RikoteMaster/aqua-rat-mcqa huggingface dataset:
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 K of the gasoline in the tank is brand Z?
A.50%
B.40%
C.37.5%
D.331⁄3%
Answer: C.37.5%
Explanation: 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) K= 3/8 = 37.5%
Answer (C)
Question: A seller bought tea powder packet at 6 for each, how many for a rupee must he sell to gain 20%?
A.5
B.6
C.7
D.9
Answer: A.5
Explanation: C.P. of 6 toffees = Re. 1
S.P. of 6 toffees = 120% of Re. 1 = Rs.	6
5
For Rs.	6	, toffees sold = 6.
5
For Re. 1, toffees sold = 6 x	5 = 5
6
A
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good?
A.125/167
B.125/118
C.125/126
D.125/128
Answer: C.125/126
Explanation: Required probability
= 1 - 1/126 = 125/126
Answer: C
Question: The average marks scored by Ganesh in English, Science, Mathematics and History is less than 16 from that scored by him in English, History, Geography and Mathematics. What is the difference of marks in Science and Geography scored by him?
A.40
B.50
C.64
D.Data inadequate
Answer: C.64
Explanation: E+H+G+M/4âˆ’E+S+M+H/4=16
â‡’ G - S = 64
Answer C
Question: A house wife saved $2.50 in buying an item on sale. If she spent $25 for the item, approximately how much percent she saved in the transaction?
A.8%
B.9%
C.10%
D.11%
Answer: B.9%
Explanation: Actual price = 25+2.50 = $27.50
Saving = 2.50/27.50 * 100 = 100/11 = 9% approximately
Answer is B
Question: Find the amount on Rs.4000 in 2 years, the rate of interest being 4% per first year and 5% for the second year?
A.4368
B.6369
C.5460
D.5635
Answer: A.4368
Explanation: 4000 * 104/100 * 105/100
=> 4368
Answer:A
Question: There are 1500 jelly beans divided between two jars, Jar X and Jar Y. If there are 200 fewer jelly beans in jar X than three times the number of beans in jar Y, how many beans are in jar X?
A.1050
B.1075
C.1100
D.1125
Answer: B.1075
Explanation: X+Y=1500 so Y=1500-X
X=3Y-200
X=3(1500-X)-200
4X=4300
X=1075
The answer is B.
Question: If the simple interest on a certain amount in at 4% rate 5 years amounted to Rs.2000 less than the principal. What was the principal?
A.1500
B.2500
C.2507
D.3200
Answer: B.2500
Explanation: P - 2000 = (P*5*4)/100
P = 2500
Answer: B
Question: If the average of 201, 202, 204, 205, 206, 209, 209, 210, 212 and x is 207, what is the value of x?
A.207
B.209
C.211
D.212
Answer: D.212
Explanation: Sum of the deviations of the numbers in the set from the mean is always zero
201, 202, 204, 205, 206, 209, 209, 210, 212
mean is 207
so the list is -6-5-3-2-1+2+2+3+5... this shud total to zero
but this is -5 , hence we need a number that is 5 more than the mean to get a +5 and make it zero
hence the answer is 207+ 5 = 212
D
Question: A train 360 m long runs with a speed of 45 km/hr. What time will it take to pass a platform of 130 m long?
A.39.2 sec
B.35 sec
C.44 sec
D.40 sec
Answer: A.39.2 sec
Explanation: Speed = 45 km/hr = 45 Ã— (5/18) m/s
= 150/12 = 50/4 = 25/2 m/s
Total distance = length of the train + length of the platform
= 360 + 130 = 490 meter
Time taken to cross the platform = 490/(25/2) = 490 Ã— 2/25 = 39.2 seconds
ANSWER:A
Question: The length and breadth of a room are 8 m and 6 m respectively. A cat runs along all the four walls and finally along a diagonal order to catch a rat. How much total distance is covered by the cat?
A.10
B.14
C.38
D.48
Answer: C.38
Explanation: diagonal=10
2(l+b)+d=38
ANSWER:C
Question: In a certain game, you perform three tasks. You flip a coin, and success would be heads. You roll a single die, and success would be a six. You pick a card from a full playing-card deck, and success would be picking a spades card. If exactly one of these three tasks is successful, then you win the game. What is the probability of winning?
A.23/48
B.11/16
C.15/32
D.14/36
Answer: A.23/48
Explanation: The answer is A
Probability of just one enent will be happining
So, Probability heads=1/2
Probability number 6 =1/6
Probability picking a spades card =1/4
so, Probability win by getting heads= 1/2*5/6*3/4 = 15/48
Probability win by getting number 6 = 1/2*1/6*3/4 = 3/48
Probability win by picking a spades card =1/2*5/6*1/4=5/48
Probability wining= 15/48+3/48+5/48 =23/48
Question: If y is an integer, which of the following must be an even integer?
A.y^2-y-1
B.y^2-4y+6
C.y^2-5y+5
D.y^2+3y+8
Answer: D.y^2+3y+8
Explanation: Check the options by plugging in some values ( Preferably smaller integers like 1 and 2 )
A: y^2-y-1 = -1 { If y = 1 }
B: y^2-4y+6 = 3 { If y = 1 }
C: y^2-5y+5 = 1 { If y = 1 }
D: y^2+3y+8 = 12 { If y = 1 }y^2+3y+8 = 18 { If y = 2 }
E: y^2+2y+10 = 13 { If y = 1 }
Thus the only possible answer is (D)
Question: At a meeting of 5 Chiefs of Staff, the Chief of Naval Operations does not want to sit next to the Chief of the National Guard Bureau. How many ways can the Chiefs of Staff be seated around a circular table?
A.9
B.12
C.15
D.18
Answer: B.12
Explanation: 5 people can be arranged around a table in 4! ways.
Consider the two chiefs who will not sit together as a single unit.
The number of ways to arrange 4 units around a table is 3!
We need to multiply this by 2 as the two people can be switched in each arrangement.
The total number of ways to arrange the chiefs is 4! - 2*3! = 2*3! = 12
The answer is B.
Question: If 11.25 m of a uniform iron rod weight 42.75 kg, what will be the weight of 6 m of the same rod ?
A.22.8 kg
B.25.6 kg
C.28 kg
D.26.5 kg
Answer: A.22.8 kg
Explanation: Solution
Let the required weight be x kg. Then, Less length, Less weight
∴ 11.25 : 6 :: 42.75 : x ⇔ 11.25 × x = 6 × 42.75 ⇔ x = ⇔ x = (6x42.75)/11.25=22.8. Answer A
Question: If a and b are positive integers of Y such that a/b=2.86, which of the following must be a divisor of a?
A.10
B.B.13
C.18
D.26
Answer: B.B.13
Explanation: The prompt gives us a couple of facts to work with:
1) A and B are positive INTEGERS
2) A/B = 2.86
We can use these facts to figure out POSSIBLE values of A and B. The prompt asks us for what MUST be a divisor of A. Since we're dealing with a fraction, A and B could be an infinite number of different integers, so we have to make both as SMALL as possible; in doing so, we'll be able to find the divisors that ALWAYS divide in (and eliminate the divisors that only SOMETIMES divide in).
The simplest place to start is with...
A = 286
B = 100
286/100 = 2.86
These values are NOT the smallest possible values though (since they're both even, we can divide both by 2)...
A = 143
B = 50
143/50 = 2.86
There is no other way to reduce this fraction, so A must be a multiple of 143 and B must be an equivalent multiple of 50. At this point though, the value of B is irrelevant to the question. We're asked for what MUST divide into A....
Since A is a multiple of 143, we have to 'factor-down' 143. This gives us (11)(13). So BOTH of those integers MUST be factors of A. You'll find the match in the answer choices.
Final Answer:
B
Question: Robert is travelling on his cycle andhas calculated to reach point A at 2 PM. if he travels at 10 kmph, he will reach there at 12Pm if he travels at 15 kmph. At what speed musthe travel to reach A at 1 PM?
A.10 kmph
B.11 kmph
C.12 kmph
D.13 kmph
Answer: C.12 kmph
Explanation: Let the distance travelled by x km.
Then, x - x = 2
10 15
3x - 2x = 60
x = 60 km.
Time taken to travel 60 km at 10 km/hr = 60 hrs = 6 hrs.
10
So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M.
Required speed = 60 kmph. = 12 kmph.
5
C
Question: select which is different..342,511,126,215.
A.342
B.511
C.126
D.215
Answer: C.126
Explanation: 7*7*7=343,343-1=342
8*8*8=512,512-1=511
5*5*5=125,125+1=126
6*6*6=216,216-1=215
answer C
Question: A man invests Rs. 7,000 at the rate of 5% per annum. How much more should he invest at the rate of 8%, so that he can earn a total of 6% per annum?
A.Rs. 1200
B.Rs. 1300
C.Rs. 3500
D.Rs. 2000
Answer: C.Rs. 3500
Explanation: Explanation :
Interest on Rs.7000 at 5% per annum = ( 7000 × 5 × 1) / 100 = Rs. 350
Let his additional investment at 8% = x
Interest on Rs.x at 8% per annum = ( x × 8 × 1 ) / 100 = 2x/25.
To earn 6% per annum for the total, interest = (7000 + x) × 6 × 1/100.
=> 350 + 2x/25 = (7000 + x) × 6 × 1/100.
=> 35000 + 8x = (7000 + x) × 6.
=> 35000 + 8x = 42000 + 6x.
=> 2x=7000.
=> x=3500.
Answer : C
Question: If xy > 0, which of the following must be negative?
A.-x/y
B.x/y
C.x+y
D.x^2
Answer: A.-x/y
Explanation: Given xy> 0 So both will be the positive integers. If both are positive, then B,C,D,E also positive.
Answer : A
Question: One tap, working alone at its maximum constant rate, can fill a certain sink in 287 seconds. A second tap, working alone at its maximum constant rate, can fill the same sink in 283 seconds. If both taps work together at their respective maximum constant rates, the time it will take to fill the sink is closest to
A.142 seconds
B.150 seconds
C.177 seconds
D.200 seconds
Answer: A.142 seconds
Explanation: Tap 1 : 283 secs
Tap 2 : 287 secs
Considering the average of these 2 taps : 285 secs.
So 1 tap can fill the tank in 285 secs, so 2 taps can fill the tank in 285/2 = 142.5 secs.
Closest answer is A.
Question: A BAG CONTAINS 6 RED AND 4 BLUE BALLS .2 BALLS ARE DRAWN AT RANDOM. FIND THE PROBABILITY THAT THEY ARE OF SAME COLOUR.
A.4/15
B.5/15
C.6/15
D.7/15
Answer: D.7/15
Explanation: LET S BE THE SAMPLE SPACE
THEN N(S)=NO OF WAYS OF DRAWING 2 BALLS OUT OF (6+4)=10C2=(10*9)/(2*1)=45
LET E=EVENT OF GETTING BOTH BALLS OF SAME COLOUR
THEN N(E)=NO OF WAYS(2 BALLS OUT OF SIX) OR(2 BALLS OUT OF 4)
=(6C2+4C2)=(6*5)/(2*1)+(4*3)/(2*1)=15+6=21
P(E)=N(E)/N(S)=21/45=7/15
Option: D
Question: A man walks at a speed of 6 km/hr and runs at a speed of 7 km/hr. How much time will the man require to cover a distance of 10 1/2 km, if he completes half of the distance, i.e., (5 1/4) km on foot and the other half by running?
A.1 4/2 hours
B.1 5/8 hours
C.2 1/6 hours
D.2 1/1 hours
Answer: B.1 5/8 hours
Explanation: Required time
= (5 1/4)/6 + (5 1/4)/7
= 1 5/8 hours.
Answer:B
Question: A sucrose solution contains 10 grams of sucrose per 100 cubic centimeters of solution. If 60 cubic centimeters of the solution were poured into an empty container, how many grams of sucrose would be in the container?
A. 4.00
B. 6.00
C. 5.50
D. 6.50
Answer: B. 6.00
Explanation: We are given that a sucrose solution contains 10 grams of sucrose per 100 cubic centimeters of solution. Since we are dealing with a solution, we know that the grams of sucrose is proportional to the number of cubic centimeters of solution. Thus, to determine how many grams of sucrose would be in the container when we have 60 cubic centimeters of solution, we can set up a proportion.
We can say: “10 grams of sucrose is to 100 cubic centimeters of solution as x grams of sucrose is to 60 cubic centimeters of solution.” Let’s now set up the proportion and solve for x.
10/100 = x/60
When we cross multiply we obtain:
(10)(60) = 100x
600 = 100x
6.00 = x
There are 6.00 grams of sucrose in the solution in the container.
The answer is B.
Question: The workforce of Company X is 60% female. The company hired 20 additional male workers, and as a result, the percent of female workers dropped to 55%.How many employees did the company have after hiring the additional male workers?
A.160
B.220
C.240
D.360
Answer: C.240
Explanation: Let's xx be total quantity of employees
0.6x=females before adding men
0.55(x+20)=females after adding men
as quantity of women doesn't change we can make an equation:
0.6x=0.55(x+20)
0.05x=11
x=220 - this is quantity of employees before adding 2020 men
So after adding it will be 240
Answer is C
Question: The product of the squares of two positive integers is 9. How many pairs of positive integers satisfy this condition?
A.0
B.1
C.2
D.3
Answer: B.1
Explanation: Ans:B - 1 pairs
(xˆ2)(yˆ2) = 9 [square root both sides]
xy = 3
3 = 1x3, 3x1
Cancel the repeats
This leaves us with exactly 1 options.
Hence, B
Question: 4, 7, 13, 25, 49, (...)
A.22
B.35
C.97
D.32
Answer: C.97
Explanation: Explanation :
4
4 × 2 - 1= 7
7 × 2 - 1 =13
13 × 2 - 1 = 25
25 × 2 - 1 = 49
49 × 2 - 1 = 97
Answer : Option C
Question: What is the greatest possible length which can be used to measure exactly the lengths 8 m, 4 m 20 cm and 12 m 20 cm?
A.20 cm
B.23 cm
C.25cm
D.10 cm
Answer: A.20 cm
Explanation: Required length = HCF of 800 cm, 420 cm, 1220 cm = 20 cm
Answer is A
Question: For a finite sequence of non zero numbers, the number of variations in sign is defined as the number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative. What is the number of variations in sign for the sequence 3, -3, 2, 5, -4, -6 ?
A.1
B.2
C.3
D.4
Answer: A.1
Explanation: Given sequence: {1, -3, 2, 5, -4, -6}
The questions basically asks: how manypairs of consecutive termsare there in the sequence such that the product of these consecutive terms is negative.
1*(-3)=-3=negative;
-3*2=-6=negative;
2*5=10=positive;
5*(-4)=-20=negative;
(-4)*(-6)=24=positive.
So there are 3 pairs of consecutive terms of the sequence for which the product is negative.
Answer: A.
Question: The price of a jacket is reduced by 25%. During a special sale the price of the jacket is reduced another 20%. By approximately what percent must the price of the jacket now be increased in order to restore it to its original amount?
A.66.67
B.35
C.48
D.65
Answer: A.66.67
Explanation: 1) Let the price of jacket initially be $100.
2) Then it is decreased by 25% , therefore bringing down the price to $75.
3) Again it is further discounted by 20%, therefore bringing down the price to $60.
4) Now 60 has to be added byX %in order to equal the original price.
60 + ( X% ) 60 = 100.
Solving this eq for X, we get X = 66.67
Ans is A.
Question: walking at ¾ of his usual speed ,a man is late by 2 ½ hr. the usual time is
A.7 1/9
B.7 1/2
C.7 1/5
D.7 1/8
Answer: B.7 1/2
Explanation: Usual speed = S Usual time = T Distance = D New Speed is ¾ S New time is 4/3 T 4/3 T – T
= 5/2 T=15/2
= 7 1/2
Aswer: B
Question: United Telephone charges a base rate of $6.00 for service, plus an additional charge of $0.25 per minute. Atlantic Call charges a base rate of $12.00 for service, plus an additional charge of $0.20 per minute. For what number of minutes would the bills for each telephone company be the same?
A.20 minutes
B.110 minutes
C.120 minutes
D.140 minutes
Answer: C.120 minutes
Explanation: Lets take number of minutesx.
Given that, 6+0.25x=12+0.2x ->0.05x=2 -> x=120minutes
ANS C
Question: Eight people are on an elevator that stops at exactly 8 floors. What is the probability that exactly one person will push the button for each floor?
A.8!/8^8
B.8^8/8!
C.8/8!
D.8/8^8
Answer: A.8!/8^8
Explanation: Each person out of 8 has 8 options, hence total # of outcomes is 8^8;
Favorable outcomes will be 8!, which is # of ways to assign 8 different buttons to 8 people
So basically # of arrangements of 8 distinct objects: 8!.
P=favorable/total=8!/8^8
Answer: A.
Question: How long does a train 150 m long traveling at 36 kmph takes to cross a signal post?
A.8 sec
B.15 sec
C.20 sec
D.10 sec
Answer: B.15 sec
Explanation: D = 150 m
S = 36 * 5/18 = 10
T = 150 * 1/10 = 15 sec
ANSWER:B
Question: A boat running downstream covers a distance of 20 km in 2 hours while for covering the same distance upstream,it takes 5 hours.What is the speed of the boat in still water ?
A.4 km/hr
B.6 km/hr
C.7 km/hr
D.Data inadequate
Answer: C.7 km/hr
Explanation: Solution
Rate downstream =(20/2) kmph = 10 kmph, Rate upstream =(20/5) = 4 kmph.
∴ Speed in still water =1/2(10+4) kmph = 7 kmph. Answer C
Question: The editor of an anthology of short stories will select authors from a pool of 11 authors, of which 4 are female. If the anthology is to include the work of 7 authors of which at least 2 are female, in how many ways can the editor select the authors?
A.301
B.312
C.323
D.334
Answer: A.301
Explanation: 11C7 = 330
The number of ways to select 7 males is 7C7 = 1
The number of ways to select 6 males and 1 female is 7C6*4C1 = 28
330 - 1 - 28 = 301
The answer is A.
Question: Tough and Tricky questions: Arithmetic.
(14^2 + 14^2)/7^2 =
A.4
B.58
C.29
D.8
Answer: D.8
Explanation: Ans is 8
my approach was:
(14^2 + 14^2)/29^2 =14(14+14)/7*7
=14*28/7*7=2*4=8
D
Question: Find out Difference between SI and CI if p=1000000 r=4% ant t=3 yr?
A.4864
B.4854
C.4844
D.4868
Answer: A.4864
Explanation: p=1000000, r=4% annual , t=3 yr
SI = p*r*t/100 = 1000000*4*3/100 = 120000
CI = p[(1+ r/100)^t -1] = 1000000[(1+ 4/100)^3 -1] = 124864
difference = CI - SI = 124864 - 120000 = 4864
ANSWER:A
Question: The length of rectangle is thrice its breadth and its perimeter is 96 m, find the area of the rectangle?
A.432
B.787
C.288
D.212
Answer: A.432
Explanation: 2(3x + x) = 96
l = 36 b = 12
lb = 36 * 12 = 432
Answer: A
Question: A train is 360 meter long is running at a speed of 54 km/hour. In what time will it pass a bridge of 140 meter length?
A.27 seconds
B.33 seconds
C.40 seconds
D.11 seconds
Answer: B.33 seconds
Explanation: Speed = 54 Km/hr = 54*(5/18) m/sec = 15 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (1/15) = 33 seconds
Answer:B
Question: Find the value of (70+ 28/100) × 100
A.7028
B.4028
C.3128
D.3256
Answer: A.7028
Explanation: (7000 +28)/100 * 100 = 7028
Answer : A
Question: A circular well with a diameter of 2 meters, is dug to a depth of 14 meters. What is the volume of the earth dug out.
A.48m3
B.94m3
C.44m3
D.04m3
Answer: C.44m3
Explanation: Volume=πr2hVolume=(227∗1∗1∗14)m3=44m3
Answer:C
Question: What is the smallest five digit number that is divisible by 15, 32, 45, and 54?
A.11260
B.11860
C.12360
D.12960
Answer: D.12960
Explanation: 15 = 3 * 5
32 = 2^5
45 = 3^2 * 5
54 = 2 * 3^3
LCM = 2^5 * 3^3 * 5 = 4320
The smallest five-digit number that is a multiple of 4320 is 3*4320 = 12,960
The answer is D.
Question: Horse started to chase a dog as it relived stable two hours ago. And horse started to ran with average speed of 22kmph, horse crossed 10 meters road and two ponds with depth 3 meters and it crossed 2 small streets with 200 meters length. After travelling 6 hours, 2 hours after the sunset it got dog. Compute the speed of dog?
A.16.5 kmph
B.16.6 kmph
C.16.4 kmph
D.16.9 kmph
Answer: A.16.5 kmph
Explanation: In an average speed of 22 kmph horse got dog in 6 hours
So distance=speed*time
distance=22*6=132km
Dog takes 8 hours to travel 132 km. So the speed if dog is
speed=distance/time
speed=132/8=16.5 kmph
Answer: 16.5 kmph
Answer A
Question: A & B can make paintings in 6 days, B & C can can make those paintings in 10 days. If A, B & C together can finish the work in 4 days, then A & C together will do it in ________ days.
A.4 (2/7) days
B.1/ 8 days
C.2 (2/5) days
D.6 (3/ 8) days
Answer: A.4 (2/7) days
Explanation: EXPLANATION:
Hint:
We are given that, A,B, & C together complete the work in 4 days.
We can write, (A+B+C) 's 1 day work =	1/4
Similarly, (A+B) 's 1 day work = 1/6 days & (B+C)'s 1 day work =	1/10
Since the work is divided in combination and we are asked to find out the combined work of (A + C), so we can find out,
(A + C)'s 1 day work = [2 (A+B+C)'s 1 day work] – [(A+ B) 's 1 day work + (B+C)'s 1 day work]
=[2*1/4]-[(1/6)+(1/10)]
=	1/2	–	16/60	=	1/2	–	4/15	=	7/30
Hence, A & C together can complete the work in 30 /7 days = 4(2/7)days.
ANSWER IS A
Question: a = 4^15 - 625^3 and a/x is an integer, where x is a positive integer greater than 1, such that it does NOT have a factor p such that 1 < p < x, then how many different values for x are possible?
A.None
B.One
C.Two
D.Three
Answer: C.Two
Explanation: This is a tricky worded question and I think the answer is should be D not C...
Here is my reason :
The stem says that x is a positive integer such that has no factor grater than 2 and less than x itself . The stem wants to say that X is a PRIME NUMBER . because any prime
Number has no factor grater than 1 and Itself .
On the other hand the stem says that X COULD get how many different number NOT MUST get different number ( this is very important issue )
AS our friends say, if we simplify Numerator more we can obtain : 5^12 ( 5^3-1) = 5^12 (124) = 5^12 (31*2*2) divided by x and we are told that this fraction is
An integer . so, X COULD Be ( not Must be) 5 , 31 ,or 2 !!! so , X could get 2 different values and answer is C....
Question: the average distance between the sun and a certain planet is approximatly 2.6 10^9 inches. which of the following is the closest to the average distence between sun and the planet in kelometers? (1 km is approx 3.9 x 10^4 inches)
A.7 x (10)^5
B.7 x (10)^7
C.6.7 x (10)^4
D.7 x (10)^8
Answer: C.6.7 x (10)^4
Explanation: No need to solve entire problem.
Distance in KM = 26*(10)^9/39*(10)^4 which is -260*(10)^8/39*(10)^4 = 6.7 x(10)^4
Answer : C
Question: If W is the set of all the integers between 59 and 99, inclusive, that are either multiples of 3 or multiples of 2 or multiples of both, then W contains how many numbers?
A.27
B.32
C.33
D.34
Answer: A.27
Explanation: Multiples of 2 from 59 to 99=Multiples of 2 from 1 to 99-Multiples of 2 from 1 to 58=[99/2]-[58/2]=49-29=20
Multiples of 3 from 59 to 99=Multiples of 3 from 1 to 99-Multiples of 3 from 1 to 58=[99/3]-[58/3]=33-169=14
Multiples of2 and 3 bothi.e.6 from 59 to 99=Multiples of 6 from 1 to 99-Multiples of 6 from 1 to 58=[99/6]-[58/6]=16-9=7
These 8 Numbers have been counted twice in both the above calculation while calculating multiples of 2 and 3
i.e. Total Numbers in W = 20 + 14 - 7 = 27
Answer Option A
Question: Which of the following equations has a solution in common with x^2 + 5x + 4 = 0?
A.2x^2 + 5x +4 = 0
B.x^2 - 3x - 4 = 0
C.2x^2 - 14 1/2x + 7/2 = 0
D.x^2 + 4x - 21 = 0
Answer: B.x^2 - 3x - 4 = 0
Explanation: Given : x^2 + 5x + 4 = 0 => (x+1) (x+4) = 0 => -1 and -4 are the roots..
A. 2x^2 + 4x + 3/2 = 0 => (x+1/2) (2x+3)
B. x^2 - 3x - 4 = 0 => (x-7) (2x-1/2)
C. 2x^2 - 14 1/2x + 7/2 = 0 => (x-7) (x-3)
D. x^2 + 4x - 21 = 0 => (x+7) (x-3)
None of the answer equations have exactly both the same roots as the question equation, but at least one of them does share one of the two roots.
So IMO "B" is correct answer... because it shares the one root (part of the solution), -1, from the (x+1) portion of its simplification.
Question: A is faster than B. A and B each walk 24 km. The sum of their speeds is 7 km/hr and the sum of times taken by them is 14 hours. Then, A's speed is equal to?
A.5
B.3
C.4
D.7
Answer: B.3
Explanation: Let A's speed = x km/hr. Then, B's speed = (7 - x) km/ hr.
So, 24/x + 24/(7 - x) = 14
x2 - 98x + 168 = 0
(x - 3)(x - 4) = 0 => x = 3 or 4.
Since, A is faster than B, so A's speed = 4 km/hr and B's speed = 3 km/hr.
Answer: B
Question: A train running at the speed of 52 km/hr crosses a pole in 9 sec. What is the length of the train?
A.130 m
B.786 m
C.566 m
D.546 m
Answer: A.130 m
Explanation: Speed = 52 * 5/18 = 130/9 m/sec
Length of the train = speed * time = 130/9 * 9
= 130 m
Answer: A
Question: Approximately how many revolutions will be made by a car tire with a 14-inch diameter if the car travels 1 mile?
A.120
B.180
C.1,231
D.1,433
Answer: D.1,433
Explanation: Diameter of car tire = 14 inches
Radius of car tire = 7 inches = 7*2.54 cm = 17.78 cm
Circumference of the car tire = 2*pi * 17.78 = 2 *3.14 *17.78= 111.66 cm
Distance traveled by car = 1 mile = 1 *1.6 km = 1.6 km = 1600 m = 1.6 * 10^5 cm
Number of revolutions =Distance traveled / Circumference of tire = 1.6*10^5 / 111.66 = 1432.92
Since the answer choices are far apart we should use estimation in this question .
Ideally ,in the GMAT the conversion between units would be provided .
Answer D
Question: A brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 25 m * 2 m * 0.75 m?
A.29798
B.27908
C.78902
D.25000
Answer: D.25000
Explanation: 25 * 2 * 0.75 = 20/100 * 10/100 * 7.5/100 * x
25 = 1/100 * x => x
= 25000
Answer: D