divelab/Sys2Bench huggingface dataset:
Question: A bowl contains pecans, cashews, and almonds in a ratio of 4 : 6 : 9, respectively. If some of the nuts of one of the three types are removed, which of the following could be the ratio of pecans to cashews to almonds remaining in the bowl? i. 1 : 2 : 3 ii. 2 : 3 : 4 iii. 4 : 7 : 10
Options:
A)II only
B)III only
C)I only
D)II,III only
E)I,III only
Rationale: i. The ratio 2 : 3 is the same as the given ratio 6 : 9. If one pecan were removed, the new ratio would be 3 : 6 : 9, or 1 : 2 : 3.
ii. None of the nuts currently have a ratio of 3 : 4. The cashews and almonds do have a ratio of 2 : 3, but there are not enough pecans in the bowl to complete the ratio.
iii. The ratio 4 : 10 is the same as the given ratio 6 : 15. To see this, multiply the ratio by 3/2 . The new ratio is 6 : 10.5 : 15. Unfortunately, this means that there are fewer cashews that this ratio would require. Removing cashews won’t create the desired ratio.
Answer : C
Answer: C
Question: In the coordinate plane, points (x, 1) and (12, y) are on line k. If line k passes through the origin and has slope 1/2, then x + y =
Options:
A) 4.5
B) 7
C) 8
D) 11
E) 12
Rationale: Line k passes through the origin and has slope 1/2 means that its equation is y=1/2*x.
Thus: (x, 1)=(2, 1) and (12, y) = (12,6) --> x+y=2+6=8.
Answer: C.
Answer: C
Question: Johnny borrows $30,000 from Tony at 4% daily interest compounded daily. How much does Johnny owe Tony after 6 weeks?
Options:
A)30000*0.02^56
B)30000*1.12
C)30000*2.12
D)30000*1.04^42
E)(30000*1.02)^56
Rationale: A=A= P(1+r100)^n
So, A=30000(1+4/100)^7âˆ—6
So, A=A= 30000(1.04)^42
Hence answer will be (D)
Answer: D
Question: The annual interest rate earned by an investment increased by 10 percent from last year to this year. If the annual interest rate earned by the investment this year was 13 percent, what was the annual interest rate last year?
Options:
A)1%
B)1.1%
C)9.1%
D)11.81%
E)11.50%
Rationale: 13=1.1*x
X=11.81%
Answer D)
Answer: D
Question: The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is?
Options:
A)65 years
B)40 years
C)54 years
D)46 years
E)13 years
Rationale: Sum of the present ages of husband, wife and child
= (27 * 3 + 3 * 3) = 90 years.
Sum of the present age of wife and child
= (20 * 2 + 5 * 2) = 50 years.
Husband's present age
(90 - 50) = 40 years.
Answer:B
Answer: B
Question: Two cars started at the same time, from the same point, driving along the same road. The rate of the first car is 50 mph and the rate of the second car is 60 mph. How long will it take for the distance between the two cars to be 30 miles?
Options:
A)1 hrs
B)2 hrs
C)3 hrs
D)4 hrs
E)5 hrs
Rationale: car 1 50 50 50 total=150
car 2 60 60 60 total=180 differece=30miles after 3 hrs.
ANSWER:C
Answer: C
Question: A starts business with Rs.3500 and after 9 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is Bâ€™s contribution in the Capital ?
Options:
A)24887
B)20778
C)23788
D)21000
E)2811
Rationale: Explanation:
A invested Rs.3500 for 12 months.
Let B joined with investment x. And he invested for 12 - 9 = 3 months.
So there profit ratio = (3500 Ã— 12) : (3x) = 2 : 3
â‡’ x = 21000
Answer: D
Answer: D
Question: Rajeev's age after 15 years will be 5 times his age 5 years back. What is the present age of Rajeev?
Options:
A)5 years
B)10 years
C)20 years
D)25 years
E)None
Rationale: Solution
Let Rajeev's present age be x years. Then
Rajeev's age 15 years	= (x+15) years.
Rajeev's age 5 years back	= (x-5) years.
Therefore	‹=› x+15=5(x-5)
‹=› x+15= 5x-25
‹=› 4x=40
‹=› x=10.
Answer B
Answer: B
Question: When positive integer N is divided by positive integer J, the remainder is 14. If N/J = 134.08, what is value of J?
Options:
A)22
B)56
C)78
D)112
E)175
Rationale: 1) We know that
decimal part of decimal quotient ={remainder/divisor}
So 0.08, the decimal part of the decimal quotient, must equal the remainder, 14, divided by the divisor J.
0.08 = 14/J
0.08*J = 14
J = 14/0.08 = 1400/8 = 700/4 = 350/2 = 175
So J = 175, answer = E.
Answer: E
Question: A certain barrel, which is a right circular cylinder, is filled to capacity with 50 gallons of oil. The first barrel is poured into a second barrel, also a right circular cylinder, which is empty. The second barrel is twice as tall as the first barrel and has twice the diameter of the first barrel. If all of the oil in the first barrel is poured into the second barrel, how much empty capacity, in gallons, is left in the second barrel?
Options:
A)There is no empty capacity
B)100 gallons
C)350 gallons
D)700 gallons
E)800 gallons
Rationale: Radius of first cylinder=r, diameter=2r, height=h
Radius of second cylinder=2r, diameter=2d and height=2h
Volume of first cylinder=pie (r^2)*h=50
Volume of second cylinder=pie(2r^2)2h
Put the value of pie (r^2)*h=50 in the second cylinder,volume= pie (r^2)*4*2=50*8=400 gallons
Empty capacity=350 gallons
Answer C
Answer: C
Question: Suresh started a business with Rs.20,000. Kiran joined him after 4 months with Rs.30,000. After 2 more months, Suresh withdrew Rs.5,000 of his capital and 2 more months later, Kiran brought in Rs.20,000 more. What should be the ratio in which they should share their profits at the end of the year?
Options:
A)21:32
B)32:21
C)12:17
D)17:12
E)34:21
Rationale: Here capital is not the same.
Suresh invested 20000 for initial 6 months and 15000 for the next 6 months. Hence his term of ratio
=(20000×6+15000×6)
Kiran invested Rs.30000 for 4 months and Rs.50000 for next 4 months. Hence his term of ratio
=(30000×4+50000×4)
Suresh : Kiran
=(20000×6+15000×6):(30000×4+50000×4)
=(20×6+15×6):(30×4+50×4)=(20×3+15×3):(30×2:50×2)
=105:160
=21:32 Answer: Option A
Answer: A
Question: If m and n are both negative and mn < n^2, which of the following must be true?
Options:
A)m < n < m^2 < n^2
B)m < n < n^2 < m^2
C)n < m < m^2 < n^2
D)m^2 < n^2 < n < m
E)n^2 < m^2 < n < m
Rationale: Because mn < n^2 and both are negative, I thought m < n. So I crossed off answers c), d), and e).
And because m < n , m^2 < n^2
ans C
Answer: C
Question: If p/q =4/5, then the value of 6/7 + {(2q - p) / (2q + p)} is ?
Options:
A)3 / 7
B)34
C)10/7
D)2
E)3
Rationale: Answer
Given Exp. = 6 / 7 + {(2q - p) / (2q + p)}
Dividing numerator as well as denominator by q,
Exp = 6/7 + {2-p/q) / (2 + p/q)}
= 6/7 + {(2 - 4/5) / (2 + 4/5)}
= 6/7 + 6/14
= 6/7 + 3/7
=10/7
Correct Option: C
Answer: C
Question: In 10 years,A will be thrice as old as B was 10 years ago.If A is now 9 years older than B,the present age of B is :
Options:
A)19 Years
B)24.5 Years
C)39 Years
D)49 Years
E)59 Years
Rationale: Solution
Let B's present age = x years.Then,A's present age =(x +9) years.
âˆ´ (x + 9)+ 10 = 3 (x - 10) â‡” x + 19 = 3x- 30 â‡” 2x = 49 x = 24.5.Answer B
Answer: B
Question: When positive integer c is multiplied by positive integer n, the units digit of the product is 3. Which of the following are factors of n?
I. 8
II. 15
III. 30
Options:
A)I only
B)II only
C)I and II only
D)II and III only
E)None of the above
Rationale: ans E..
we can tell the ans w/o using examples..
the units digit of product c*n is 3..
this means c and n are odd positive integers..
therefore n cannot have an even factor so 8 and 30 are out..
n cannot have a factor ending in 5 because in that case the units digit has to be 5 or 0... so 15 is also out
Answer: E
Question: Two pipes can fill a tank in 18 minutes and 15 minutes. An outlet pipe can empty the tank in 45 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank?
Options:
A)30 minutes
B)17 minutes
C)15 minutes
D)10 minutes
E)12 minutes
Rationale: Part of the filled by all the three pipes in one minute
= 1/18 + 1/15 - 1/45 = (5 + 6 - 2)/90 = 9/90 = 1/10
So, the tank becomes full in 10 minutes.
Answer: D
Answer: D
Question: How long does a bus 100 m long traveling at 50 kmph takes to cross a bridge of 150 m in length?
Options:
A)18
B)16
C)15
D)11
E)12
Rationale: D = 100 + 150 = 250 m
S = 50 * 5/18 = 125/9
T = 250 * 9/125 = 18 sec
Answer:A
Answer: A
Question: Which of the following integers is a divisor of(15!+12)?
Options:
A)15
B)14
C)12
D)7
E)2
Rationale: When we say 15!, it just means 1*2*3*4*5*...*13*14*15
So you need to find the integer which is a divisor of
(1*2*3*4*5*...*13*14*15 + 12) = 12 (1*2*3*4*5*...11*13*14*15 + 1) We obtain this by taking 12 common.
Hence 12 is definitely a divisor of (15! + 12).
C
Answer: C
Question: Pipe A can fill a tank in 16 minutes and pipe B cam empty it in 24 minutes. If both the pipes are opened together after how many minutes should pipe B be closed, so that the tank is filled in 30 minutes?
Options:
A)21
B)22
C)25
D)26
E)28
Rationale: 30/16 - x/24 = 1 => x/24 = 30/16 - 1 = 14/16
=> x = 14/16 * 24 = 21.
ANSWER A
Answer: A
Question: Based on this year's costs, an orcharde grower budgets P dollars for planing N new trees next year. If the average cost of planting each tree were to increase 25% from this year's cost, then the greatest number of trees that the orchard grower could plant next year using P dollars would be
Options:
A)20% less than N
B)25% less than N
C)equal to N
D)20% greater than N
E)25% greater than N
Rationale: This year, the price of a tree is price1=P/N.
If this price increases by 25% it becomes price 2=P/N*1.25
Then with P dollars, you can grow P/price 2 tress i.e. P/(P/N*1.25) i.e. N/1.25 i.e. .80*N
Correct answer is (A).
Answer: A
Question: The number of new words that can be formed by rearranging the letters of the word 'ALIVE' is
Options:
A)288
B)767
C)119
D)287
E)112
Rationale: Explanation:
Number of words which can be formed = 5! - 1 = 120 - 1 = 119.
Answer: C
Answer: C
Question: A rectangular block 8cm by 24cm by 56cm is cut into an exact number of equal cubes. Find the least possible number of cubes?
Options:
A)6
B)10
C)15
D)40
E)21
Rationale: Volume of the block = 8*24*56= 10752 cm^3
Side of the largest cube = H.C.F of 8,24,56 = 8cm
Volume of the cube = 8*8*8= 512 cm^3
Number of cubes = 10752/512 = 21
Answer is E
Answer: E
Question: The floor of a rectangular room is 17 m long and 12 m wide. The room is surrounded by a veranda of width 2 m on all its sides. The area of the veranda is :
Options:
A)124 m2
B)132 m2
C)148 m2
D)152 m2
E)None of these
Rationale: Area of the outer rectangle = 21 Ã— 16 = 336 m2
Area of the inner rectangle = 17 Ã— 12 = 204 m2
Required area = (336 â€“ 204) = 132 m2
Answer B
Answer: B
Question: There are two positive numbers in the ratio 5 : 8. If the larger number exceeds the smaller by 15, then find the smaller number?
Options:
A)25
B)24
C)28
D)88
E)99
Rationale: Let the two positive numbers be 5x and 8x respectively.
8x - 5x = 15 => 3x = 15 => x = 5.
Smaller number = 5x = 25.
Answer:A
Answer: A
Question: Insert the missing number.
7, 26, 63, 124, 215, 342, (....)
Options:
A)222
B)737
C)388
D)511
E)200
Rationale: Numbers are (23 - 1), (33 - 1), (43 - 1), (53 - 1), (63 - 1), (73 - 1) etc.
So, the next number is (83 - 1) = (512 - 1) = 511.
Answer:D
Answer: D
Question: A crew can row a certain course up the stream in 84 minutes; they can row the same course down stream in 7 minutes less than they can row it in still water. How long would they take to row down with the stream
Options:
A)45 or 23 minutes
B)73 or 12 minutes
C)77 minutes
D)19 minutes
E)25 minutes
Rationale: A method has been discussed here to nullify the calculations though.
All I can input here is,
speed of a crew in still water = 1/2 ( speed upstream + speed downstream)
approximating this for time,
t = 1/2(84+ (t-7))
giving t = 77
C
Answer: C
Question: A big container is 30% full with water. If 54 liters of water is added, the container becomes 3/4 full. What is the capacity of the big container?
Options:
A)36 liters
B)40 liters
C)45 liters
D)54 liters
E)120 liters
Rationale: A big container is 30% full with water and after 54 liters of water is added, the container becomes 75% full. Hence these 54 liters account for 45% of the container, which means that the capacity of it is 54/0.45=120 liters.
OR: if the capacity of the container is x liters then: 0.3x+54=0.75x --> x=120 liters.
Answer: E
Answer: E
Question: A rectangular circuit board is designed to have a width of W inches, a length of L inches, a perimeter of P inches, and an area of Y square inches. Which of the following equations must be true?
Options:
A)2W^2 + PW + 2Y = 0
B)W^2 − PW + 2Y = 0
C)2W^2 − PW − 2Y = 0
D)W^2 + PW + Y = 0
E)2W^2 − PW + 2Y = 0
Rationale: P = 2(L+W)-----------------1)
Y= LW------------------------2)
option A is not possible why ?? because all the terms are positive.
lets try option B , put value of P and A from 1 and 2 we have,
2W^2-2(L+W)W + 2(LW)
2W^2 - 2LW - 2W^2 + 2LW=0.
hence answer is B.
Answer: B
Question: Kyle received a bag of 82 marbles for his birthday. If he shares his marbles equally with his 5 best friends (including himself) how many more marbles will he have than his friends?
Options:
A)1 marble
B)2 marbles
C)3 marbles
D)4 marbles
E)5 marbles
Rationale: In order to divide the marbles into 6 parts, the amount must be divisible by 6.
Divisibility rule of 6: A number is divisible by 6 if it is divisible by both 2 and 3
Divisibility rule of 3: A number is divisible by 3 if the sum of the digits is divisible by 3
We need to make subtract an even this number even in order for it to be divisible by 2.
sum of digits of 82 = 10 and 6 is divisible by 3. Subtracting 4 yeilds an even number.
Hence we need to subtract 4 for the number to be divisible by 6.
Correct Option: D
Answer: D
Question: The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
Options:
A)76 cm2
B)56 cm2
C)18 cm2
D)98 cm2
E)35 cm2
Rationale: Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle
= 2.5 * 28/2
= 35 cm2
Answer:E
Answer: E
Question: Two numbers are in the ratio 3:5. If 9 is subtracted from each, the new numbers are in the ratio 12:23. The smaller number is:
Options:
A)15
B)33
C)58
D)56
E)91
Rationale: Let the numbers be 3x and 5x.
Then, (3x - 9)/(5x - 9)
= 12/23
9x = 99 => x = 11
The smallest number
= 3 * 11 = 33.
AnswerB
Answer: B
Question: There are 6 positive and 8 negative numbers. Four numbers are choosen at random and multiplied.the probability that the product is positive is:
Options:
A)500/1001
B)503/1001
C)303/1001
D)301/1001
E)505/1001
Rationale: 6c4/14c4 + (6c2*8c2)/14c4 + 8c4/14c4 =505/1001
case1: only 4 positive no.
case2: 2 positive and 2 negative no.
case3: 4 negative no.
ANSWER:E
Answer: E
Question: If a=(10^10)-47, what is the sum of all the digit of a?
Options:
A)40
B)45
C)50
D)55
E)80
Rationale: Start small and check for any pattern:
10^2 - 47 = 53 -> number of digits = power of 10; number of 9s = (power of 10) - 2; 53 is the last 2 digits
10^3 - 47 = 953 -> number of digits = power of 10; number of 9s = (power of 10) - 2; 53 is the last 2 digits
...extrapolate
10^10 - 47 -> number of digits = 10; number of 9s = 8; 53 will be the last 2 digits
Sum,a = 9*8 + 5 + 3 = 80.
Answer (E).
Answer: E
Question: In May Mrs Lee's earnings were 60 percent of the Lee family's total income. In June Mrs Lee earned 10 percent more than in May. If the rest of the family's income was the same both months, then, in June, Mrs Lee's earnings were approximately what percent of the Lee family's total income ?
Options:
A)62%
B)68%
C)72%
D)76%
E)80%
Rationale: Let in May Lee family's total income =100
in May Mrs Lee's income =60
in May rest of the family's income = 40
In june Mrs Lees income = 60*110/100 = 66
In june Total income = 66+ 40 = 106
% of Mrs Lee's income = 66/106 =62.26
(A)
Answer: A
Question: One half of a two digit number exceeds its one third by 9. What is the sum of the digits of the number?
Options:
A)A)3
B)B)5
C)C)7
D)D)9
E)E)11
Rationale: x/2 – x/3 = 9 => x =54
5 + 4 = 9
ANSWER:D
Answer: D
Question: A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did B get in a profit of Rs.2400 ?
Options:
A)s. 532
B)s. 600
C)s. 822
D)s. 812
E)s. 810
Rationale: Let the total amount in the partnership be 'x'.
Then A's share = x/3
B's share = x/4
C's share = x/5
D's share = x - (x/3 + x/4 +x/5) = 13x/60
A : B : C : D = x/3 : x/4 : x/5 : 13x/60 = 20 : 15 : 12 : 13
B's share in the profit of Rs. 2400 = 15 (2400/60) = Rs. 600.
Answer: B
Answer: B
Question: A and B can do a piece of work in 4 days. B and C can do it in 12 days and A and C in 16 days. Working together they will complete the work in how many days?
Options:
A)4.05 days
B)5.05 days
C)14.76 days
D)8.05 days
E)15.05 days
Rationale: A + B = 1/4
B + C = 1/12
C + A = 1/16
-------------------------------
2(A + B +C) = 1/4 + 1/12 + 1/16 = 19/48
A + B +C = 19/96
96/19 = 5.05 days
ANSWER:B
Answer: B
Question: In a street, there are certain number of houses. People in that street are decided to paint their houses with certain colours. If four houses are painted with each colour, then one house will be left without any colour. If five houses are painted with each colour, then one colour will remain. Find the number of houses in that street?
Options:
A)6
B)36
C)25
D)7
E)9
Rationale: on the basis of question
x = 4y+1
x = 5(y-1)
on solving these 2 equations x = 25
ANSWER:C
Answer: C
Question: There are 5 bags three of which each contains 4 white and 2 black balls, and remaining 2 bags each contains 1 white and 4 black ball; a black ball has been drawn, find the chance that it came from first group.
Options:
A)2/7
B)6/35
C)8/25
D)5/13
E)3/5
Rationale: Please go through my solution and suggest any mistake.
Chances of selecting a black ball from group 1: 1/3----------------------Chances of selecting a black ball from group 2: 4/5
Thus combined probability of section of black ball from group 1:
3/5 x 1/3 = 1/5
Thus combined probability of section of black ball from group 2:
2/5 x 4/5 = 8/25
Out of these chances, chance of occurrence of first case : (1/5) / (1/5 + 8/25) = 5/13
D
Answer: D
Question: The total of the ages of Amar, Akbar and Anthony is 56 years. What was the total of their ages three years ago ?
Options:
A)71
B)47
C)66
D)16
E)18
Rationale: Explanation:
Required sum = (56 - 3 x 3) years = (56 - 9) years = 47 years.
Answer: B
Answer: B
Question: Each week a restaurant serving Mexican food uses the same volume of chili paste, which comes in either 25-ounce cans or 15-ounce cans of chili paste. If the restaurant must order 30 more of the smaller cans than the larger cans to fulfill its weekly needs, then how many larger cans are required to fulfill its weekly needs?
Options:
A)60
B)70
C)80
D)100
E)45
Rationale: let x be the number of 25 ounce cans. Therefore (x+30) is the number of 15 ounce cans.
Total volume is same, therefore
25x=15(x+30)
10x=450
x=45
Ans - E
Answer: E
Question: A man can row upstream at 10kmph and downstream at 20kmph. Find the rate of current ?
Options:
A)10km/hr
B)15km/hr
C)20km/hr
D)5km/hr
E)3km/hr
Rationale: Rate of current = 1/2 (20-10) = 5km/hr
Answer is D
Answer: D
Question: A jar full of whisky contains 40% alcohol. A part of this whisky is replaced by another containg 19% alcohol and now the percentage of alcohol was found to be 24%. What quantity of whisky is replaced ?
Options:
A)1/3
B)2/3
C)2/5
D)3/5
E)16/21
Rationale: Let us assume the total original amount of whiskey = 10 ml ---> 4 ml alcohol and 6 ml non-alcohol.
Let x ml be the amount removed ---> total alcohol left = 4-0.4x
New quantity of whiskey added = x ml out of which 0.19 is the alcohol.
Thus, the final quantity of alcohol = 4-0.4x+0.19x ----> (4-0.21x)/ 10 = 0.24 ---> x = 160/21 ml.
Per the question, you need to find the x ml removed as a ratio of the initial volume ---> (160/21)/10 = 16/21.
Hence, E is the correct answer.
Answer: E
Question: 12. What is the dividend. divisor 17, the quotient is 9 and the remainder is 7.
Options:
A)150
B)152
C)154
D)158
E)160
Rationale: D = d * Q + R
D = 17 * 9 + 7
D = 153 + 7
D = 160
ANSWER E
Answer: E
Question: The price of a Maruti car rises by 30% while the sales of the car come down by 20%. What is the percentage change in the total revenue?
Options:
A)-4%
B)-2%
C)+4%
D)+2%
E)None of these
Rationale: Explanation :
Let initial price of Maruti car be Rs. 100.
As price increases 30%, the price of car become 100 + 30% of 100 = Rs. 130.
Due to increase in price, sales is down by 20 %.
It means, it is going to make 20% less revenue as expected after increment of price.
So, new revenue = 130 - 20 % of 130 = Rs 104.
The initial revenue was Rs 100 which becomess Rs 104 at the end.
It means there is 4% increment in the total revenue.
Answer : C
Answer: C
Question: total dinning bill of 6 people was $139.00 and 10% tip divided the bill evenly ?what is the bill amount each person shared .
Options:
A)21.84
B)22.84
C)23.84
D)24.84
E)25.48
Rationale: dinner bill of 6 person = 139 + 10% tip
so,
10% of 139 = (139*10)/100 = 13.9
So, the actual total amount = 139+13.9 = $ 152.9
so per head bill = 152.9/6 = $ 25.48
ANSWER:E
Answer: E
Question: A person travels from P to Q a speed of 40 km/hr and returns by increasing his speed by 50%. What is his average speed for both the trips?
Options:
A)37
B)26
C)48
D)21
E)92
Rationale: Speed on return trip = 150% of 40 = 60 km/hr.
Average speed = (2 * 40 * 60)/(40 + 60)
= 48 km/hr.
Answer:C
Answer: C
Question: If you roll 2 dice, what is the probability of rolling a 7?
Options:
A)1/2
B)1/3
C)2/13
D)3/14
E)1/6
Rationale: Counting how many times the sum of the two numbers equals 7, you will find that 6/36 times, there is a 7 as a sum, thus Answer: E
Answer: E
Question: A cricketer whose bowling average is 12.4 runs per wicket takes 5 wickets for 26 runs and there by decreases his average by 0.4. The number age of the family now is?
Options:
A)17
B)98
C)88
D)85
E)83
Rationale: Let the number of wickets taken till the last match be x. Then,
(12.4x + 26)/(x + 5) = 12
= 12.4x + 26 = 12x + 60
= 0.4x = 34
= x = 340/4 = 85.
Answer: D
Answer: D
Question: If two balls are randomly selected from a green urn containing 9 black and 9 white balls and placed into a yellow urn initially containing 5 black and 3 white balls. What is the probability that the yellow urn will contain an equal number of black and white balls after the change?
Options:
A)A.2/9
B)B.4/9
C)C.4/17
D)D.1/3
E)E.1/9
Rationale: To have equal number of black and white balls, the yellow urn must have 5 black and 5 white balls. So the balls we select out of the green urn must be both white.
Probability (first ball is white) = 9/18
Probability(second ball is white) = 8/17
Probability (both balls are white) = (9/18)*(8/17) = 4/17
Answer C
Answer: C
Question: -24x29+36=?
Options:
A)2436
B)2801
C)-2801
D)-660
E)None of them
Rationale: Given exp.=-24x(30-1)+36
=-(24x30)+24+36
=-720+60
=-660
Answer is D
Answer: D
Question: Nina has exactly enough money to purchase 6 widgets. If the cost of each widget were reduced by $2, then Nina would have exactly enough money to purchase 8 widgets. How much money does Nina have?
Options:
A)$22
B)$24
C)$30
D)$36
E)$48
Rationale: E its is.
Let price = X
(x-2)8 = 6X
X= 8
hence total money = 6*8 = 48
Answer: E
Question: The ratio of the present ages of Sunita and Vinita is 4:5. Six years hence the ratio of their ages will be 14:17. What will be the ratio of their ages 12 years hence?
Options:
A)3
B)4
C)5
D)1
E)7
Rationale: Explanation:
Present age sunita : vinita = 4 : 5
Let their age is 4x and 5x respectively..
After 6 yrs their age ratio will be 14 : 17
Therefore 4x+65x+6=14174x+65x+6=1417
⇒ x = 9
Therefore their present ages are 36,45 respectively.
After 12 yrs their ages will be 48, 57 respectively.
⇒ Ratio after 12 years will be 48: 57 = 16: 19 = 16 : 19
Answer: A
Answer: A
Question: Of the female students at Barkely University, 5/6 are on the honor roll. Of the male students, 2/3 are on the honor roll. If 3/5 of the students are female, what is ratio of male to female students on honor roll?
Options:
A)5/9
B)8/15
C)23/30
D)43/60
E)53/90
Rationale: let the total students be 30
given 3/5 of the students are females = 18
then males = 2/5 = 12
5/6 of the females are on honor roll = 15
males on the honor roll = 2/3= 8
ratio of M:F students on honor roll = 8/15
B
Answer: B