divelab/Sys2Bench huggingface dataset:
Question: Let the function R(n) represent the product of the first n prime numbers, where n > 0. If x = R(n) + 1, which of the following must be true?
(i) x is always odd
(ii) x is always prime
(iii) x is never the square of an integer
Options:
A)ii only
B)iii only
C)i and ii only
D)i and iii only
E)ii and iii only
Rationale: R(n) is always even, because the first prime is 2 and no matter what n is, 2 always will be a divisor of R(n). Thus, R(n) + 1 = even + 1 = odd. So, (i) is always true.
Now, use logic:
If (ii) is true (so if x is always prime), then (iii) must automatically be true: no prime is the square of an integer. So, the correct answer must be i only; i, ii, and iii only; or i and iii only. since onlyi and iii onlyis among the options, then it must be true.
Or, since (i) is always true, then from options the answer must be either C or D. C cannot be correct because if (ii) is true, then so must be (iii). Thus only D remains.
Answer: D.
Answer: D
Question: Two sets of 3 consecutive positive integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?
Options:
A)4
B)7
C)6
D)12
E)it cannot be determined from the information given.
Rationale: A=(2,3,4), sum of this=9
B=(4,5,6), sum of this=15,
The differenct between 15-9=6
Hence,6 is the answer i.e.C
Answer: C
Question: Find the least number must be subtracted from 568219 so that remaining no.is divisible by 5?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: On dividing 568219 by 5 we get the remainder 4, so 4 should be subtracted
E
Answer: E
Question: In how much time will a train of length 110 m, moving at 36 kmph cross an electric pole?
Options:
A)sec
B)sec
C)sec
D)sec
E)sec
Rationale: Convert kmph to mps. 36 kmph = 36 * 5/18 = 10 mps.
The distance to be covered is equal to the length of the train.
Required time t = d/s = 110/10 = 11 sec.
Answer:D
Answer: D
Question: A motorboat, whose speed in 15 km/hr in sƟll water goes 30 km downstream and comes back in a
total of 4 hours 30 minutes. The speed of the stream (in km/hr) is
Options:
A)2 km/hr
B)3 km/hr
C)4 km/hr
D)5 km/hr
E)None of these
Rationale: Explanation:
Let the speed of the stream be x km/hr. Then,
Speed downstream = (15 + x) km/hr,
Speed upstream = (15 - x) km/hr
So we know from quesƟon that it took 4(1/2)hrs to travel back to same point.
So,
3015+x−3015−x=412=>900225−x2=92=>9x2=225=>x=5km/hr
Answer: D
Answer: D
Question: If 7 spiders make 7 webs in 7 days, then how many days are needed for 1 spider to make 1 web?
Options:
A)1
B)7
C)3
D)14
E)16
Rationale: Explanation:
Let, 1 spider make 1 web in x days.
More spiders, Less days (Indirect proportion)
More webs, more days (Direct proportion)
Hence we can write as
(spiders)7:1
(webs) 1:7}::x:7
⇒7×1×7=1×7 × x
⇒x=7
Answer: Option B
Answer: B
Question: Ram professes to sell his goods at the cost price but he made use of 950 grms instead of a kg, what is the gain percent?
Options:
A)5 15/19%
B)3 15/19%
C)4 15/19%
D)6 15/19%
E)9 15/19%
Rationale: 950 --- 50
50 --- ? =>
=50/950 *100
= 5 15/19%
Answer: A
Answer: A
Question: If x^3 = y^2 > z, which of the statements could be true?
I. x < y < z
II. x < z < y
III. y < x < z
Options:
A)I only
B)III only
C)I and II only
D)II and III only
E)I, II and III
Rationale: Given : x^3 = y^2 > z
x^3 = y^2 is possible only when 9^3=27^2=729
I. x < y < z is true for x=9, y=27, z=30 i.e. Answers can only be Options A, C or E
II. x < z < y is true for x=9, y=27, z=10 i.e. Answers can only be Options C or E
III. y < x < z is not true for x=9, y=27
Answer: option C
Answer: C
Question: If f(x) = x^3/(x^5 - 1), what is f(1/x) in terms of f(x)?
Options:
A)-f(x)
B)1/f(x)
C)2/f(x)
D)3/f(x)
E)f(x)
Rationale: If x = 2 then f(x) = 8/31 and f(1/x) = -8/31 which is equal to -f(x)
answer A
Answer: A
Question: If p, q and r are positive integers and satisfy x = (p + q -r)/r = (p - q + r)/q = (q + r - p)/p, then the value of x is?
Options:
A)1/2
B)1
C)-1/2
D)-1
E)0
Rationale: When two or more ratios are equal, each of the ratios are equal to sum of the numerators divided by the sum of the denominators, provided sum of the denominators is non-zero.
Hence, x = (p + q -r)/r = (p - q + r)/q = (q + r - p)/p
=> x = (p + q - r + p - q + r + q + r - p) / (r + q + p)
=> x = (r + q + p) / (r + q + p) = 1
p + q + r is non-zero.
ANSWER:B
Answer: B
Question: If 2 cards are selected (with replacement) at random from the deck of 52 cards then what is the probability that both of the selected cards will be a king, a queen, or a jack? A deck of cards has a total of 52 cards, consisting of 4 suits: spades (black), hearts (red), diamonds (red), and clubs (black). In each suit, there are 13 cards including 1 king, 1 queen, and 1 jack.
Options:
A)1/16
B)2/25
C)3/64
D)5/128
E)9/169
Rationale: P(both cards are king, queen, or jack) = 12/52*12/52 = 9/169
The answer is E.
Answer: E
Question: Income of A is 25% more than the income of B. What is the income of B in terms of income of A?
Options:
A)80%
B)75%
C)78.66%
D)71.25%
E)None of these
Rationale: Explanation:
One of the most basic questions.
Let income of B be 100. Income of A is 25% more than income of B which means Income of A becomes 125
Now income of B in terms of A = 100/125 *100 = 80%
ANSWER A
Answer: A
Question: A sum of money at simple interest amounts to Rs. 1717 in 1 year and to Rs. 1734 in 2 years. The sum is:
Options:
A)Rs. 1200
B)Rs. 1690
C)Rs. 1600
D)Rs. 1700
E)Rs. 1500
Rationale: S.I. for 1 year = Rs. (1734 - 1717) = Rs. 17.
Principal = Rs. (1717 - 17) = Rs. 1700.
Answer: Option D
Answer: D
Question: Two pipes A and B can fill a cistern in 12 and 24 minutes respectively, and a third pipe C can empty it in 36 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
Options:
A)10 2/7 min
B)10 1/8 min
C)11 1/7 min
D)12 8/7 min
E)11 3/7 min
Rationale: 1/12 + 1/24 - 1/36
= 7/72
72/7 = 10 2/7
Answer:A
Answer: A
Question: The Guests at a football banquet consumed a total of 323 pounds of food. if no individual guest consumed more than 2 pounds of food, What is the minimum number of guests that could have attended the banquet?
Options:
A)160
B)161
C)162
D)163
E)164
Rationale: To minimize one quantity maximize other.
161*2 (max possible amount of food a guest could consume) = 322 pounds, so there must be more than 161 guests, next integer is 162.
Answer: C.
Answer: C
Question: If 20 % of certain quantity of work is done by A and the rest 80% by B, the work is completed in 20 days. If 80% of the work is done by A and the remaining 20% by B, then the work is completed in 30 days. How many days are required to complete the work , if A and B work together.
Options:
A)11 1/9
B)10 1/9
C)12
D)15
E)Source: TIME material.
Rationale: Use algebra :
0.2/A + 0.8/B = 20
1/A + 4/B = 100
0.8/A + 0.2/B = 30
4/A+ 1/B = 150
15/B = 250
B = 3/50 work per day
A = 3/100 work per day
Combined rate = 3/40 + 3/100 = 9/100
Time taken when working together = 100/9 = 11(1/9) days
Answer (A)
Answer: A
Question: Three friends A, B and C decided to share a lot of apples. Each of them had half of the total plus half an apple in order. After each of them took their share twice, no apples were left.How many apples were there?
Options:
A)62
B)63
C)64
D)65
E)66
Rationale: Whenever the rate of reduction is 'half of the total and half of it', the answer is always (2^n)-1, where 'n' is the number of times the process is repeated. Here, the process is repeated 6 times. So answer is (2^6)-1=63.
ANSWER:B
Answer: B
Question: The percentage profit earned by selling an article for Rs. 1520 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?
Options:
A)3000
B)1230
C)1750
D)5600
E)3400
Rationale: C.P. be Rs. x.
Then, (1520 - x)/x * 100 = (x - 1280)/x * 100
1520 - x = x - 1280
2x = 2800 => x = 1400
Required S.P. = 125 % of Rs. 1400 = 125/100 * 1400 = Rs. 1750.
ANSWER C
Answer: C
Question: Jeremy bought 2Q steaks for P dollars. Jerome buys R steaks for a 50% discount, how much will the steaks cost him in cents?
Options:
A)50RP/Q.
B)50QR/P.
C)25RQ/P.
D)25RP/Q.
E)RP/(4Q).
Rationale: Jeremy bought 2Q steaks for P dollars, so 1 steak = P/2Q
Jerome buys R steaks for a 50% discount: r* (P/4Q)
in cents the answer will be : r* (100 P/4Q)= 25 RP/ Q=D
Answer: D
Question: There are two buildings P and Q. If 15 persons are sent from P to Q, then the number of persons in each building is the same. If 20 persons are sent from Q to P, then the number of persons in P is double the number of persons in Q. How many persons are there in building P?
Options:
A)80
B)140
C)120
D)100
E)150
Rationale: Let the number of persons in building P = p
and the number of persons in building Q = q
If 15 persons are sent from P to Q,
then the number of persons in each building is the same
=> p-15 = q+15
=> p - q = 30 ----(Equation 1)
If 20 persons are sent from Q to P,
then the number of persons in P is double the number of persons in Q
=> 2(q - 20) = (p + 20)
=> 2q - 40 = p + 20
=> 2q - p = 60 ----(Equation 2)
(Equation 1) + (Equation 2)=> q = 90
From Equation 1, p = 30 + q = 30 + 90 = 120
i.e., Building P has 120 persons
Answer : Option C
Answer: C
Question: There are 12 cans in the refrigerator. 7 of them are red and 5 of them are blue. In how many ways we can remove 9 cans so that at least one red and at least one blue cans to remain the refrigerator.
Options:
A)460
B)175
C)493
D)455
E)445
Rationale: Ways to pick 3 cans so that at least one red and at least one blue cans to remain the refrigerator =
total ways to pick 3 can out of 12 - ways to pick 3 red out of 7 red - ways to pick 3 blue out of 5 blue
12C3âˆ’7C3âˆ’5C3=220âˆ’35âˆ’10=175
ANSWER:B
Answer: B
Question: In Country S, the unemployment rate among construction workers dropped from 16 percent on September 1, 1992, to 9 percent on September 1, 1996. If the number of construction workers was 20 percent greater on September 1, 1996, than on September 1, 1992, what was the approximate percent change in the number of unemployed construction workers over this period?
Options:
A) 50% decrease
B) 30% decrease
C) 15% decrease
D) 30% increase
E) 55% increase
Rationale: In Country S 1992 1996
No of construction workers 100 120
Unemployment Rate 16% 9%
Unemployed workers 16 11
% change in unemployed workers=(16-11)=5/16=~33% decrease
Closest ans=30% decrease
Ans=B
Answer: B
Question: What will be the compound interest on a sum of Rs. 26,000 after 3 years at the rate of 12% p.a.?
Options:
A)s.10123.77
B)s.10123.21
C)s.10123.20
D)s.10123.28
E)s.10528.12
Rationale: Amount = [26000 * (1 + 12/100)3]
= 26000 * 28/25 * 28/25 * 28/25
= Rs. 36528.12
C.I. = (36528.12 - 26000)
= Rs. 10528.12
Answer:E
Answer: E
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 4 hours and 36 hours respectively. The ratio of their speeds is?
Options:
A)4:9
B)4:3
C)4:5
D)3:1
E)4:2
Rationale: Let us name the trains A and B.
Then, (A's speed) : (B's speed)
= √b : √a = √36 : √4
= 6:2 = 3:1
Answer:D
Answer: D
Question: A sells his goods 50% cheaper than B but 50% dearer than C. The cheapest is?
Options:
A)A
B)B
C)C
D)all alike
E)None of these
Rationale: Let B = 100
A = 50
C * (150/100) = 50
3C = 100
C = 33.3 then 'C' Cheapest
ANSWER:C
Answer: C
Question: If three numbers are randomly selected from a set, what is the probability that sum will be greater than 18 if he given set is
{5,6,7,8,9,10}
Options:
A)7/18
B)5/13
C)5/16
D)5/19
E)5/9
Rationale: First problem is 6C3 = 18 .. Not 20..
Point 2, your sum should be greater than 18, so these are the following possibilities you have
({5,7,8},{5,9,10},{6,7,8},{6,9,10},{8,9,10}) which leads to 5 combinations
So the probability is 5 on 18 or 5/18..
ANSWER:D
Answer: D
Question: . Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is
Options:
A)5/0
B)5/9
C)5/1
D)5/3
E)5/6
Rationale: Explanation:
No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways.
Thus 6 * 5 * 4 = 120 favourable cases.
The total cases are 6 * 6 * 6 = 216.
The probability = 120/216 = 5/9.
Answer:B
Answer: B
Question: On 8th Feb, 2005 it was Tuesday. What was the day of the week on 8th Feb, 2004?
Options:
A)Sunday
B)Friday
C)Saturday
D)Monday
E)NONE OF THESE
Rationale: Explanation :
Given that 8th Feb, 2005 was Tuesday
Number of days from 8th Feb, 2004 to 7th Feb, 2005 = 366 (Since Feb 2004 has 29 days as it is a leap year)
366 days = 2 odd days
Hence 8th Feb, 2004 = (Tuesday - 2 odd days) = Sunday. Answer : Option A
Answer: A
Question: A and B start a business with Rs.6000 and Rs.8000 respectively. Hoe should they share their profits at the end of one year?
Options:
A)3:3
B)3:4
C)3:8
D)3:1
E)3:2
Rationale: They should share the profits in the ratio of their investments.
The ratio of the investments made by A and B =
6000 : 8000 => 3:4.Answer: B
Answer: B
Question: A customer purchased a package of ground beef at a cost of $1.76 per pound. For the same amount of money, the customer could have purchased a piece of steak that weighed 36 percent less than the package of ground beef. What was the cost per pound of the steak?
Options:
A)$2.00
B)$2.25
C)$2.50
D)$2.75
E)$3.00
Rationale: For simplicity, let's assume the customer bought 1 pound of ground beef for $1.76.
Let x be the price per pound for the steak.
Then 0.64x = 176
x = 176/0.64 = $2.75
The answer is D.
Answer: D
Question: Natasha climbs up a hill, and descends along the same way she went up. It takes her 4 hours to reach the top and 2 hours to come back down. If her average speed along the whole journey is 1.5 kilometers per hour, what was her average speed (in kilometers per hour) while climbing to the top?
Options:
A)1.065
B)1.125
C)1.225
D)1.375
E)1.425
Rationale: Let the distance to the top be x, so the total distance traveled by Natasha is 2x.
The total time is 4 + 2 = 6 hours
The average speed = total distance/total time taken = 2x/6 = x/3
The average speed of the complete journey is 1.5 km/hour
x/3 = 1.5
x = 4.5 km
The average speed while climbing = distance/time = 4.5/4 = 1.125 km/h
The answer is B.
Answer: B
Question: Griffin has a bag of marbles that contains 7 black marbles and 4 red marbles. If he removes 3 marbles at random without replacing any of the marbles, what is the probability that all 3 marbles selected will be red?
Options:
A)2/55
B)3/85
C)4/105
D)4/165
E)8/165
Rationale: P(3 red marbles) = 4/11*3/10*2/9 = 4/165
The answer is D.
Answer: D
Question: The length of the rectangular field is double its width. Inside the field there is square shaped pond 8m long. If the area of the pond is 1/8 of the area of the field. What is the length of the field?
Options:
A)26
B)32
C)87
D)20
E)23
Rationale: A/8 = 8 * 8 => A = 8 * 8 * 8
x * 2x = 8 * 8 * 8
x = 16 => 2x = 32
Answer:B
Answer: B
Question: A 280 meter long train running at the speed of 120 kmph crosses another train running in the opposite direction at the speed of 80 kmph in 9 seconds.What is the lenght of other train.
Options:
A)210m
B)220m
C)230m
D)240m
E)250m
Rationale: Relative speeds=(120+80)km/hr
=200km/hr=(200*5/18)m/s=(500/9)m/s
let length of train be xm
x+280/9=500/9
x=220
Ans is 220m
ANSWER:B
Answer: B
Question: There are two numbers. If 20% of the first number is added to the second number, then the second number increases to its five-fourth. Find the ratio of the first number to the second number?
Options:
A)A)5/4
B)B)5/8
C)C)6
D)D)6/7
E)E)7
Rationale: Let the two numbers be x and y.
20/100 * x + y = 5/4y
=> 1/5 x = 1/4 y => x/y = 5/4
A)
Answer: A
Question: In a kilometer race, A beats B by 25 meters or 10 seconds. What time does A take to complete the race?
Options:
A)290 sec
B)390 sec
C)199 sec
D)192 sec
E)193 sec
Rationale: Time taken by B run 1000 meters
= (1000 * 10)/25 = 400 sec.
Time taken by A = 400 - 10 = 390 sec.
Answer: B
Answer: B
Question: Which of the following CANNOT be a value of 9/(x–9)?
Options:
A)-1
B)-1/2
C)0
D)2
E)9
Rationale: The question doesn't ask for the value of x here, but for the possible results of the equation.
If 9/(x-9) = 0, then the numerator must be 0. But since the numerator is 9, the fraction can not be equal to 0.
The answer is C.
Answer: C
Question: An empty fuel tank is filled with brand Z gasoline. When the tank is half empty, it is filled with brand Y gasoline. When the tank is half empty again, it is filled with brand Z gasoline. When the tank is half empty again, it is filled with brand Y gasoline. At this time, what percent H of the gasoline in the tank is brand Z?
Options:
A)50%
B)40%
C)37.5%
D)331⁄3%
E)25%
Rationale: Work with fraction of brand Z in the tank.
1st step: brand Z is 1
2nd step: brand Z is 1/2
3rd step: brand Z is (1/2)*(1/2) + 1/2 = 3/4
4th step: brand Z is (1/2)*(3/4) H= 3/8 = 37.5%
Answer (C)
Answer: C
Question: If f(f(n))+f(n)=2n+3 and f(0)=1, what is the value of f(2012)?
Options:
A)222
B)2787
C)2013
D)2778
E)10222
Rationale: Put n = 0
Then f(f(0))+f(0) = 2(0) + 3 ⇒⇒ f(1) + 1 = 3 ⇒⇒ f(1) = 2
Put n = 1
f(f(1)) + f(1) = 2(1) + 3 ⇒⇒ f(2) + 2 = 5 ⇒⇒f(2) = 3
Put n = 2
f(f(2)) + f(2) = 2(2) + 3 ⇒⇒ f(3) + 3 = 7 ⇒⇒ f(3) = 4
......
f(2012) = 2013
Answer:C
Answer: C
Question: P and Q started a business with respective investments of Rs. 4 lakhs and Rs. 10 lakhs. As P runs the business, his salary is Rs. 5000 per month. If they earned a profit of Rs. 2 lakhs at the end of the year, then find the ratio of their earnings?
Options:
A)1:9
B)1:8
C)1:4
D)1:1
E)1:2
Rationale: Ratio of investments of P and Q is 2 : 5
Total salary claimed by P = 12 * 5000 = Rs. 60000
Total profit = Rs. 2 lakhs.
Profit is to be shared = Rs. 140000
Share of P = (2/7) * 140000 = Rs. 400000
Share of Q = Rs. 100000
Total earnings of P = (60000 + 40000) = Rs. 100000
Ratio of their earnings =1:1
Answer:D
Answer: D
Question: A circle is circumscribed around a quadrilateral, and the quadrilateral is ABCD, What is the value of v when angle D is 140 degrees?
Options:
A)20
B)40
C)60
D)80
E)100
Rationale: An inscribed angle is an angle in a circle composed of two chords with a common endpoint, that is, an angle with its vertex on the circle. In this problem, all four lettered angles are inscribed angles.
An inscribed angle necessarily opens to intersect an arc (the technical word is to subtend an arc). The Inscribed Angle Theorem said that the measure of an inscribed angle is always half the measure of the arc it intersects, or subtends.
angle D = 140 degrees
Thus,
arc ABC = 280 degrees
A whole circle has 360 degrees of arc, so arc ADC should be the rest of the circle.
arc ADC = 360 - 280 = 80 degrees
The angle that intersects this arc, angle B, should have half this measure.
angle B = v = 80/2 = 40 degrees
Answer =(B)
Answer: B
Question: What is the next number: 2, 10, 82, __
Options:
A)630
B)730
C)830
D)848
E)900
Rationale: 3^0 + 1 = 2
3^2 + 1 = 10
3^4 + 1 = 82
3^6 + 1 = 730
The answer is B.
Answer: B
Question: After decreasing 24% in the price of an article costs Rs.912. Find the actual cost of an article?
Options:
A)1218
B)2777
C)1200
D)2688
E)1991
Rationale: CP* (76/100) = 912
CP= 12 * 100 => CP = 1200
Answer: C
Answer: C
Question: The average age 9 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number?
Options:
A)65 years
B)88 years
C)18 years
D)55 years
E)11 years
Rationale: 9 * 2 = 18 years
Answer: C
Answer: C
Question: If 0 < a< 1 < b, which of the following must be true?
Options:
A)1 < 1/a< 1/b
B)1/a< 1 < 1/b
C)1/a< 1/b< 1
D)1/b< 1 < 1/a
E)1/b< 1/a< 1
Rationale: 0<a<1<b. Let a=1/2 and b=2
Substituting values:
A. 1<2<1/2 ---Wrong
B. 2<1< 1/2 ---Wrong
C. 2<1/2<1 ---Wrong
D. 1/2<1<2 ---Correct
E. 1/2<2<1 ---Wrong
Hence answer is D
Answer: D
Question: 4000 was divided into two parts such a way that when first part was invested at 3% and the second at 5%, the whole annual interest from both the investments is Rs.144, how much was put at 3%?
Options:
A)2178
B)1087
C)2800
D)2689
E)2081
Rationale: (x*3*1)/100 + [(4000 - x)*5*1]/100 = 144
3x/100 + 200 – 5x/100 = 144
2x/100 = 56 è x = 2800
Answer: C
Answer: C
Question: A man gains 20% by selling an article for a certain price. If the sells it at double the price, the percentage of profit will be?
Options:
A)76%.
B)66%.
C)89%.
D)140%.
E)91%.
Rationale: Let C.P. = Rs. x.
Then, S.P. = Rs. (12% of x) = Rs. 6x/5
New S.P. = 2 * 6x/5 = Rs. 12x/5
Profit = 12x/5 - x = Rs. 7x/5
Profit = 7x/5 * 1/x * 100 = 140%.
Answer: D
Answer: D
Question: How many times in a day, the hands of a clock are straight?
Options:
A)42
B)41
C)44
D)45
E)46
Rationale: Explanation:
In 12 hours, the hands coincide or are in opposite direction 22 times.
In 24 hours, the hands coincide or are in opposite direction 44 times a day.
Answer is C
Answer: C
Question: Two consultants can type up a report in 12.5 hours and edit it in 7.5 hours. If Mary needs 30 hours to type the report and Jim needs 12 hours to edit it alone, how many E hours will it take if Jim types the report and Mary edits it immediately after he is done?
Options:
A)41.4
B)34.1
C)13.4
D)12.4
E)10.8
Rationale: Break down the problem into two pieces: typing and editing.
Mary needs 30 hours to type the report--> Mary's typing rate = 1/30 (rate reciprocal of time)(point 1 in theory below);
Mary and Jim can type up a report in 12.5and --> 1/30+1/x=1/12.5=2/25 (where x is the time needed for Jim to type the report alone)(point 23 in theory below)--> x=150/7;
Jim needs 12 hours to edit the report--> Jim's editing rate = 1/12;
Mary and Jim can edit a report in 7.5and --> 1/y+1/12=1/7.5=2/15 (where y is the time needed for Mary to edit the report alone) --> y=20;
How many E hours will it take if Jim types the report and Mary edits it immediately after he is done--> x+y=150/7+20=~41.4
Answer: A.
Answer: A
Question: A vessel of capacity 50 litres is fully filled with pure milk. Nine litres of milk is removed from the vessel and replaced with water. Nine litres of the solution thus formed is removed and replaced with water. Find the quantity of pure milk in the final milk solution?
Options:
A)23.89
B)72.9
C)33.62
D)78.3
E)79.3
Rationale: Explanation:
Let the initial quantity of milk in vessel be T litres.
Let us say y litres of the mixture is taken out and replaced by water for n times, alternatively.
Quantity of milk finally in the vessel is then given by [(T - y)/T]^n * T
For the given problem, T = 50, y = 9 and n = 2.
Hence, quantity of milk finally in the vessel
= [(50 - 9)/50]^2 (50) = 33.62 litres.
Answer: Option C
Answer: C
Question: If 9a - b = 10b + 70 = -12b - 2a, what is the value of 11a + 11b?
Options:
A)-4
B)-2
C)0
D)2
E)4
Rationale: (i) 9a - 11b = 70
(ii) 2a + 22b = -70
Adding (i) and (ii):
11a + 11b = 0
The answer is C.
Answer: C
Question: A man has Rs.10350 in the form of Rs.50 notes and Rs.500 notes. The total number of notes are 108.Find the number of notes of Rs.50 denomination.
Options:
A)15
B)21
C)17
D)19
E)97
Rationale: Total Money = Rs. 10350.
Let 50 rupees note was X.
Then 500 rupees note = 108 - X
Now,
50*X + 500 * (108 - X) = 10350
50X + 54000 - 500X = 10350
- 450X = - 43650
X = 97.
No. of 50 rupees note = 97.
Answer: Option E
Answer: E
Question: If x is an integer, then x(x – 1)(x – k) must be evenly divisible by three when k is any of the following values EXCEPT
Options:
A)-4
B)-2
C)-1
D)2
E)5
Rationale: There is probably an easier way, but I just used the picking numbers option for this.
I chose x=2
2(1)(2-k) then just plugged in the answer choices for K until one wasn't evenly divisible by 3.
B gives you 8. 8/3 is not an integer.
B is the answer
Answer: B