divelab/Sys2Bench huggingface dataset:
Question: 3 machines a,b,c can be used to produce a product. Machine a will take 60 hours to produce a million units. Machine b is twice as fast as machine a. Machine c takes the same amount of time as machine a and b taken together. How much time will be required to produce a million units if all the three machines are used simultaneously?
Options:
A)12 hours
B)10 hours
C)8 hours
D)9 hours
E)None of these
Rationale: 1 hour capacity of
Machine a =1/60 million
Machine b =2*(1/60)=1/30 million
Machine c =(1/60)+(1/30)=1/20 million
So in 1 hour Machines a,b & c will produce (1/60)+(1/30)+(1/20)=1/10 million
Time taken to produce 1 million units=1/(1/10)=10 hours
ANSWER:B
Answer: B
Question: Five persons are to be selected from a group of 7 males and 6 females to form party so that at least 3 male members are there on the committee. What are the possible number of ways to form the party ?
Options:
A)756
B)765
C)785
D)789
E)None
Rationale: From a group of 7 men and 6 women, five persons are to be selected with at least 3 men. So we can have (5 men) or (4 men and 1 woman) or (3 men and 2 woman) (7C5)+(7C4 * 6C1)+(7C3** 6C2)=[21+35*6+35*15]=756
Answer A
Answer: A
Question: If 0.75 : x :: 10 : 8, then x is equal to:
Options:
A)A)0.6
B)B)0.8
C)C)0.85
D)D)0.5
E)E)none
Rationale: (x * 10) = (0.75 * 8)
x = 6/10
x = 0.6
Answer = A
Answer: A
Question: In country Z, 18% of the people do not have a university diploma but have the job of their choice, and 25% of the people who do not have the job of their choice have a university diploma. If 40% of the people have the job of their choice, what percent of the people have a university diploma?
Options:
A)37%
B)45%
C)55%
D)65%
E)75%
Rationale: Setting up a matrix is how I solve this one.
Diploma No Diploma Totals
Job of Choice w/Diploma
Job of Choice w/o Diploma = 18%
Job of Choice Total = 40%
Not Job of Choice with Diploma =.25X
Not Job of Choice w/o Diploma= .75X
Total Not Job of Choice = X
Total with Diploma
Total without Diploma
Total citizen = 100
If 40% of people have their job of choice, then 60% of people do NOT have their job of choice. 25% of 60% = 15%. We can also see that 30% of the people have their job of choice and a diploma (40%-18%=22%). 22% + 15% =37%. Therefore 37% of the people in Country Z have a diploma.
Ans A
Answer: A
Question: On a certain day, Tim invested $1,000 at 10 percent annual interest, compounded annually, and Lana invested 2,000 at 5 percent annual interest, compounded annually.The total amount of interest earned by Tim’s investment in the first 2 years was how much greater than the total amount of interest earned by Lana’s investment in the first 2 years?
Options:
A)$5
B)$15
C)$50
D)$100
E)$105
Rationale: Compounded annually means that the interest is applied once per year. One can have 10% annual interest compounded monthly - in this case 10%/12 would be applied each month, or 10% annual interest compounded daily etc.
With respect to the problem at hand, at the end of two years, Tim would have
1,000(1.10)^2 = 1,000(1.21) = 1,210
and Lana would have
2,000(1.05)^2 = 2,000(1.1025) = 2,205
Thus, Tim earned 210 dollars, while Lana earned 205 dollars
The difference is $5 and the answer is A.
Answer: A
Question: Peter invests $100,000 in an account that pays 12% annual interest: the interest is paid once, at the end of the year. Martha invests $100,000 in an account that pays 12% annual interest, compounding monthly at the end of each month. At the end of one full year, compared to Peter's account, approximately how much more does Martha’s account have?
Options:
A)Zero
B)$68.25
C)$682.50
D)$6825.00
E)$68250.00
Rationale: At the end of 1 year Peter gets an interest of - Rs 12000
At the end of 1 year Martha gets an interest of = 100000(1+0.12/12)^12=100000(1.01^12)= 112682.50 -100000 = 12682.50 $
Therefore Martha has 12682.50-12000 = 682.50 $ more than Peter at the end of 1 year.
Option (C)
Answer: C
Question: A crow leaves its nest, and flies back and forth from its nest to a nearby ditch to gather worms. The distance between the nest and the ditch is 300 meters. In one and a half hours, the crow manages to bring worms to its nest 15 times. What is the speed of the crow in kilometers per hour?
Options:
A)1
B)2
C)4
D)6
E)8
Rationale: The distance between the nest and the ditch is 300 meters.
15 times mean = A crow leaves its nest, and flies back ( going and coming back) i.e. 2 times we get total 30 rounds.
So the distance is 30 * 300 = 9000.
D = ST
9000/1.5 = T , I think we can take 9000 meters as 9 km, then only we get T = 6.( 1000 meters = 1 km)
D)
Answer: D
Question: How many pieces of 75 cm can be cut from a rope 60 meters long?
Options:
A)80
B)40
C)60
D)None
E)Cannot be determined
Rationale: Explanation :
Total pieces of 75 cm that can be cut from a rope of 60 meters long is
= (60 meters)/(75 cm)
= (60 meters)/(0.75 meters)
= 80
Answer : A
Answer: A
Question: How many cubes of edge 2 dm can be cut out of a meter cube?
Options:
A)296
B)289
C)270
D)125
E)278
Rationale: 1 * 1* 1 = 2/10 * 2/10 * 2/10 * x
x = 125
Answer:D
Answer: D
Question: Father is aged three times more than his son Sunil. After 8 years, he would be two and a half times of Sunil's age. After further 8 years, how many times would he be of Sunil's age?
Options:
A)4 times
B)2 times
C)3 times
D)5 times
E)1 times
Rationale: Assume that Sunil's present age =x.
Then, father's present age =3x+x=4x
After 8 years, father's age =212 times of Sunils' age
⇒(4x+8)=212(x+8)⇒4x+8=52(x+8)⇒8x+16=5x+40⇒3x=40−16=24⇒x=243=8
After further 8 years,
Sunil's age =x+8+8=8+8+8=24
Father's age =4x+8+8=4×8+8+8=48
Father's age/Sunil's age =4824=2.
Answer is B.
Answer: B
Question: The C.P of 15 pens is equal to the S.P of 18 pens. Find his gain% or loss%?
Options:
A)12 2/4%
B)17 2/6%
C)16 2/3%
D)16 2/7%
E)34 2/5%
Rationale: C
15 CP = 18 SP
18 --- 3 CP loss
100 --- ? => 16 2/3% loss
Answer: C
Question: If a quarter kg of onions costs 90 paise, how many paise will 100 gm cost?
Options:
A)36 paise
B)65 paise
C)56 paise
D)87 paise
E)15 paise
Rationale: Explanation:
Let the required cost be x paise.
Less weight, Less cost (Direct proportion)
250 : 100 : : 90 : x
250 * x = (100 * 90)
x = (100 * 90) / 250
x = 36
ANSWER: A
Answer: A
Question: In what time will a train 100 meters long cross an electric pole, if its speed is 36 km/hr
Options:
A)8.5 seconds
B)10 seconds
C)3.5 seconds
D)2.5 seconds
E)2.6 seconds
Rationale: First convert speed into m/sec
Speed = 36*(5/18) = 10 m/sec
Time = Distance/speed
= 100/10 = 10 seconds
Answer: B
Answer: B
Question: Which of the following is the lowest positive integer that is divisible by the first 8 positive integer multiples of 5?
Options:
A)2100
B)4200
C)6300
D)8400
E)10,500
Rationale: The number must be divisible by 5, 2*5, 3*5, 2^2*5, 5^2, 2*3*5, 7*5, and 2^3*5.
The lowest such number is 2^3*3*5^2*7 = 4200.
The answer is B.
Answer: B
Question: All the stocks on the over-the-counter market are designated by either a 7 letter or 6 letter codes that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be designated with these codes?
Options:
A)2(26^5)
B)26(26^4)
C)27(26^6)
D)26(26^5)
E)27(26^5)
Rationale: with 7 letters: 26^7
with 6 letters: 26^6
26^7 + 26^6 = 27*(26^6)
C
Answer: C
Question: A tank is filled in eight hours by three pipes A, B and C. Pipe A is twice as fast as pipe B, and B is twice as fast as C. How much time will pipe B alone take to fill the tank?
Options:
A)22 hours
B)28 hours
C)77 hours
D)75 hours
E)66 hours
Rationale: 1/A + 1/B + 1/C = 1/8 (Given)
Also given that A = 2B and B = 2C
=> 1/2B + 1/B + 2/B = 1/8
=> (1 + 2 + 4)/2B = 1/8
=> 2B/7 = 8
=> B = 28 hours.
Answer:B
Answer: B
Question: A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 1500. The difference between the profit shares of A and C is?
Options:
A)200
B)929
C)400
D)600
E)832
Rationale: Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6
And also given that, profit share of B is Rs. 1500
=> 5 parts out of 15 parts is Rs. 1500
Now, required difference is 6 - 4 = 2 parts
Required difference = 2/5 (1500) = Rs. 600
Answer:D
Answer: D
Question: The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is?
Options:
A)6.99%
B)6.89%
C)6.08%
D)6.09%
E)6.19%
Rationale: Amount of Rs. 100 for 1 year when compounded half-yearly
= [100 * (1 + 3/100)2]
= Rs. 106.09 Effective rate
= (106.09 - 100) = 6.09%
Answer:D
Answer: D
Question: Firm A's revenues are described by the equation Ra = 17.12x and its costs by Ca = 12.87x + 2400.
Firm B's revenues are described by the equation Rb = 13.27x and its costs by Cb = 8.77x + 1500.
(x denotes the quantity of sales).
If A's volume of sales increases from 1000 to 3000 over the same period that B's volume increases from 2000 to 3000, the percent increase in profits for the firm with the biggest dollar increase in profits is
Options:
A)20%
B)30%
C)60%
D)50%
E)33%
Rationale: Ok, I do not know whether it is exactly what you want to hear but I did it that way: first look at difference between revenue and variable cost => take the bigger one (b) which gives you: 4.5x-1500 just plug in 2000 and 3000. you get 7500 and 12000 (difference 4500). 4500> 0.5*7500 so 30%
B
Answer: B
Question: How many multiples of 4 are less than 6540, and also multiples of 7?
Options:
A)234
B)208
C)340
D)237
E)267
Rationale: LCM of 4 & 7 = 28
Tried dividing 6540 by 28
Got quotient 233.5'So A is answer
Answer: A
Question: In a 150 member association consisting of men and women, exactly 10% of men and exactly 20 % women are homeowners. What is the least number of members who are homeowners?
Options:
A)22
B)21
C)20
D)19
E)18
Rationale: Solution simple
Out of 150 10% are male i.e 15 and 20% are female i.e 30 , so total homeowner is 45.
Now min number homeowner is 15 and max is 30 so question ask us to find least and 18 has least value among all option.
So ans is 18.
Ans: E
Answer: E
Question: A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used?
Options:
A)6
B)5
C)4
D)7
E)9
Rationale: 7 * 8 : 9 * x = 8:9 => x= 7
Answer: D
Answer: D
Question: A cricketer has a certain average for 10 innings. In the eleventh inning, he scored 108 runs, there by increasing his average by 5 runs. His new average is:
Options:
A)50 runs
B)58 runs
C)56 runs
D)59 runs
E)62 runs
Rationale: Let average for 10 innings be x. Then,
(10x + 108)/11 = x + 5
= 11x + 55 = 10x + 108
= x = 53.
New average = (x + 5) = 58 runs.
Answer:B
Answer: B
Question: An urn contains 15 black and 5 white balls. Two balls are drawn from the urn one after the other
without replacement. What is the probability that both drawn balls are black?
Options:
A)1/5
B)3/7
C)2/5
D)3/5
E)21/38
Rationale: Let E and F denote respectively the events that first and second ball drawn
are black. We have to find P(E n F) or P (EF).
Now P(E) = P (black ball in first draw) = 15/20
Also given that the first ball drawn is black, i.e., event E has occurred, now there are 14 black balls and five white balls left in the urn. Therefore, the probability that the second ball drawn is black, given that the ball in the first draw is black, is nothing but the conditional probability of F given that E has occurred.
That is P(F|E) = 14/19
By multiplication rule of probability, we have
P (E n F) = P(E) P(F|E)
= 15/20 × 14/19 = 21/38
E
Answer: E
Question: If n is a prime number greater than 17, what is the remainder when n^2 is divided by 12 ?
Options:
A)0
B)1
C)2
D)3
E)5
Rationale: There are several algebraic ways to solve this question, but the easiest way is as follows:since we cannot have two correct answers just pick a prime greater than 17, square it and see what would be the remainder upon division of it by 12.
n=19 --> n^2=361 --> remainder upon division 361 by 12 is 1.
Answer: B.
Answer: B
Question: The length of a rectangular floor is more than its breadth by 500%. If Rs. 324 is required to paint the floor at the rate of Rs. 6 per sq m, then what would be the length of the floor?
Options:
A)24.6m.
B)23.4m.
C)22.5m.
D)23.8m.
E)25.5m.
Rationale: Let the length and the breadth of the floor be l m and b m respectively.
l = b + 500% of b = l + 5b = 6b
Area of the floor = 324/6 = 54 sq m
l b = 54 i.e., l * l/6 = 108
l2 = 648 => l = 25.5m.
ANSWER:E
Answer: E
Question: Anmol can eat 27 pastries in a hour.
Aakriti can eat 2 pastries in 10 minutes.
Divya can eat 7 pastries in 20 minutes.
How long will it take them to eat a 240 pastries ?
Options:
A)2 hours.
B)1 hours.
C)5 hours.
D)4 hours.
E)3 hours.
Rationale: In one hour, Anmol eats 27 pastries, Aakriti eats 12, and Divya eats 21. A total of 60 pastries. Therefore 240 pastries would take 240 ÷ 60 = 4 hours.
ANSWER D
Answer: D
Question: How many different 3 digit numbers can be formed from the number 891 by re-arranging its digits so that the odd digits occupy even position
Options:
A)5
B)2
C)8
D)7
E)6
Rationale: There are 2 odd numbers which have to be placed at 2 even places =2!=2 ways
There are 1 even numbers which have to be placed at 1 odd places. So 1! = 1 ways
so total number of ways of arranging all these numbers are 1 * 2 = 2 ways
Answer:B
Answer: B
Question: Two sets A and B consists only of positive integers such that mean of set A is 55 . If set R consist of all the elements of both A and B such that mean of R is 80 then the mean of set B is =>
Options:
A)[A] 65
B)[B] 60
C)[C] 70
D)[D] 55
E)[E] cannot be determined
Rationale: For this question, we have zero information about the size of two sets, sets AB. These two sets may have the same size or may be wildly different. Thus, the answer is (E), the mathematical answer cannot be determined. This is a very weak math question. As someone who writes GMAT practice questions, I would give this a grade of anD-as a question.
Answer E
Answer: E
Question: What decimal of an hour is a second ?
Options:
A).0025
B).0256
C).00027
D).000126
E)None of these
Rationale: Explanation:
Required decimal =	1=	1= .00027
60 x 60=3600
Answer- C
Answer: C
Question: A store owner estimates that the average price of type A products will increase by 35% next year and that the price of type B products will increase by 10% next year. This year, the total amount paid for type A products was $4500 and the total price paid for type B products was $8300. According to the store owner's estimate, and assuming the number of products purchased next year remains the same as that of this year, how much will be spent for both products next year?
Options:
A)$14,755
B)$15,205
C)$16,000
D)$16,225
E)$17,155
Rationale: cost of type A products next year = 1.35 * 4500 = 6075
cost of type B products next year = 1.1 * 8300 = 9130
total 6075 + 9130 = 15205 option B
Answer: B
Question: Average of five numbers is 27. If one number is excluded the average becomes 25. The excluded
number is
Options:
A)35
B)45
C)55
D)65
E)75
Rationale: Explanation:
Number is (5*27) - (4*25) = 135-100 = 35
Answer: Option A
Answer: A
Question: A gambler bought $3,000 worth of chips at a casino in denominations of $20 and $100. That evening, the gambler lost 13 chips, and then cashed in the remainder. If the number of $20 chips lost was 3 more or 3 less than the number of $100 chips lost, what is the largest amount of money that the gambler could have received back?
Options:
A)$2,040
B)$2,120
C)$2,240
D)$1,920
E)$1,400
Rationale: In order to maximize the amount of money that the gambler kept, we should maximize # of $20 chips lost and minimize # of $100 chips lost, which means that # of $20 chips lost must be 2 more than # of $100 chips lost.
So, if # of $20 chips lost is x then # of $100 chips lost should be x-2. Now, given that total # of chips lost is 13: x+x-3=13 --> x=8: 8 $20 chips were lost and 8-2=6 $100 chips were lost.
Total worth of chips lost is 8*20+6*100=$760, so the gambler kept $3,000-$760=$2,240.
Answer: C.
Answer: C
Question: An article is bought for Rs.675 and sold for Rs.900, find the gain percent?
Options:
A)33 1/8%
B)33 8/3%
C)33 1/3%
D)35 1/3%
E)32 1/3%
Rationale: 675 ---- 225
100 ---- ? => 33 1/3%
Answer: C
Answer: C
Question: The measures of the 2 acute angles of a triangle are in the ratio of 2:7. What are the measures of the 2 angles?
Options:
A)40°
B)70°
C)80°
D)100°
E)180°
Rationale: If the ratio of the two angles is 2:7, then the measures of two angles can be written as 2x and 7x. Also the two acute angles of a triangle is equal to 90°. Hence
2x + 7x = 90
9x = 90
x = 10
Measures of the two acute angles are
2x = 2 × 10 = 20°
7x = 7 × 10 = 70°
B
Answer: B
Question: Find the area of a parallelogram with base 22 cm and height 14 cm?
Options:
A)298 cm2
B)384 cm2
C)308 cm2
D)286 cm2
E)276 cm2
Rationale: Area of a parallelogram = base * height = 22 * 14
= 308 cm2
Answer:C
Answer: C
Question: Find √? /20 = 4 ?
Options:
A)76
B)6400
C)304
D)1296
E)None
Rationale: Answer
Let √N/20= 4
Then √N = 20 x 4 = 80
∴ N = 80 x 80= 6400.
Correct Option: B
Answer: B
Question: 24 oz of juice P and 25 oz of juice V are mixed to make smothies M and Y . The ratio of p to V in smothie M is 4 is to 1 and that in Y is 1is to 5.How many ounces of juice P are contained in the smothie M?
Options:
A)5
B)10
C)15
D)20
E)25
Rationale: The ratio of p to V in smothie M is 4 is to 1 and that in Y is 1is to 5.p1 + p2 = 24
v1 + v2 = 25
p1 = 4v1
p2 = v2/5
4v1 + v2/5 = 24
v1 + v2 = 25
4v2 - v2/5 = 76
19v2/5 = 76 => v2 = 20
=> v1 = 5
=> p1 = 20
Answer - D
Answer: D
Question: If n = 30! + 27, then n is divisible by which of the following?
I. 25
II. 27
III. 29
Options:
A)None
B)I only
C)II only
D)I and II
E)II and III
Rationale: 27 divides 30! so 27 also divides 30! + 27.
25 and 29 divide 30! so they do not divide 30! + 27.
The answer is C.
Answer: C
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 6400 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
Options:
A)140 sq.units
B)320 sq.units
C)367sq.units
D)178sq.units
E)176sq.units
Rationale: Given that the area of the square = 6400 sq.units
=> Side of square = √6400 = 80 units
The radius of the circle = side of the square = 80 units Length of the rectangle = 2/5 * 80 = 32 units
Given that breadth = 10 units
Area of the rectangle = lb = 32 * 10 = 320 sq.units
Answer:B
Answer: B
Question: The least number,which when divided by 48,60,72,108 and 140 leaves 38,50,62,98 and 130 as remainder respectively, is :
Options:
A)11115
B)15110
C)15120
D)15210
E)12510
Rationale: Solution
Here (48 - 38) = 10 , (60 - 50) = 10,(72 - 62) = 10,(108 - 98) = 10 & (140 - 130) = 10.
So, Required number = (L.C.M. of 48,60,72,108,140) - 10 = 15120 - 10 = 15110. Answer B
Answer: B
Question: A buffet costs rs300. owner reduced the price 20% less. he got profit of 25% on its revenue. what is the percentage increase in number of customers?
Options:
A)56%
B)57%
C)58%
D)45%
E)35%
Rationale: let assume he sells 1 buffet daily,
now
then 300*1 = revenue (eq -1)
if he reduced his price by 20% then ,
240*(customer) = 125/100*revenue
customer = 1.25*300/240 = 1.56
means 56 % increase in customer.
ANSWER:A
Answer: A
Question: The population of a village is 10000. It increases annually at the rate of 20% p.a. What will be its population after 2 years?
Options:
A)10000
B)12000
C)13000
D)14000
E)14400
Rationale: Formula :
( After =100 denominator
Ago = 100 numerator)
10000 × 120/100 × 120/100 = 14400
E
Answer: E
Question: For any integer k greater than 1, the symbol k* denotes the product of all the fractions of the form 1/t, where t is an integer between 1 and k, inclusive. What is the value of 5*/6* ?
Options:
A)5
B)5/4
C)4/5
D)1/4
E)1/5
Rationale: When dealing with 'Symbolism' questions, it often helps to 'play with' the Symbol for a few moments before you attempt to answer the question that's asked. By understanding how the Symbol 'works', you should be able to do the latter calculations faster.
Here, we're told that K* is the PRODUCT of all the fractions of the form 1/T, where T is an integer between 1 and K, inclusive.
Based on this definition....
IF....
K = 2
K* = (1/1)(1/2) = 1/2
IF....
K = 3
K* = (1/1)(1/2)(1/3) = 1/6
We're asked to find the value of 5*/4*
Now that we know how the Symbol 'works', solving this problem shouldn't be too difficult. You can actually choose to do the math in a couple of different ways....
5* = (1/1)(1/2)(1/3)(1/4)(1/5)
Don't calculate this just yet though....since we're dividing by 4*, many of those fractions will 'cancel out.'
4* = (1/1)(1/2)(1/3)(1/4)
We're looking for the value of:
(1/1)(1/2)(1/3)(1/4)(1/5) / (1/1)(1/2)(1/3)(1/4)
Since the first four fraction in the numerator and denominator cancel out, we're left with just one fraction:
1/4
D
Answer: D
Question: A man can row upstream at 25 kmph and downstream at 41 kmph, and then find the speed of the man in still water?
Options:
A)33
B)67
C)30
D)15
E)17
Rationale: US = 25
DS = 41
M = (41 + 25)/2
= 33
Answer: A
Answer: A
Question: Let the polynomials be:
P1(x)=3x2−7x+4,
P2(x)=−5x2−4x+2,
P1(x)+P2(x)=
Options:
A)2x2 + 11x - 7
B)-2x2 - 11x + 6
C)-2x2 - 11x + 6
D)2x2 - 9x + 7
E)None of these
Rationale: Solution:
P1(x)+P2(x)=(3x2−7x+4)+(−5x2−4x+2)=P1(x)+P2(x)=(3x2−7x+4)+(−5x2−4x+2)=
3x2−7x+4−5x2−4x+2=3x2−7x+4−5x2−4x+2=
−2x2−11x+6
Answer B
Answer: B
Question: A certain galaxy is known to comprise approximately 10^11 stars. Of every 50 million of these stars, one is larger in mass than our sun. Approximately how many stars in this galaxy are larger than the sun?
Options:
A)800
B)1,250
C)2,000
D)12,000
E)80,000
Rationale: 10^11
50 mln = 5*10^7
we divide 10^11 by 10^7 and we get 10^4=10,000 and divide by 5. the result is 2,000
C
Answer: C
Question: A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?
Options:
A)30
B)50
C)40
D)60
E)70
Rationale: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (2/25) = 40 seconds
Answer: Option C
Answer: C
Question: In a race of 200 m, A can beat B by 40 m and C by 20 m. In how many meter race, C will beat B by 50m ?
Options:
A)225 m
B)285 m
C)200 m
D)250 m
E)150 m
Rationale: Explanation:
A:B = 100 : 60
A:C = 100 : 80
=>B:C = 60:80 = 3:4
When C covers 80 m , B Covers 60 m
When C covers x m , B Covers
=> x - 50 m
3x/4 = x - 50
x = 200 m
Answer: C
Answer: C
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. What is the ratio of the first number to the second number?
Options:
A)2 : 9
B)3 : 8
C)8 : 5
D)5 : 4
E)7 : 3
Rationale: Let the two numbers be x and y.
(2/10) * x + y = (5/4) * y
(2/10) * x = (1/4) * y
x/y = 10/8 = 5/4
The answer is D.
Answer: D
Question: Of 55 players on a cricket team, 37 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total?
Options:
A)49
B)55
C)59
D)71
E)92
Rationale: Total = 55
Thrower = 37
Rest = 55 - 37 = 18
Left Handed = 18/3 = 6
Right handed = 12
If all Thrower are right handed then total right handed is 37 + 12 = 49
so A. 49 is the right answer
Answer: A
Question: When the smallest of 3 consecutive odd integers is added to four times the largest, it produces a result 730 more than 4times the middle integer. Find the numbers?
Options:
A)650
B)678
C)698
D)710
E)730
Rationale: x + 4 (x + 4) = 730 + 4 (x + 2)
Solve for x and find all three numbers
x + 4 x + 16 = 730 + 4 x + 8
x = 722
x + 2 = 724
x + 4 = 726
Check: the smallest is added to four times the largest
722 + 4 * 726 = 3626
four times the middle
4 * 724 = 2896
3626 is more than 2896 by
3626 - 2896 = 730
E
Answer: E
Question: What is the smallest number which when increased by 3 is divisible by 18, 70, 25 and 21?
Options:
A)2327
B)2757
C)3147
D)3587
E)3997
Rationale: When increased by 3, the number must include at least 2*3^2*5^2*7 = 3150
The answer is C.
Answer: C