mathewhe/aqua_rat huggingface dataset:
Question: Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1120?
(A) Rs.1000
(B) Rs.1100
(C) Rs.1050
(D) Rs.1200
(E) Rs.1500
Rationale: Explanation:
1120 = P [1 + (5*12/5)/100]
P= 1000
ANSWER IS A
Answer: (A) Rs.1000
Question: The average weight of 18 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg. Find the average weights of all the boys in the class.
(A) 48.68077
(B) 42.25983
(C) 50
(D) 51.25388
(E) 52.25
Rationale: Explanation:
Average weight of 18 boys = 50.25
Total weight of 18 boys = 50.25 × 18
Average weight of remaining 8 boys = 45.15
Total weight of remaining 8 boys = 45.15 × 8
Total weight of all boys in the class = (50.25 × 18)+ (45.15 × 8)
Total boys = 18 + 8 = 26
Average weight of all the boys = (50.25×18)+(45.15×8)/26
=48.68077
Answer: Option A
Answer: (A) 48.68077
Question: The CP of 20 apples are the same as the SP of y apples. If the profit is 25%, then the value of y is?
(A) 8
(B) 12
(C) 16
(D) 18
(E) 20
Rationale: Let C.P. of each article be Re. 1 C.P. of x articles = Rs. x.
S.P. of x articles = Rs. 20.
Profit = Rs. (20 - x).
20 - x	x 100 = 25
x
2000 - 100x = 25x
125x = 2000
x = 16
C
Answer: (C) 16
Question: If x and y are positive integers and 42x=56y what is the least possible value of xy?
(A)  14
(B)  28
(C)  63
(D)  196
(E)  252
Rationale: 42x=56y
=> x/y = 4/3
=> 3x=4y
3(14)=4(14) => x*y=196
E
Answer: (E)  252
Question: The greatest possible length which can be used to measure exactly the length 8m, 4m 84cm, 11 m 90 cm is
(A) 11 cm
(B) 12 cm
(C) 5 cm
(D) 2 cm
(E) 43 cm
Rationale: Explanation:
Required Length = H.C.F of 800 cm, 484 cm and 1190 c
= 2 cm. Answer: D
Answer: (D) 2 cm
Question: What is the diagonal of a square field whose perimeter is 24m?
(A) 8 m
(B) 2 m
(C) 7 m
(D) 10 m
(E) 6√2 m
Rationale: Sol:
Let the side of the square be x meters.
Therefore,
4x=24
x=6
Diagonal of the square is= √2*(6)^2=6√2
Answer: E
Answer: (E) 6√2 m
Question: If 13 and 17 are prime numbers, which of the following CANNOT be the sum of a and b?
(A) 30
(B) 60
(C) 90
(D) 120
(E) 31
Rationale: ans: E
Answer: (E) 31
Question: A bag contains 6 green balls and 7 white balls. If two balls are drawn simultaneously, what is the probability that both balls are the same colour?
(A) 2/7
(B) 3/10
(C) 5/11
(D) 6/13
(E) 11/21
Rationale: The total number of ways to draw two balls is 13C2 = 78
The number of ways to draw two green balls is 6C2 = 15
The number of ways to draw two white balls is 7C2 = 21
P(two balls of the same colour) = 36/78 = 6/13
The answer is D.
Answer: (D) 6/13
Question: a man purchased earphone on friday.but he forgot how much it cost.the data he have are mean expenditure of all 7 days is 500.expenditure on mon,tue,wed,thurs,sat,sun are 450,600,400,500,550,300.on friday he purchased three things one earphone,one pen and one notebook.pen cost 30 and notebook cost 50.then what is cost of earphone?
(A) 620
(B) 530
(C) 450
(D) 470
(E) 500
Rationale: solution
let expenditure on Friday be x
(450+600+400+500+x+550+300)/7=500
2800+x=3500
x=700
pen+notebook+earphone=700
earphone=700-80=620
answer A
Answer: (A) 620
Question: A, B and C completed a piece of work, A worked for 6 days, B for 9 days and C for 4 days. Their daily wages were in the ratio of 3:4:5. Find the daily wages of C, if their total earning was Rs.1850?
(A) s.125
(B) s.108
(C) s.100
(D) s.103
(E) s.102
Rationale: 3x 4x 5x
6 9 4
18x + 36x + 20x = 1850
74x = 1850 => x = 25
5x = 125 Rs.
Answer:A
Answer: (A) s.125
Question: xy=1 then what is (5^(x+y)^2) / (5^(x-y)^2)
(A) 2
(B) 625
(C) 8
(D) 16
(E) 32
Rationale: (x+y)^2 - (x-y)^2
(x+y+x-y)(x+y-x+y)
(2x)(2y)
4xy
4
5^4 = 625
Answer B
Answer: (B) 625
Question: The diagonals of a rhombus are 12 cm and 20 cm. Find its area?
(A) 120
(B) 266
(C) 150
(D) 288
(E) 212
Rationale: 1/2 * 12 * 20 = 120
Answer: A
Answer: (A) 120
Question: k, l, m together started a business. k invested Rs.6000 for 5 months l invested Rs.3600 for 6 months and m Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of l ?
(A) Rs. 1640
(B) Rs. 2500
(C) Rs. 2160
(D) D) Rs. 3000
(E) NONE OF THESE
Rationale: Explanation:
=> 60x5 : 36x6 : 75x3
=> 100 : 72 : 75
=> 72/247 x 7410 = Rs. 2160
ANSWER IS C
Answer: (C) Rs. 2160
Question: Divide Rs. 1200 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?
(A) 300
(B) 368
(C) 375
(D) 337
(E) 639
Rationale: A+B+C = 1200
A = 1/3(B+C); B = 2/3(A+C)
A/(B+C) = 1/3
A = 1/4 * 1200 => 300
Answer:A
Answer: (A) 300
Question: The side of a cube is 12 m, find the lateral surface area?
(A) 816
(B) 516
(C) 716
(D) 216
(E) 916
Rationale: Lateral surface = 4 a(power)2
4 × 12(power)2 = 4 × 144 => 516 m(power)2
Answer is B.
Answer: (B) 516
Question: Subtracting 4% of A from A is equivalent to multiplying A by how much ?
(A) 0.96
(B) 9.4
(C) 0.094
(D) 94
(E) None
Rationale: Answer
Let A - 4% of A = AB.
⇒ (96 x A) / 100 = AB
∴ B = 0.96
Correct Option: A
Answer: (A) 0.96
Question: The ratio of pens to pencils is 5 to 6. There are 6 more pencils than pens. How many pencils are there?
(A) 32
(B) 36
(C) 40
(D) 44
(E) 48
Rationale: Let the number of pens be 5x and the number of pencils be 6x.
6x - 5x = 6
x = 6
The number of pencils is 36.
The answer is B.
Answer: (B) 36
Question: A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price?
(A) 18%
(B) 13%
(C) 12%
(D) 32%
(E) 15%
Rationale: Original price = 100
CP = 80
S = 80*(140/100) = 112
100 - 112 = 12%
Answer: C
Answer: (C) 12%
Question: The number of positive integer solutions for the equation x +y +z + t = 21 is
(A) 1140
(B) 1145
(C) 1240
(D) 1340
(E) 15640
Rationale: The number of positive integer solutions for the equatio fx1+x2+⋯+xn=k
(k-1)C(n-1)- where k is the number and n is number of variable in the equation.
21-1 C 4-1 = 20C3 = 1140
Answer : A
Answer: (A) 1140
Question: In ΔPQS above, if PQ =4 and PS = 5, then
(A)  9/4
(B)  12/5
(C)  16/5
(D)  15/4
(E) 10/3
Rationale: there are two ways to calculate area of PQS. area remains same, so both are equal.
4*5/2 = PR*6/2
PR = 10/3
E
Answer: (E) 10/3
Question: If 4 men working 10 hours a day earn Rs. 1400 per week, then 9 men working 6 hours a day will earn how much per week?
(A) Rs 840
(B) Rs 1320
(C) Rs 1620
(D) Rs 1890
(E) None of these
Rationale: Explanation :
(Men 4:9) : (Hrs/Day 10:6) :: 1400 : x
hence 4 * 10 *x = 9 * 6 * 1400
or x = 9*6*1400/ 4*10 = 1890
Answer : D
Answer: (D) Rs 1890
Question: A contractor hires 100 men to finish a job in 50 days. After 20 days, n men leave. After some more days, the contractor hires 2n more men to complete the job on time. For how many days did these 2n men work?
(A) 20
(B) 18
(C) 15
(D) 12
(E) 8
Rationale: Step1: Find Each day what % of work is finished ; it requires 50 days to complete which means each day 1/50= 2% work will be completed.
Step 2 : After 20 Days = 20* 2= 40% of work is finished. remaining is 60% ( which means if same 100 men were about to complete the job they would have required 30 more days)
Step3: Let us assume all people have left job. therefore contractor hires 2n people. initially it was taking 30 days to compete for n people. at present 2n people are present to finish job. hence 15 more days.
C
Answer: (C) 15
Question: A sum of Rs. 1550 was lent partly at 5% and partly at 8% p.a. simple interest. The total interest received after 3 years was Rs. 300. The ratio of the money lent at 5% to that lent at 8% is:
(A) 16 : 15
(B) 15 : 16
(C) 15 : 8
(D) 8 : 15
(E) 8 : 17
Rationale: Explanation :
Let the partial amount at 5% be x and the partial amount at 8% be (1550-x)
Interest on x at 5% for 3 years + interest on (1550-x) at 8% for 3 years = 300
x × 5 × 3 /100+(1550-x) × 8 × 3 /100=300
x × 5 /100+(1550-x) ×8 /100=100
5x+8(1550−x)=10000
5x+12400−8x=10000
3x=2400
x=800
Required Ratio = x : (1550-x) = 800 : (1550-800) = 800 : 750 = 16 : 15
Answer : Option A
Answer: (A) 16 : 15
Question: A dealer purchases 15 articles for Rs. 25 and sells 12 articles for Rs. 30. Find the profit percentage?
(A) 80%
(B) 50%
(C) 59%
(D) 40%
(E) 53%
Rationale: L.C.M of 15 and 12
= 60
CP of 60 articles
= Rs. 100 (25 * 4)
SP of 60 articles
= Rs. 150 (30 * 5)
Profit percentage
= (150 - 100)/100 * 100 = 50%
Answer: B
Answer: (B) 50%
Question: A train 280 m long passed a pole in 20 sec. How long will it take to pass a platform 720 m long?
(A) 12 sec
(B) 59 sec
(C) 71 sec
(D) 61 sec
(E) 66 sec
Rationale: Speed = 280/20
= 14 m/sec.
Required time = (280 + 720)/14
= 71.4 sec.
Answer: C
Answer: (C) 71 sec
Question: Baseball's World Series matches 2 teams against each other in a best-of-seven series. The first team to win four games wins the series and no subsequent games are played. If you have no special information about either of the teams, what is the probability W that the World Series will consist of fewer than 7 games?
(A)  12.5%
(B)  25%
(C)  31.25%
(D)  68.75%
(E)  75%
Rationale: Your explanation is very close toManhattan GMAT's official answer - it's quite uncanny:
"There are many other ways this could happen. Using the permutation formula, there are 6!/(3!)(3!) = 20 ways for the two teams to split the first 6 games (3 wins for each).
There are then 2 possible outcomes to break the tie in Game 7. Thus, there are a total of 202 = 40 ways for the World Series to last the full 7 games.
The probability that any one of these 40 ways occurs can be calculated from the fact that the probability of a team winning a game equals the probability of a team losing a game = 1/2.
Given that 7 distinct events must happen in any 7 game series, and that each of these events has a probability of 1/2, the probability that any one particular 7 game series occurs is.
Since there are 40 possible different 7 game series, the probability that the World Series will last exactly 7 games is: (1/2)^7 = 1/128
40*1/128 = 40/128 = 31.25%
Thus the probability W that the World Series will last less than 7 games is 100% - 31.25% = 68.75%.
The correct answer is D."
Answer: (D)  68.75%
Question: If the day before yesterday was Wednesday, when will Sunday be?
(A) Day after tomorrow
(B) Tomorow
(C) Two days after today
(D) Today
(E) none
Rationale: Explanation:
Day before yesterday was Wednesday
=>Yesterday was a Thursday
=> Today is a Friday
=> Tomorrow is a Saturday
=> The day after tomorrow will be a Sunday
Answer: Option A
Answer: (A) Day after tomorrow
Question: After taking N tests, each containing 100 questions, John had an average of 70% of correct answers. How much does John need to score on the next test to make his average equal 71%?
M13-03.
(A) N−35
(B) N+72
(C) 2N+70
(D) 2N+72
(E) 2N−35
Rationale: Say N=1.
So, after 1 test John has 70 correct answers.
In 2 tests, so in 200 questions he needs to have 0.71*200=142 correct answers, so in the second test he must get 142-70=72 questions correctly.
Now, plug N=1 into the answer choices to see which one yields 72. Only option D fits.
Answer: C.
Answer: (C) 2N+70
Question: A person can row at 9 kmph and still water. He takes 4 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?
(A) 76 km
(B) 16 km
(C) 26 km
(D) 36 km
(E) 20 km
Rationale: Let the distance between A and B be x km.
Total time = x/(9 + 1) + x/(9 - 1) = 4.5
=> x/10 + x/8 = 9/2 => (4x + 5x)/40 = 9/2 => x
= 20 km
Answer:E
Answer: (E) 20 km
Question: The average marks of a class of 30 students is 40 and that of another class of 50 students is 60. Find the average marks of all the students?
(A) 52.6
(B) 52.4
(C) 52.1
(D) 52.5
(E) 52.9
Rationale: Sum of the marks for the class of 30 students = 30 * 40 = 1200
Sum of the marks for the class of 50 students = 50 * 60 = 3000
Sum of the marks for the class of 80 students =
1200 + 3000 = 4200
Average marks of all the students = 4200/80 = 52.5.Answer: D
Answer: (D) 52.5
Question: The average of six numbers is 30. If the average of first four is 25 and that of last three is 35, the fourth number is :
(A) 25
(B) 26
(C) 18
(D) 19
(E) 10
Rationale: Let the six numbers be, a, b, c, d, e, f.
a + b + c + d + e + f = 30 × 6 = 180 - - - - (1)
a + b + c + d = 25 × 4 = 100 - - - - (2)
d + e + f = 35 × 3 = 105 - - - - (3)
Add 2nd and 3rd equations and subtract 1st equation from this.
d = 25
Answer: A
Answer: (A) 25
Question: A jar full of whiskey contains 40% alcohol. A part of this whisky is replaced by another containing 19% alcohols and now the percentage of alcohol was found to be 26%. The quantity of whisky replaced of whisky replaced is
(A) 1 / 3
(B) 2 / 3
(C) 2 / 5
(D) 3 / 5
(E) None
Rationale: Solution
ratio of 1st and 2nd quantities = 7 : 14 = 1 : 2.
Required quantity replaced = 2/3
Answer B
Answer: (B) 2 / 3
Question: How many different two-letter initials with none of the letters repeated can people have?
(A) 550
(B) 650
(C) 750
(D) 950
(E) 850
Rationale: for first latter it has 26 way
and for 2 latter it has 25 way
hence 25*26=650
ANSWER:B
Answer: (B) 650
Question: During a poker game, 8 people are to be seated around a circular table. two seating arrangement are considered different only when the position of the people are different relative to each other. what is the total number of possible seating arrangements for the group?
(A) a.1
(B) b.5,040
(C) c.24
(D) d.303
(E) e.120
Rationale: for 8 people seating arrangement around a circular table = (8-1)!
= 7!
= 7*6*5*4*3*2*1
=5,040
OA is B
Answer: (B) b.5,040
Question: ((-1.9)(0.6) – (2.6)(1.2))/8.0 = ?
(A) -0.53
(B) 1.0
(C) 1.07
(D) 1.71
(E) 2.71
Rationale: Dove straight into calculation
((-1.9)(0.6) – (2.6)(1.2))/7.0 = -0.53
Answer A
Answer: (A) -0.53
Question: An association of mathematics teachers has 1,500 members. Only 525 of these members cast votes in the election for president of the association. What percent of the total membership voted for the winning candidate if the winning candidate received 60 percent of the votes cast?
(A) 75%
(B) 58%
(C) 42%
(D) 34%
(E) 21%
Rationale: Total umber of members = 1500
Number of members that cast votes = 525
Since , winning candidate received 60 percent of the votes cast
Number of votes for winning candidate = (60/100)*525 = 315
Percent of total membership that voted for winning candidate = (315/1500)*100 = 21%
Answer E
Answer: (E) 21%
Question: The ratio of three numbers is 5:3:4 and their sum is 108. The second number of the three numbers is?
(A) 25
(B) 27
(C) 29
(D) 31
(E) 32
Rationale: 5:3:4
Total parts = 12
12 parts --> 108
1 part ---->9
The second number of the three numbers is = 3
3 parts ----> 27
B
Answer: (B) 27
Question: Solve the following system of equations:
x-y-z = 0
3x+4y+3z = 4
5x+2y+7z = 22
(A) x=1, y=2, z=3
(B) x=-1, y=-2, z=1
(C) x=-2, y=3, z=1
(D) x=1, y=-2, z=3
(E) x=3, y=-1, z=2
Rationale: Solve the first equation for x.
x-y-z = 0
x = y+z
Substitute the solution for x into the second and third equations.
3*(y+z)+4y+3z = 4
3y+3z+4y+3z = 4
7y+6z = 4
5*(y+z)+2y+7z = 22
5y+5z+2y+7z = 22
7y+12z = 22
Subtract the new second equation from the new third equation and solve for z.
7y+12z = 22
- (7y+6z = 4)
6z = 18
z=3
Substitute the solution for z back into 7y+6z = 4 and solve for y.
7y+6*3 = 4
7y+18 = 4
7y = -14
y=-2
Substitute the values for y and z back into x-y-z = 0.
x-(-2)-3 = 0
x-1 = 0
x=1
Answer A
Answer: (A) x=1, y=2, z=3
Question: Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.85. How much was lent at 5%?
(A) 197
(B) 119
(C) 279
(D) 500
(E) 502
Rationale: (x*5*1)/100 + [(1500 - x)*6*1]/100 = 85
5x/100 + 90 – 6x/100 = 85
x/100 = 5
=> x = 500
Answer:D
Answer: (D) 500
Question: Mary goes into labor at her local grocery store and is rushed to a hospital in an ambulance traveling 60mph. Her husband Don drives after the ambulance at an average speed of 30mph. Mary reaches the hospital fifteen minutes later. How long does it take Don to get there from the store?
(A) 25 minutes
(B) 30 minutes
(C) 10 minutes
(D) 15 minutes
(E) 7 minutes
Rationale: Distance covered by the ambulance in 15 minutes = 15 miles
60 mph is one mile per minute, therefore 30 mph will be 1/2 a mile per minute.
So, he reaches the hospital half an hour after leaving the store.
Correct Answer: B
Answer: (B) 30 minutes
Question: Set A consists of integers -9, 8, 3, 10, and J; Set B consists of integers -2, 5, 0, 7, -6, and W. If R is the median of Set A and W is the mode of set B, and R^W is a factor of 34, what is the value of W if J is negative?
(A) -2
(B) W=0
(C) 1
(D) 2
(E) 5
Rationale: since j is negative, therefore median of the set will be 3. which is an odd number. also, we know that odd^n will always be odd. now since 34 is even, therefore 3^w will have only one factor with 34 for w=0.
mode of the set is a number which occurs maximum number of time in the set. now, since W is the mode of the set. therefore W=0. hence answer is B
Answer: (B) W=0
Question: James took a 3-hour bike ride. In the second hour he traveled 36 miles, which was 20 percent farther than he traveled the first hour. If he traveled 25 percent farther in the third hour than he did in the second hour, how many miles did jose travel during the entire ride?
(A) 54.0
(B) 54.9
(C) 111.0
(D) 157.0
(E) 163.0
Rationale: Let the distance travelled in the first hour be x. Thus, 1.2x = 36 , x = 30. Now, the distance travelled in the 3rd hour = 36+1/4âˆ—36=45. 36+30+45 = 111
ANSWER:C
Answer: (C) 111.0
Question: If k and w are the dimensions of a rectangle that has area 60, and if k and w are integers such that k > w, what is the total number of possible values of k?
(A)  Two
(B)  Three
(C)  Four
(D)  Five
(E)  Six
Rationale: kw=60=60*1=30*2=15*4=20*3=12*5=10*6--> k can take 6 values
Answer: E
Answer: (E)  Six
Question: A number when divided successively by 4 and 5 leaves remainders 1 and 4 respectively. When it is successively divided by 5 and 4, then the remainders will be.
(A) 1,2
(B) 2,3
(C) 3,2
(D) 4,1
(E) 5,1
Rationale: 4 l X
--l---
5 l Y - 1 Therefore Y = (5 x 1 + 4) = 9
--l------ X = (4 x Y + 1) = (4 x 9 + 1) = 37
l 1 - 4
Now 37 divided successively by 5 and 4, we get
5 l 37
--l---
4 l 7 - 2 Therefore Y = (5 x 1 + 4) = 9
--l------ X = (4 x Y + 1) = (4 x 9 + 1) = 37
l 1 - 3
so the respective remainders are 2 and 3.
Answer B.
Answer: (B) 2,3
Question: What is the area of square field whose side of length 12 m?
(A) 225 sq m
(B) 144 sq m
(C) 586 sq m
(D) 287 sq m
(E) 296 sq m
Rationale: 12 * 12
= 144 sq m
Answer: B
Answer: (B) 144 sq m
Question: Positive integer y is 50 percent of 50 percent of positive integer x, and y percent of x equals 100. what is the value of x ?
(A) 50
(B) 100
(C) 200
(D) 1000
(E) 2000
Rationale: Given:
x >0 and y > 0
y = 5010050100(5010050100*x) = 0.25x - (i)
y100y100*x = 100. Hence xy = 10000 - (ii)
Required: Value of x
Substituting the value of y in (ii)
x*0.25x = 10000
x2x2 = 100*100*100/25 = 4*100*100
x = 200 and - 200
We will consider only the positive value as we are told that x > 0
x = 200
Option C
Answer: (C) 200
Question: John and Jacob set out together on bicycle traveling at 12 and 9 miles per hour, respectively. After 40 minutes, John stops to fix a flat tire. If it takes John one hour to fix the flat tire and Jacob continues to ride during this time, how many hours will it take John to catch up to Jacob assuming he resumes his ride at 12 miles per hour? (consider John's deceleration/acceleration before/after the flat to be negligible)
(A) 3
(B) 2 1/3
(C) 3 1/2
(D) 4
(E) 4 1/2
Rationale: John's speed - 12 miles/hr
Jacob's speed - 9 miles/hr
After 40min (i.e 2/3hr), distance covered by John = 12x2/3 = 8 miles.
Jacob continues to ride for a total of 1hour and 40min (until John's bike is repaired). Distance covered in 1 hour 40min (i.e 5/3hr) = 9x5/3 = 15 miles.
Now, when John starts riding back, the distance between them is 7 miles. Jacob and John are moving in the same direction.For John to catch Jacob, the effective relative speed will be 12-9 = 3 miles/hr.
Thus, to cover 7 miles at 3 miles/hr, John will take 7/3 = 2 1/3 hours
Answer B
Answer: (B) 2 1/3
Question: Divide 71 into 2 parts such that 1 part exceeds the other by 8. What are the 2 no.'s in that part?
(A) 23
(B) 25
(C) 31
(D) 34
(E) 36
Rationale: Let $let n$ be the smaller and 71 - n be the larger number. Now, since the larger number exceeds the smaller number by 7, we can form the equation
larger number – smaller number = 7
which is equivalent to
Simplifying, we have 71 - 2n = 7. This gives us 2n = 78 which implies that the larger number is . The smaller is 71-39=31.
C
Answer: (C) 31
Question: If 5.51*10^k = 0.0551, then the value of k is:
(A) –4
(B) –3
(C) –2
(D) –1
(E) 0
Rationale: 10^K/5.51 = 0.0551/551
=5.51/551
= 5.51* 10^2 /551* 10^2
= 1/10^2 = 10^-2
ANSWER:C
Answer: (C) –2
Question: If "x" is an integer, which of the following inequalities have a finite range of values of "x" satisfying them?
(A) x2 + 5x + 6 > 0
(B) |x + 2| > 4
(C) 9x - 7 < 3x + 14
(D) x2 - 4x + 3 < 0
(E) (B) and (D)
Rationale: Explanatory Answer
We have to find the values of "x" that will satisfy the four inequalities given in the answer choices and identify the choice for which the range of values satisfying it is finite.
Choice A: x2 + 5x + 6 > 0
Factorize the given equation: x2 + 5x + 6 > 0 = (x + 2)(x + 3) > 0.
This inequality will hold good when both (x + 2) and (x + 3) are simultaneously positive or simultaneously negative.
Evaluating both the options, we get the range of values of "x" that satisfy this inequality to be x < -2 or x > -3. i.e., "x" does not lie between -2 and -3.
i.e., x takes values lesser than 2 or greater than 3.
The range of values that x takes is infinite.
Choice B: |x + 2| > 4
|x + 2| > 4 is a modulus function and therefore, has two options
Option 1: x + 2 > 4 or
Option 2: (x + 2) < -4.
Evaluating the two options we get the values of "x" that satisfy the inequality as x > 2 and x < -6.
i.e., "x" does not lie between -6 and 2.
An infinite range of values.
Choice C: 9x - 7 < 3x + 14
Simplifying, we get 6x < 21 or x < 3.5.
An infinite range of values.
Choice D: x2 - 4x + 3 < 0
Factorizing x2 - 4x + 3 < 0 we get, (x - 3)(x - 1) < 0.
This inequality will hold good when one of the terms (x - 3) or (x - 1) is positive and the other is negative.
Evaluating both the options, we get 1 < x < 3. i.e., a finite range of values for "x".
Choice D
Answer: (D) x2 - 4x + 3 < 0
Question: Find the value of (√1.21)/(√0.64) + (√1.44)/(√0.49) is
(A) 195/63
(B) 145/63
(C) 155/63
(D) 3.089
(E) 185/63
Rationale: (√1.21)/(√0.64) + (√1.44)/(√0.49)
11/8 + 12/7=> 3.089
Answer is D
Answer: (D) 3.089
Question: A train 550 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
(A) 8
(B) 6
(C) 5
(D) 54
(E) 30
Rationale: Speed of train relative to man = 60 + 6 = 66 km/hr.
= 66 * 5/18 = 55/3 m/sec.
Time taken to pass the men = 550 * 3/55 = 30 sec.
Answer: E
Answer: (E) 30
Question: The combined age of husband and wife on their 20th wedding anniversary was twice than it was at the time of wedding. If the husband is 3 years older than his wife. How old was he at the time of his marriage?
(A) 29 years
(B) 38.5 years
(C) 21.5 years
(D) 32 years
(E) None of these
Rationale: Explanation:
Let the ages of husband and wife at the time of their 20th wedding anniversary be X years and Y years respectively and X > Y.
Their combined age = (X + Y) years.
The ages of both husband and wife at the time of wedding will be (X – 20) years and (Y – 20) years respectively.
Their combined age = (X – 20) + (Y – 20)
= (X + Y – 40) Years
By first information, we have
(X + Y) = 2( X + Y – 40)
X + Y = 2X + 2Y - 80
Therefore, X + Y = 80-------A
and by second information, we have
X – Y =3 ----------------------B
Solving A and B, we get X = 41.5 years
Therefore, the age of husband at the time of their 20th wedding anniversary X = 41.5 years
Age at the time of marriage = 41.5 years – 20 years = 21.5 years.
ANSWER IS C
Answer: (C) 21.5 years
Question: A man walking at a rate of 15km/hr crosses a bridge in 15 minutes. The length of the bridge is?
(A) 1250m
(B) 1110m
(C) 950m
(D) 750m
(E) 1300m
Rationale: Speed = 15*5/18 = 15/18 m/sec
Distance covered in 15 minutes = 15/18 *15 *60 = 750m
Answer is D
Answer: (D) 750m