + 6)/6 + (9w +8)/2 = 22
or, [7w + 6 + 3(9w + 8)]/6 = 22
or, 7w + 6 + 27w + 24 = 132
or, 34w + 30 = 132
or, 34w = 132 - 30
or, 34w = 102
or, w = 102/34
Therefore, w = 3
Answer: C
Answer: C
Question: What is the square root of 81, divided by 3?
Options:
A)9
B)36
C)122
D)3
E)1
Rationale: Square root is a number times itself
Square root of 81=6, 9/3=3
(D)3
Answer: D
Question: Bill made a profit of 10% by selling a product. If he had purchased that product for 10% less and sold it at a profit of 30%, he would have received $ 56 more. What was his original selling price?
Options:
A) $770
B) $660
C) $700
D) $1100
E) $880
Rationale: Let the original purchase price be X
So original selling price at 10% profit = 1.1X
If product is purchased at 10% less of original = 0.9X
Profit of 30% on this price = 1.3(0.9X)
He would have received $56 more in second scenario => 1.3(0.9X) - 1.1X = 56
=> 0.07X = 56
=> X = $800
Original purchase price = $800
Hence, original selling price (at 10% of profit) = 1.1(800) = $880
Option E
Answer: E