divelab/Sys2Bench huggingface dataset:
Question: If John invested $ 1 at 4 percent interest compounded annually, the total value of the investment, in dollars, at the end of 5 years would be
Options:
A)(1.5)^4
B)(1.04)^5
C)(1.05)^4
D)1 + (0.05)^4
E)1 + 4(0.05)
Rationale: In this prompt, the answer choices show that we don't actually have to calculate anything - we just need to 'format' the calculation correctly. We're told that the interest is COMPOUNDED ANNUALLY, so we need the Compound Interest Formula, with a Principal of $1, an R of 4% (which would 'translate' as .05) and a T of 5.We'd have....
B
Answer: B
Question: Marco rode his dirt bike at 35 miles per hour (mph) for two hours. If he then continued to ride at a different constant rate for another three hours, and at the end of the three hours his average speed for the entire five hour ride was 30mph, what was his average speed over the three hour portion of his ride?
Options:
A)14 mph
B)20 mph
C)70/3 mph
D)80/3 mph
E)34 mph
Rationale: Average speed for first two hours, S1 = 35 mph
Distance travelled in these two hours, D1 = 70 miles
Average speed for the entire 5 hour ride, S = 30 mph
Total Distance traveller in the entire 5 hour ride, D = 30 x 5 = 150 miles.
Hence, distance traveller in the latter 3 hour period, D2 = D - D1 = 150 - 70 = 80
Average speed for the latter 3 hour period S2 = D2/3 = 80/3
Hence, the correct answer is D
Answer: D
Question: Sreenivas sells a table to Shiva at 10% profit and Shiva sells it to Mahesh at 10% loss. At what price did Sreenivas purchase the table if Mahesh paid Rs. 2574?
Options:
A)2277
B)2669
C)2200
D)2766
E)2600
Rationale: Let the cost price of table for Sreenivas be Rs. x and given that, cost price of table for Mahesh = Rs. 2574.
=> (90%) of (110%) of x = Rs. 2574.
=> (90/100)(110/100)x = 2574
=> x = (2574 * 100)/(9 * 11)
=> x = Rs. 2600
Answer: E
Answer: E
Question: The area of a square is 4096 sq cm. Find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square.
Options:
A)5:18
B)5:71
C)5:19
D)5:17
E)5:16
Rationale: Let the length and the breadth of the rectangle be l cm and b cm respectively. Let the side of the square be a cm.
a2 = 4096 = 212
a = (212)1/2 = 26 = 64
L = 2a and b = a - 24
b : l = a - 24 : 2a = 40 : 128 = 5 : 16
Answer: E
Answer: E
Question: Hammers and wrenches are manufactured at a uniform weight per hammer and a uniform weight per wrench. If the total weight of two hammers and three wrenches is one-third that of 8 hammers and 4 wrenches, then the total weight of one wrench is how many times that of one hammer?
Options:
A)1/2
B)2/5
C)1
D)3/2
E)2
Rationale: x bé the weight of a hammer and y be the weight of a wrench.
(2x+3y)=1/3*(8x+4y)
3(2x+3y)=(8x+4y)
6x+9y=8x+4y
5y=2x
y=2x/5
Ans - B
Answer: B
Question: At a certain conference, 70% of the attendees registered at least
two weeks in advance and paid their conference fee in full. If
10% of the attendees who paid their conference fee in full did
not register at least two weeks in advance, what percent of
conference attendees registered at least two weeks in
advance?
Options:
A) 18.0%
B) 62.0%
C) 77.76%
D) 80.0%
E) 82.0%
Rationale: I do not think that Venn will be helpful here. A table will make more sense. But here is my approach.
70% regestered at least 2 weeks and paid full fee.
10% paid full fee and did not registered at least 2 weeks in advance. Then 90% paid full fee and registered at least 2 weeks before.
90% *X=70% where X is the number of people who registerd 2 weeks in advance and paid full fee.(ANSWER C)
Answer: C
Question: A credit card company has a cash back option for their customers which is based on the annual amount that they charge on their credit cards. The customer receives 1% cash on their first $5000 of purchase, 2% on the next $5000 of purchase and a 3% on cash back on portion that exceeds $10,000. If a customer receives a cash back of 2.5% on their total annual charges made on the credit card, then what was the customer's annual charge?
Options:
A)$24,000
B)$26,000
C)$28,000
D)$30,000
E)$32,000
Rationale: The customer receives $50 for the first $5000.
The customer receives $100 for the next $5000.
Let x be the total amount of the customer's annual charge.
$150 + 0.03(x-10,000)=0.025x
0.005x=150
x=30,000
The answer is D.
Answer: D
Question: A hiker walked for 3 days. She walked 18 miles on the first day, walking 3 miles per hour. On the second day she walked for one less hour but she walked one mile per hour, faster than on the first day. On the third day she walked the same number of hours as on the first day at 1 mile faster than 2nd day for same hours. How many miles in total did she walk?
Options:
A)63
B)44
C)58
D)60
E)62
Rationale: First day - 18 miles with 3 miles per hours then total - 6 hours for that day
Second day - 4 miles per hour and 5 hours - 20 miles
Third day - 5 miles per hour and 5 hours - 25 miles
Total 18+20+25 = 63
Answer: option A.
Answer: A
Question: A reduction of 10% in the price of oil enables a house wife to obtain 6kgs more for Rs.900, what is the reduced price for kg?
Options:
A)13
B)15
C)25
D)17
E)19
Rationale: 900*(10/100) = 90 ---- 6
? ---- 1 => Rs.15
Answer:B
Answer: B
Question: Given that x = 2^b – (8^31 + 16^5), which of the following values for b yields the lowest value for |x|?
Options:
A)91
B)92
C)93
D)94
E)113
Rationale: 8^31 + 16^5 = 2^93 + 2^20
Compared to 2^93, the value of 2^20 is negligible.
2^93 - (2^93 +2^20) will minimize the value of |x|.
The answer is C.
Answer: C
Question: In a class, 20% of the members own only two cars each, 40% of the remaining own three cars each and the remaining members own only one car each. Which of the following statements is definitely true from the given statements ?
Options:
A)Only 20% of the total members own three cars each.
B)48% of the total members own only one car each.
C)60% of the total members own at least two cars each.
D)80% of the total members own at least one car.
E)None of these
Rationale: Let total number of members be 100,
Then, number of members owning only 2 cars = 20.
Number of members owning 3 cars = 40% of 80 = 32.
Number of members owning only 1 car = 100 - (20 + 32) = 48.
Thus, 48% of the total members own one car each.
ANSWER:B
Answer: B
Question: Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles?
Options:
A)Rs.1000
B)Rs.1500
C)Rs.2000
D)Rs.3000
E)Rs.3500
Rationale: (10*10)/100 = 1%loss
100 --- 99
? --- 1980 => Rs.2000
C)
Answer: C
Question: John was born 8 years after his father's marriage. His mother is 4 years younger than his father but 25 years older than John who is 15 years old. At what age did the father get married ?
Options:
A)18 years
B)20 years
C)22 years
D)24 years
E)21 years
Rationale: Explanation:
John's present age = 15 years.
His mother's present age = (25 + 15) years = 40 years.
His father's present age = (40+ 4) years = 44 years.
His father's age at the time of John's birth = (44 - 15) years = 29 years.
Therefore John's father's age at the time of marriage = (29 - 8) years = 21 years.
Answer: E
Answer: E
Question: A 25 cm wide path is to be made around a circular garden having a diameter of 4 meters. Approximate area of the path is square meters is
Options:
A)3.34
B)3.36
C)3.34
D)6.32
E)3.31
Rationale: Area of the path = Area of the outer circle - Area of the inner circle = ∏{4/2 + 25/100}2 - ∏[4/2]2
= ∏[2.252 - 22] = ∏(0.25)(4.25) { (a2 - b2 = (a - b)(a + b) }
= (3.14)(1/4)(17/4) = 53.38/16 = 3.34 sq m.Answer:A
Answer: A
Question: A person walks from one end to the other of a 100-meter long moving walkway at a constant rate in 50 seconds, assisted by the walkway. When this person reaches the end, they reverse direction and continue walking with the same speed, but this time it takes 150 seconds because the person is traveling against the direction of the moving walkway. If the walkway were to stop moving, how many seconds would it take this person to walk from one end of the walkway to the other?
Options:
A)63
B)66
C)69
D)72
E)75
Rationale: Let v be the speed of the person and let x be the speed of the walkway.
50(v+x)=100 then 150(v+x)=300
150(v-x)=100
When we add the two equations:
300v=400
v=4/3
time = 100 / (4/3) = 75 seconds
The answer is E.
Answer: E
Question: You make a cube that is made of 10 x 10 x 10 smaller cubes which sums up to a total of 1000 smaller cubes.
Now, if someone takes one layer of cubes, how many will remain?
Options:
A)357
B)834
C)500
D)512
E)216
Rationale: D
512
The cube that remains will be 8 x 8 x 8. This will make a total of 512. This is because, when a layer is taken, it will be taken from all sides of the cube which will reduce the dimension be two and not one.
Answer: D
Question: Two equal sums of money were invested, one at 4% and the other at 4.5%. At the end of 7 years, the simple interest received from the latter exceeded to that received from the former by 31.50. Each sum was :
Options:
A)1,200
B)600
C)750
D)900
E)None of these
Rationale: Difference of S.I. = √31.50
Let each sum be x. Then
x×4 1/2×7 /100−x×4×7/100=31.50
or 7⁄100x × 1⁄2 = 63⁄2
or x = 900
Answer D
Answer: D
Question: A student must answer 6 out of 10 questions on an examination. If at least 3 of the first 5 questions must be answered, how many possible combinations of 6 questions are available to the student?
Options:
A)150
B)200
C)210
D)170
E)180
Rationale: as there is ONLY one possiblity of choosing 6 out of 10, while choosing less than 3 in first five
choose 2 in first 5 and all 4 from later half..
ways = 5C2 = 10..
total ways = 10C4 = 210
ans = 210-10 = 200
B
Answer: B
Question: Suppose 12 monkeys take 12 minutes to eat 12 bananas. How many monkeys would it take to eat 72 bananas in 72 minutes?
Options:
A)9
B)10
C)11
D)12
E)13
Rationale: One monkey takes 12 min to eat 1 banana , so in 72 mins 1 monkey will eat 6 bananas , so for 72 bananas in 72 min we need 72/6 =12 monkeys
ANSWER:D
Answer: D
Question: A shipment of 8 TV sets contains 4 black and white sets and 4 color sets. If 2 TV 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)11/14
C)5/14
D)11/28
E)13/28
Rationale: 4/8 * 3/7 = 12/56
1-(12/56) = 44/56 = 11/14
Answer B
Answer: B
Question: If x and y are integers and x + y = 3, which of the following must be true?
Options:
A)If x < 0, then y > 0.
B)x and y are consecutive integers.
C)If x > 0, then y < 0.
D)Both x and y are even.
E)Both x and y are less than 5.
Rationale: In option C if x > 0,then y<0 means x is +ve and y is -ve
In option B if x < 0, then y>0 means y is +ve and x is -ve, both are same and satisfying x+y = 5.
How option A is right could you explain
Answer: A
Question: What is the 4 digit number whose second digit is thrice the first digit and 3rd digit is sum of 1st and 2nd and last digit is thrice the second digit.
Options:
A)2674
B)1349
C)3343
D)3678
E)3679
Rationale: let four digits is a,b,c&d ...so by given
b is 3a
c is 4a
d is 9a so
ans is 1349
ANSWER:B
Answer: B
Question: Solution X is 10 percent alcohol by volume, and solution Y is 30 percent alcohol by volume. How many milliliters of solution Y must be added to 250 milliliters of solution X to create a solution that is 25 percent alcohol by volume?
Options:
A)250/3
B)750
C)400
D)480
E)600
Rationale: we know that X is 10% , Y is 30% and W.Avg = 25% . what does this mean with respect to W.Avg technique ?
W.Avg is 1 portion away from Y and 3 portion away from X so for every 1 portion of X we will have to add 3 portions of Y.
If X = 250 then Y = 750
ANSWER:B
Answer: B
Question: Marge has 3 pumps for filling her swimming pool. When all 3 pumps work at their maximum rates, the swimming pool is filled in 66 minutes. Pump 1's maximum rate is twice the maximum rate of pump 2 and four times the maximum rate of pump 3. How long would it take Marge to fill the pool if she used only pump 3 at its maximum rate ?
Options:
A)2hrs, 48mins
B)6hrs, 32mins
C)7hrs, 12mins
D)13hrs, 4mins
E)7hrs, 42mins
Rationale: The rate of pump 1 = 4x job/minute.
The rate of pump 2 = 2x job/minute.
The rate of pump 3 = x job/minute.
Given that x+2x+4x=1/66 --> x=1/462 --> (time) = (reciprocal of rate) = 462 minutes = 7 hours and 42 minutes.
Answer: E
Answer: E
Question: For any non-zero a and b that satisfy |ab| = ab and |a| = -a
|b + 4| + |ab - b| = ?
Options:
A)a) ab - 4
B)b) 2b - a - 4
C)c) ab - 2b - 4
D)d) ab - 2b + 4
E)e) 4 - ab
Rationale: |a| = -a Suggests that 'a' is Negative
|ab| = ab Suggests that 'ab' is Positive
'ab' is Positive Suggests that 'a' and 'b' have same Sign i.e. either both positive or both negative
But since 'a' is Negative therefore 'b' is Negative too.
Since b is negative so |b - 4| = -b-4
Since ab is Positive and b is Negative so |ab - b| = ab - b
i.e. |b + 4| + |ab - b| = -b-4 + ab - b =ab - 2b - 4
Answer: Option C
Answer: C
Question: A can finish a piece of work in 5 days. B can do it in 10 days. They work together for two days and then A goes away. In how many days will B finish the work?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: 2/5 + (2 + x)/10 = 1 => x = 4 days
Answer: A
Answer: A
Question: Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $9 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the two discounts rates is 22 percent, what is the discount rate on Pony jeans?
Options:
A)9%
B)10%
C)11%
D)12%
E)13%
Rationale: Let X be the percentage decrease in fox jeans
pony jeans = 22- X
(15*x/100)*3 + (18(22-X)/100)*2 = 9 ........... given
45X/100 + 792-36x/100 = 9
9x+792/100 = 9
9x+ 792 = 900
9x= 108
X = 12 = fox jeans
hence pony jeans = 22-12 = 10
ANSWER:B
Answer: B
Question: A certain sum is invested at simple interest at 18% p.a. for two years instead of investing at 12% p.a. for the same time period. Therefore the interest received is more by Rs. 240. Find the sum?
Options:
A)7000
B)7029
C)2778
D)2800
E)2000
Rationale: Let the sum be Rs. x.
(x * 18 * 2)/100 - (x * 12 * 2)/100 = 240 => 36x/100 - 24x/100 =240
=> 12x/100 = 240 => x = 2000.Answer:E
Answer: E
Question: The workforce of Company nokia is 60% female. The company hired 20 additional male workers, and as a result, the percent of female workers dropped to 50%.How many employees did the company have after hiring the additional male workers?
Options:
A)130
B)135
C)150
D)145
E)140
Rationale: let x be the total worker then 0.6x =female worker and 0.4x is male worker then 20 male worker added
06x/(0.4x +20) = 50/100 or 60x = 50*( 0.4x+100) = 20x+ 5000 or 40x = 5000 , x = 125
total worker = 125 +20= 145
D
Answer: D
Question: For a lottery, three numbers are drawn, each from 1 to 40. A player can win if the product of his or her three numbers is odd. Initially, the same number may be picked up to three times. Later, the rules are changed so that each number may only be picked once. Approximately how much does this reduce a person's probability of winning?
Options:
A)01
B)025
C)115
D)125
E)5
Rationale: (1/2)∗(1/2)∗(1/2))−((1/2)∗(19/39)∗(18/38))((1/2)∗(1/2)∗(1/2))−((1/2)∗(19/39)∗(18/38))
((1/8)−(9/78))((1/8)−(9/78))
(0.125−approx.0.1111)(0.125−approx.0.1111)
Approximately 0.010.01
ANSWER :A
Answer: A
Question: In a car company, the company made A type cars numbering 20% of B type cars. What is the number of B type of cars as a percentage of A type cars?
Options:
A)7%
B)5%
C)8%
D)16%
E)12%
Rationale: A type cars made in a company is 20% of B type of cars
If B type of cars=10
A type of cars=2
We are asked to find the number of B type of cars as a percentage of A type of cars
B/A=10/2=5%
Answer is B
Answer: B
Question: If 2^(2w) = 8^(w−1), what is the value of w?
Options:
A)3
B)6
C)9
D)12
E)15
Rationale: 2^(2w) = 8^(w−1)
2^(2w) = 2^(3*(w−1))
2^(2w) = 2^(3w-3)
Let's equate the exponents as the bases are equal.
2w = 3w-3
w = 3
The answer is A.
Answer: A
Question: Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is:
Options:
A)2 : 3
B)4 : 3
C)6 : 7
D)9 : 16
E)9 : 14
Rationale: Let the slower train have speed of 1 unit and faster train a speed of
r units of speed.
Let t = time to when the trains meet.
rt 1t
Howrah|-----------------------|----------| Patna
meet
They meet rt units from Howrah and 1t units from Patna
For the second part of the journey the fast train at speed r has 1t
unit of distance and 9 hours to do it
So 1t/r = 9
Slow train has rt units of distance at speed of 1 unit and 16 hours
to do it.
rt/1 = 16
So rt/1 16
----- = ---- giving r^2 = 16/9
1t/r 9
r = 4/3
ANSWER:B
Answer: B
Question: The jogging track in a sports complex is 528 m in circumference. Deepak and his wife start from the same point and walk in opposite directions at 4.5 km/hr and 3.75 km/hr respectively. They will meet for the first time in?
Options:
A)5.29 min
B)3.84 min
C)5.08 min
D)9.28 min
E)5.988 min
Rationale: Clearly, the two will meet when they are 528 m apart.
To be (4.5 + 3.75) = 8.25 km apart, they take 1 hour.
To be 528 m apart, they take (100/825 * 528/1000) hrs = (528/8250 * 60) min = 3.84 min.
Answer: B
Answer: B
Question: There are three guys who have equal number of bullets. All of them shoot 8 bullets. The remaining bullets are equal to the total number of bullets remaining is equal to the bullets each had after division. What was the original number of bullets each one had?
Options:
A)18
B)19
C)27
D)31
E)36
Rationale: let initially each was having x bullets
they shot 8 bullets
so 3x-24=x
x=12
so each was having 12 bullets.
total was 36.
ANSWER:E
Answer: E
Question: In a certificate by mistake a candidate gave his height as 25% more than actual height. In the interview panel, he clarified that his height was 5feet 10 inches. Find the % correction made by the candidate from his stated height to his actual height?
Options:
A)10
B)20
C)17.5
D)43
E)50
Rationale: His height was = 5 feet 5 inch = 10 + 60 = 70 inch. Required % correction =70*(1.25-1) = 17.5
C
Answer: C
Question: The length of the bridge, which a train 155 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
Options:
A)220 m
B)225 m
C)245 m
D)250 m
E)270 m
Rationale: Let the length of the bridge:L
The equation now is L+155/12.5m/s(45km/hr or12.5m/s)=30
Solving, L =220m
ANSWER:A
Answer: A
Question: If x = -14/17 and y = -11/3, what is the value of the expression -2x – y^2?
Options:
A)-1023/754
B)1456/514
C)1364/153
D)153/1805
E)-1805/153
Rationale: x = -14/17 and y = -11/3
==> -2(-14/17) - (-11/3)^2 = 28/17 - 121/9 = -1805/153
Ans: E
Answer: E
Question: If (6)(x^2) has four different prime factors, at most how many different prime factors does x have?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: x can have at most 4 prime factors, namely the prime factors 2 and 3, plus 2 others.
If x had more than this number of prime factors, then (6)(x^2) would have more than 4 prime factors.
The answer is D.
Answer: D
Question: In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7000, the number of valid votes that the other candidate got, was:
Options:
A)2800
B)2700
C)2900
D)2200
E)2520
Rationale: E
Number of valid votes = 80% of 7000 = 5600.
Valid votes polled by other candidate = 45% of 6000
= (45/100 x 5600) = 2520.
Answer: E
Question: The average age of 20 men in the class is 16.6 years. Five new men join and the new average becomes 15.56 years. What was the average age of five new men?
Options:
A)15.5
B)15.4
C)15.25
D)15.3
E)11.4
Rationale: Total age of 20 men = 16.6 x 20 = 332
Now, total age of 25 men = 389.
Total age of five men added later = 389 - 332 = 57.
Hence, the total average of five men = 57/5 = 11.4
ANSWER:E
Answer: E
Question: In the formula P = 3/(r+3)^3, if r is halved, then P is multiplied by
Options:
A)125/64
B)125
C)1/64
D)64/125
E)1/125
Rationale: Say r=2 => P1 = 3/125
when r=1; P2 = 3/64
P2 = 125/64*P1.
Answer : A
Answer: A
Question: If a 3-member subcommittee is to be formed from a certain 9-member committee, how many different such subcommittee are possible?
Options:
A)6
B)18
C)84
D)108
E)216
Rationale: 1st member can be selected in 9 ways
2nd can be selected in 8 ways
3rd can be selected in 7 ways
So total ways : 504
But to avoid the similar scenarios 504/3!=84
ANS:C
Answer: C
Question: Sam invested Rs. 15000 @ 10% per annum for one year. If the interest is compounded half-yearly, then the amount received by Sam at the end of the year will be?
Options:
A)Rs. 16,500
B)Rs. 16,525.50
C)Rs. 16,537.50
D)Rs. 18,150
E)Rs. 19,150
Rationale: P = Rs. 15000; R = 10% p.a. = 5% per half-year; T = 1 year = 2 half-year
Amount = [15000 * (1 + 5/100)2]
= (15000 * 21/20 * 21/20) = Rs. 16537.50
ANSWER:C
Answer: C
Question: 1/2, 1/4, 1/8, 1/16, 1/32, 1/64, ....
In the sequence above each term after after the first one-half the previous term. If x is the tenth term of the sequence, then x satisfies which of the following inequalities?
Options:
A)0.1 < x < 1
B)0.01 < x < 0.1
C)0.001 < x < 0.01
D)0.0001 < x < 0.001
E)0.00001 < x < 0.0001
Rationale: In the Sequence notice that the sequence is just the 1/(2^n) ...
so for 1st term=1/2^1=1/2
2nd term=1/(2^2)1/4, 3rd term=1/(2^3)=1/8 and so on...
Thus the 10th term will be 1/(2^10)=1/1024
Roughly, 1/1024 can be 1/1000=0.001 but since denominator is a bit more than 1000 therefore the actual value will be a bit less than 0.001.
thus the ans will lie btw. 0.00001 and 0.0001.(E)
Answer: E
Question: A train covers a distance at a speed of 150kmph in 3 hours. To cover the same distance in 1 hours, it must travel at a speed of?
Options:
A)320
B)250
C)560
D)400
E)450
Rationale: Distance = 150*3 = 450km
Required speed = 450/1 =450 km/hr
Answer is E
Answer: E
Question: Two trains X and Y (80 km from each other) are running towards each other on the same track with a speed of 40km/hr. A bird starts from the train X and travels towards train Y with constant speed of 100km/hr. Once it reaches train Y, it turns and starts moving toward train X. It does this till the two trains collides with each other. Find the total distance traveled by the bird?
Options:
A)120
B)100
C)240
D)232
E)221
Rationale: B
100 km
Velocity of approach for the two trains = (40 + 40) km/hr
Total time the trains will take to collide = 80km/80km/hr = 1 hour
Total distance travelled by the bird = 100km/hr * 1hr = 100 km.
Answer: B
Question: A local bank that has 18 branches uses a two-digit code to represent each of its branches. The same integer can be used for both digits of a code, and a pair of two-digit numbers that are the reverse of each other (such as 17 and 71) are considered as two separate codes. What is the fewest number of different integers required for the 18 codes?
Options:
A)3
B)4
C)5
D)6
E)18( 5 integers 25 codes
Rationale: Pick any two integer.
Integers: 12
Code: 11, 12, 21, 22 = 4 Codes
Add one more integer: 3
13, 31, 33, 23, 32 = 5 Codes
Add one more integer: 4
44, 14, 41, 24, 42, 34, 43 = 7 Codes
Add one more integer: 5
55, 15,51, 25,52,35,53,45,54 =9 codes
Total = 25 Codes. Enough. Answer: E
5 integers create 25 codes.
E
Answer: E
Question: For what value of â€œkâ€ will the equation (2kx2 + 7kx +2)=0 have equal roots?
Options:
A)2/7
B)16/49
C)16/25
D)7/1
E)7/2
Rationale: for a 2nd degree equation ax2+bx_c=0 has equal roots the condition is b2-4ac =0
in the given equation
(7k)^2-4*2k*2=0
by solving this equation
we get k=0, k=16/49
ANSWER:B
Answer: B