divelab/Sys2Bench huggingface dataset:
Question: In a sample of associates at a law firm, 30 percent are second-year associates, and 60 percent are not first-year associates. What percentage of the associates at the law firm have been there for more than two years?
Options:
A)10
B)20
C)30 %
D)40
E)50
Rationale: Let the sample be 100.
Given 60% are not first year i.e. there could be second year (x) and more than 2 years(y) possibility.
60% = (x) + y
Given 30% = second year (x)
club both , we get y = 30%.
Answer: option C is correct answer.
Answer: C
Question: Braun invested a certain sum of money at 8% p.a. simple interest for 'n' years. At the end of 'n' years, Braun got back 7 times his original investment. What is the value of n?
Options:
A)50 years
B)25 years
C)12 years 6 months
D)37 years 6 months
E)75 years
Rationale: Explanatory Answer
Let us say Braun invested $100.
Then, at the end of 'n' years he would have got back $700.
Therefore, the Simple Interest earned = 700 - 100 = $600.
We know that Simple Interest = (Principal * number of years * rate of interest) / 100
Substituting the values in the above equation we get 600 = (100 * n * 8) / 100
Or 8n = 600
Or n = 75 years.
correct choice is (E)
Answer: E
Question: Of the books standing in a row on a shelf, an atlas is the 30th book from the left and the 33rd book from the right. If 2 books to the left of the atlas and 5 books to the right of the atlas are removed from the shelf, how many books will be left on the shelf?
Options:
A)55
B)57
C)58
D)61
E)63
Rationale: 100%. There are total of 30+33-1=62 books and 2+5=7 books are removed, thus 62-7=55 books are left.
Answer: A.
Answer: A
Question: If a is the sum of u consecutive positive integers. b is the sum of v consecutive positive integers. For which of the following values of u and v is it impossible that a = b?
Options:
A)u = 2; v = 6
B)u = 3; v = 6
C)u = 7; v = 9
D)u = 10; v = 7
E)u = 10; v = 4
Rationale: I approached this in a different way, although may be longer but it's certainly more intuitive
It is impossible that a = b if one of them is necessarily even while the other is necessarily odd
for two consecutive integers the sum is necessarily odd
for six consecutive integers the sum is necessarily odd (sum of 3two consecutive integerswhich are all odd)
Thus A is incorrect.
The sum of 3 consecutive integers can be even or odd (an odd integer from the first 2 + an additional integer which can be even or odd). Thus B is incorrect. You can do a similar approach for C and D (it follows that the sum of a specified odd number of consecutive integers can be odd or even).
Leaving us with E to be the only not-wrong answer. To confirm, you can easily deduce that the sum of 4 consecutive integers (sum of 2 odd integers) is necessarily even while the sum of 10 consecutive integers (sum of 5 odd integers) is necessarily odd. Thus E is the right answer.
Answer: E
Question: X and Y are positive integers. If X is a prime factor of Y^2 , which of the following MUST be true?
Options:
A)X is even
B)X=Y^2
C)Y/X is even
D)X/Y is less than or equal to 1
E)X+1 is also a prime factor of Y^2
Rationale: A. x is even --> not necessarily true: x=3=odd x=3=odd and y=3y=3;
B. x=y^2 --> never true, as x=primex=prime then it can not equal to square of another integer;
C. y/x is even --> not necessarily true: if x=3x=3 and y=3y=3 then yx=1=odd yx=1=odd;
D. x/y is less than or equal to 1 --> always true as shown above or by POE;
E. x+1 is also a prime factor of y^2 --> not necessarily true: if x=2x=2 and y=2y=2 then x+1=3x+1=3 and 3 is not a factor of y2=4y2=4.
Answer: D.
Answer: D
Question: Which of the following is the product of two integers whose sum is 13?
Options:
A) -42
B) -28
C) 12
D) 26
E) 32
Rationale: I solved this Question like this,
Let the two integers are x,y
x+y=13 (Given)
xy=? (Needed)
instead of solving this algebraically, Test the Answer choices
C. 12
Do the factorization : (1,12)----> There sum is 13 Bingo!!!!
So, my answer is C...
As the answer is in C, it took me very less time to answer the question. but i think this method is be simple and efficient.
Answer: C
Question: A, B and C invest in the ratio of 3 : 4: 5. The percentage of return on their investments are in the ratio of 6 : 5 : 4. Find the total earnings, If B earns Rs. 150 more than A :
Options:
A)2348
B)7250
C)4350
D)1998
E)2771
Rationale: Explanation:
A B C
investment 3x 4x 5x
Rate of return 6y% 5y% 4y%
Return \inline \frac{18xy}{100} \inline \frac{20xy}{100} \inline \frac{20xy}{100}
Total = (18+20+20) = \inline \frac{58xy}{100}
B's earnings - A's earnings = \inline \frac{2xy}{100} = 150
Total earning = \inline \frac{58xy}{100} = 4350
Answer: C) Rs.4350
Answer: C
Question: If x and y are integers such that x^2= 2y and xy = 32, then x – y = ?
Options:
A)-30
B)-20
C)-5
D)-4
E)20
Rationale: here x and y are integers .
x^2=2y,xy =32.
substitute (x^2)/2=y in xy => x^3=32*2=>x^3=64.
here X3 is positive ,
X is also positive.
x=4 then y=8.
X-y=-4
so option D is correct
Answer: D
Question: A certain sum of money is divided among A, B and C such that A gets one-third of what B and C together get and B gets two-seventh of what A and C together get. If the amount received by A is $15 more than that received by B, find the total amount shared by A, B and C.
Options:
A)$250
B)$340
C)$640
D)$440
E)$540
Rationale: A = 1/3 (B+C) => C = 3A - B ---(1)
B = 2/7 (A+C) => C = 3.5 B - A --(B)
A-B = $15
A = 15+B
(1)===> C = 45+3B - B = 2B+45 ==> 2B-C = -45 ---(3)
(2)===> C = 3.5 B - B-15 = 2.5B-15==>2.5B-C = 15---(4)
from (4) and (3) 0.5B = 60
B = $120
A= $135
C =405-120=$285 Total amount = 135+120+285 = $540
Answer: E
Answer: E
Question: find the number of 6 digit numbers that can be formed using digits 1,2,3,4,5,6 once such that the 6digit number is divisible by its unit digit.
Options:
A)648
B)649
C)650
D)651
E)652
Rationale: when unit digit 1,2,3,5,6 then no. formed will be divisible by the digit at the unit place.
=> 5*5p5 numbers
when unit place is 4, tenth place should be 2 or 6
=> 2*4p4 numbers
total = 5*5p5 + 2*4p4 = 5*5! + 2*4! = 648
ANSWER:A
Answer: A
Question: In the rectangular coordinate system Point O has coordinates (0,0) and Point B has coordinates (2,2) and if point A is equidistant from points O and B and the area of the triangle OAB is 16, which of the following are the possible coordinates of point A.
Options:
A)(-2,6)
B)(0,4)
C)(2,-6)
D)(2,6)
E)(4,0)
Rationale: Area.pngSince A is equidistant from points O and B, then it must be somewhere on the green line (perpendicular bisector of OB).
(2,-6) and (2,6) are not on that line. If A is at (0,2) or (2,0), then the area is 1/2*2*2=2. Thus A must be at (4,0).
Answer: E.
Answer: E
Question: 3 candidates in an election and received 1136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election?
Options:
A)45%
B)47%
C)57%
D)60%
E)62%
Rationale: Total number of votes polled = (1136 + 7636 + 11628) = 20400
So, Required percentage = 11628/20400 * 100 = 57%
C
Answer: C
Question: In Orange County one eighth of the people are gathering mushrooms and one seventh of the people are collecting apples. What can be the number of people in Orange County?
Options:
A)60.
B)42.
C)85.
D)142.
E)112.
Rationale: The number must be an integer and multiple of both 8 and 7.
Only option E fulfill this condition and hence is the answer.
Answer: E
Question: In how many ways can 6 apples (identical) be distributed among 3 children? (Some children may get no apples.)
Options:
A)32
B)34
C)36
D)28
E)30
Rationale: Generalised form for n = number of identical objects, and r = number of children is n+r-1Cr-1.
n=6 r= 3
8C2 =28
Answer : D
Answer: D
Question: Two employees A and B are paid a total of Rs. 570 per week by their employer. If A is paid 150 percent of the sum paid to B, how much is B paid per week?
Options:
A)s.130
B)s.140
C)s.150
D)s.228
E)s.282
Rationale: Let the amount paid to A per week = x
and the amount paid to B per week = y
Then x + y = 570
But x = 150% of y = 150y/100 = 15y/10
∴15y/10 + y = 570
⇒ y[15/10 + 1] = 570
⇒ 25y/10 = 570
⇒ 25y = 5700
⇒ y = 5700/25 = Rs.228
D)
Answer: D
Question: If X, Y and Z are consecutive numbers (X>Y>Z). X +2Y +3Z = 5Y + 4. What is the value of Z?
Options:
A)6.
B)5.
C)4.
D)3.
E)2.
Rationale: Let the 3 consecutive integers be k-1 (Z), k (Y) and k+1 (X). Given : X +2Y +3Z = 5Y + 4.
k+1 + 2k + 3k - 3 = 5k+ 4 => k =6.
Thus Z = k-1 = 5.
ANSWER:B
Answer: B
Question: Four students, Jackie, Mandy, Bertrand, and Tao, took a science quiz. If Mandy scored 30% higher than Bertrand did, Tao scored 20% lower than Jackie did, and Jackie scored 40% higher than Mandy did, how much lower did Bertrand score than Tao?
Options:
A)50% lower
B)20% lower
C)5% lower
D)40% lower
E)30% lower
Rationale: In this word problem, the first key is to turn the story into equations:
Mandy scored 30% higher than Bertrand did: M = 0.30 + B
Tao scored 20% lower than Jackie did: T = J - 0.20
Jackie scored 40% higher than Mandy did: J = 0.40 + M
Then, in classic GMAT style, the problem doesn't ask you to solve for a single variable, but instead to solve for the difference between B and T (how much higher did Bertrand score than Tao did?). This means that your goal is to get the equations in terms of B and T so that you can solve for the expression B - T.
Taking the first equation and solving for B, you have B = M - 0.30.
Taking the second equation and solving for T you have T = J - 0.20, and then with the third equation you can replace J with 0.40 + M so that both B and T are in terms of M: T = (0.40 + M) - 0.20.
So if B = M - 0.30 and T = M + 0.20, then:
B - T = (M - 0.30) - (M + 0.20)
B - T = M - 0.30 - M - 0.20 (remove the parentheses by distributing the multiplication)
B - T = -0.50, so the answer is A.
Answer: A
Question: How many times digit 20 is used while writing numbers from 100 to 500?
Options:
A)20
B)30
C)15
D)25
E)20
Rationale: in 100 to 200 there are 5 20's
in 200 to 300 there are 5 20's
in 300 to 400 there are 5 20's
in 400 to 500 there are 5 20's
so, total 20 is 20's
CORRECT OPTION : A
Answer: A
Question: The sale price sarees listed for Rs.400 after successive discount is 10% and 5% is?
Options:
A)321
B)276
C)342
D)265
E)162
Rationale: Explanation:
400*(90/100)*(95/100) = 342
Answer: C
Answer: C
Question: Find the middle one when The sum of three consecutive even numbers is 42?
Options:
A)10
B)12
C)14
D)15
E)16
Rationale: 3 consecutive numbers can be a - 1, a, a + 1
So sum of numbers = 3a = 42.
Hence a = 14.
C
Answer: C
Question: A shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 3 a rupee. Find his net profit or loss percent?
Options:
A)31%
B)38 1/3%
C)33 1/3%
D)33%
E)35%
Rationale: C
33 1/3%
The total number of mangoes bought by the shopkeeper be 12.
If he buys 4 a rupee, his CP = 3
He selling at 3 a rupee, his SP = 4
Profit = SP - CP = 4 - 3 = 1
Profit Percent = 1/3 * 100 = 33 1/3 %
Answer: C
Question: A train 100 meters long completely crosses a 300-meter long bridge in 40 seconds. What is the speed of the train in km/h?
Options:
A)28 km/h
B)32 km/h
C)36 km/h
D)40 km/h
E)44 km/h
Rationale: speed = distance / time = (100 + 300)/40 = 400/40 (m/s) * 3600/1000 = 36 km/h
The answer is C.
Answer: C
Question: Henrikh lives x blocks from his office. It takes him 1 minute per block to walk to
work and 20 seconds per block to ride his bicycle to work. If it takes him exactly
10 minutes more to walk to work than to ride his bicycle, then x equals
Options:
A)4
B)7
C)10
D)15
E)20
Rationale: The best way would be...
Per km, he takes 40 secs extra if he walks
So he will take 10 mins or 10*60 secs in 10*60/40 =15 km
ANSWER:D
Answer: D
Question: A cube is painted red on all faces. It is then cut into 27 equal smaller cubes. How many cubes are painted on only 2 faces?
Options:
A)12
B)8
C)6
D)10
E)16
Rationale: The mini-cubes with 2 painted sides are ALL on the edge of the cube, in the "middle" of the edge.
There are 4 in front, 4 in back and 4 more on the "strip" that runs around the left/top/right/bottom of the cube.
4 + 4 + 4 = 12.
Answer A
Answer: A
Question: Which of the following is equal to the value of 2^6 + 2^6 + 3^6 + 3^6 + 3^6 ?
Options:
A)2^7
B)2^7 + 3^7
C)3^7
D)2^8 + 3^8
E)2^7 + 3^8
Rationale: 2^6 + 2^6 + 3^6 + 3^6 + 3^6
= 2 (2^6) + 3 (3^6)
= 2^1 (2^6) + 3^1 (3^6)
= 2^(1+6) + 3^(1+6)
= 2^7 + 3^7
Ans: B
Answer: B
Question: For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 40?
Options:
A)10
B)12
C)14
D)16
E)18
Rationale: 4n+7 > 1
4n> -6
n > -(3/2)
n> -1.5 (n = -1, 0, 1 ,2 3........ upto infinity)
From second constraint
4n+7 < 40
4n< 33
n < 8. 25
n = (-infinity, .......-3, -2, -1, 0, 1, 2, .........upto 8)
Combining the two
-1.5 < n<8.25
n = 1 to 8 (48 integers)
and n = -1 and 0
so 10 integers.
A
Answer: A
Question: Points A, B, C, and D, in that order, lie on a line. If AB = 3 cm, AC = 4 cm, and BD = 9 cm, what is CD, in centimeters?
Options:
A) 1
B) 8
C) 3
D) 4
E) 5
Rationale: Putting a value to each point, lets use the following:
A - 0
B - 3 (AB = 3)
C - 4 (AC = 4)
D - 12 (BD = 9)
CD is 12-4 = 8.
Ans B
Answer: B
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
Options:
A)40 sec
B)22 sec
C)27 sec
D)17 sec
E)37 sec
Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 2/25 = 40 sec
Answer:A
Answer: A
Question: A and B enter into a partnership with capitals in the ratio 2 : 3. At the end of 9 months, A withdraws from the business. If their profits are in the ratio 1 : 2, how long did B invest his capital?
Options:
A)12 months
B)8 months
C)10 months
D)14 months
E)None of these
Rationale: Explanation:
Let the initial investment of A and B be Rs. 2x and Rs. 3x respectively.
Let B invested for a period of y months.
Then, ratio of capitals of A and B
= (2x × 9) : (3x × y) = 1 : 2
=> 18x/(3x × y) = 1/2
=> 6/y = 1/2
=> y = 12
Hence, B's investment is for 12 months.
Answer: Option A
Answer: A
Question: Carol, Belle and Andrew are business partners. Carol's capital is Rs.12000. If his share of a profit of Rs.1000 is Rs.380 and Andrew's share is Rs.250, what is Belle's capital?
Options:
A)116847.21
B)14684.21
C)21684.21
D)11684.21
E)11685.21
Rationale: 380 + 250 = 630
1000 - 630 = 370
380 ---- 12000
370 ---- ? => 11684.21
ANSWER:D
Answer: D
Question: 12x − 12 = 12y
5y + 5x = 15
Which of the following is the number of solutions to the system of equations shown above?
Options:
A)More than three
B)Exactly three
C)Exactly two
D)Exactly one
E)None
Rationale: => 12x - 12y = 12
=> x- y =1 -- 1
5y + 5x = 15
=>x + y = 3 -- 2
From equation 1 and 2 , we get
2x = 2
=> x=1
y=1
Therefore , the given system will have Exactly one solution
Answer : D
Answer: D
Question: On dividing 109 by a number, the quotient is 9 and the remainder is 1. Find the divisor
Options:
A)12
B)14
C)16
D)18
E)19
Rationale: d = (D-R)/Q
= (109 - 1)/9
= 108/9 = 12
A)
Answer: A
Question: 12, 24, 16, 32, 24, 48, ?
Options:
A)31
B)32
C)36
D)37
E)40
Rationale: E
40
This is an alternating multiplication and subtracting series with a pattern x2, -8, x2, -8.
Answer: E
Question: A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 6km?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: M = 4
S = 2
US = 4 - 2 = 2
D = 6
T = 6/2 = 3 Answer:A
Answer: A
Question: A bag contains 4 black, 5 yellow and 6 green balls. Three balls are drawn at random from the bag. What is the probability that all of them are yellow?
Options:
A)2/91
B)1/81
C)1/8
D)2/81
E)3/40
Rationale: Total number of balls = 4 + 5 + 6 = 15
Let S be the sample space.
n(S) = Total number of ways of drawing 3 balls out of 15 = 15C3
Let E = Event of drawing 3 balls, all of them are yellow.
n(E) = Number of ways of drawing 3 balls, all of them are yellow
= Number of ways of drawing 3 balls from the total 5 = 5C3
(∵ there are 5 yellow balls in the total balls)
P(E) = n(E)/n(S)
=5C3/15C3=5C2/15C3 [∵ nCr = nC(n - r). So 5C3 = 5C2. Applying this for the ease of calculation]
=(5×4/2×1)/(15×14×13/3×2×1)=5×4/(15×14×13/3)=5×4/5×14×13=4/14×13=2/7×13=2/91
ANSWER:A
Answer: A
Question: Which of the following is equal to (n – 3)2*square* if
n = 11?
Options:
A)(n + 6)(n – 6)
B)(n + 5)(n – 7)
C)(n + 4)(n – 8)
D)(n + 3)(n – 9)
E)(n + 2)(n – 10)
Rationale: If n = 11, then:
(n – 3)2 = (11 – 3)2 = 82 = 64
Substitute 11 for n into each answer until you find one that equals 64:
(n + 6)(n – 6) = (17)(5) = 85
(n + 5)(n – 7) = (16)(4) = 64 You’ve found a match
correct answer B)(n + 5)(n – 7)
Answer: B
Question: Rs. 5000 is divided into three parts A, B and C. How much A is more than C if their ratio is 1/5:1/5:1/10?
Options:
A)1000
B)992
C)772
D)552
E)312
Rationale: 1/5:1/5:1/10 = 2:2:1
1/5*5000 = 1000
2000-1000 = 1000
Answer: A
Answer: A
Question: a, b are positive integers. The remainder of a to be divided by 7 is 6 and the remainder of b to be divided by 8 is 5.
Which is possible to be the remainder of a*b to be divided by 52
Options:
A)a) 2
B)b) 6
C)c) 8
D)d) 12
E)e) 30
Rationale: Two ways to do it...
a=7x+6..
b=8y+5..
1) convenient way..
Take x and y as 0, and you will get a*b as 6*5=30
Answer : E
Answer: E
Question: The ratio of the ages of Maala and Kala is 4 : 3. The total of their ages is 2.8 decades. The proportion of their ages after 0.8 decades will be [1 Decade = 10 years]
Options:
A)4:3
B)12:11
C)7:4
D)6:5
E)6:7
Rationale: Explanation:
Let, Maala’s age = 4A and Kala’s age = 3A
Then 4A + 3A = 28
A = 4
Maala’s age = 16 years
and Kala’s age = 12 years
Proportion of their ages after 8 is = (16 + 8) : (12 + 8)
= 24 : 20
= 6 : 5 .. Answer: D
Answer: D
Question: It is being given that (232 + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?
Options:
A)(2 16 + 1)
B)(2 16 - 1)
C)(7 x 2 23)
D)(2 96 + 1)
E)None of these
Rationale: Explanation:
Let 232 = x. Then, (232 + 1) = (x + 1).
Let (x + 1) be completely divisible by the natural number N. Then,
(296 + 1) = [(232)3 + 1] = (x3 + 1) = (x + 1)(x2 - x + 1), which is completely divisible by N, since (x + 1) is divisible by N.
ANSWER IS D
Answer: D
Question: A six-sided die is rolled once. What is the probability that the number rolled is an even number greater than 5?
Options:
A)2 / 3
B)1 / 6
C)3 / 3
D)4 / 5
E)2 / 4
Rationale: Only 6 so, 1 / 6
correct answer B
Answer: B
Question: Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 12 seconds. Find the length of the faster train?
Options:
A)270
B)288
C)266
D)120
E)126
Rationale: Relative speed = (72 - 36) * 5/18 = 2 * 5 = 10 mps.
Distance covered in 12 sec = 27 * 10 = 270 m.
The length of the faster train = 120 m.
Answer: D
Answer: D
Question: The greatest possible length which can be used to measure exactly the lengths 7 m, 3 m 85 cm, 12 m 95 cm is
Options:
A)16 cm
B)25 cm
C)30 cm
D)35 cm
E)40 cm
Rationale: Explanation:
So by now, you must be knowing this is a question of HCF, right.
H.C.F. of (700 cm, 385 cm, 1295 cm) = 35 cm.
Option D
Answer: D
Question: What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 7?
Options:
A)70,592
B)64,850
C)64,749
D)149,700
E)156,720
Rationale: Find the number , Upon Sum of 3 Digits of a number Gives a Reminder 2 when it is Divided by 7
Seeing the Options After Dividing an Finding the Reminder of 2
My Answer was A
Answer: A
Question: A person walks at a speed of 4 km/hr and runs at a speed of 8 km/hr. How many hours will the person require to cover a distance of 4 km, if the person completes half of the distance by walking and the other half by running?
Options:
A)0.25
B)0.5
C)0.75
D)1
E)1.25
Rationale: time = 2/4 + 2/8 = 6/8 = 0.75 hours
The answer is C.
Answer: C
Question: A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart is
Options:
A)1/13
B)2/13
C)1/26
D)1/52
E)1/67
Rationale: Explanation:
Total number of cases = 52
Favourable cases = 2
Probability = 2/56 = 1/26
Answer: Option C
Answer: C
Question: What is the remainder when the number Q=14^2 * 15^8 is divided by 5?
Options:
A)0
B)1
C)2
D)4
E)5
Rationale: 14^2 has units digit 6
15^8 has units digit 5
Thus Q=14^2*15^8 has units digit 0 and will be divisible by 5. The remainder will be zero
Answer: (A)
Answer: A
Question: In an electric circuit, three resistors with resistances 2 ohms, 5 ohms and 6 ohms are connected in parallel. In this case, if R is the combined resistance of these three resistors, then the reciprocal of R is equal to the sum of the reciprocals resistors. What is R value?
Options:
A)13/15 ohms
B)15/13 ohms
C)5/8 ohms
D)3/7 ohms
E)45/18 ohms
Rationale: The wording is a bit confusing, though basically we are told that 1/R = 1/2 + 1/5 + 1/6, from which it follows that R=13/15ohms
Option: A
Answer: A
Question: An amount of Rs.3120 was divided among A, B and C, in the ratio 1/2 : 1/3 : 1/4. Find the share of A?
Options:
A)1320
B)1196
C)1210
D)1440
E)1050
Rationale: Let the shares of A, B and C be a, b and c respectively.
a : b : c = 1/2 : 1/3 : 1/4
Let us express each term with a common denominator which is the last number divisible by the denominators of each term i.e., 12.
a : b : c = 6/12 : 4/12 : 3/12 = 6 : 4 : 3.
Share of A = 6/13 * 3120 = Rs. 1440
Answer: D
Answer: D
Question: Ann and Bob drive separately to a meeting. Ann's average driving speed is greater than Bob's avergae driving speed by one-third of Bob's average driving speed, and Ann drives twice as many miles as Bob. What is the ratio Q of the number of hours Ann spends driving to the meeting to the number of hours Bob spends driving to the meeting?
Options:
A)8:3
B)3:2
C)4:3
D)2:3
E)3:8
Rationale: Say the rate of Bob is 3mph and he covers 6 miles then he needs 6/3=2 hours to do that.
Now, in this case the rate of Ann would be 3+3*1/3=4mph and the distance she covers would be 6*2=12 miles, so she needs 12/4=3 hours for that.
The ratio Q of Ann's time to Bob's time is 3:2.
Answer: B.
Answer: B
Question: The sum of four consecutive even numbers is 292. What would be the smallest number?
Options:
A)33
B)88
C)70
D)123
E)12
Rationale: Let the four consecutive even numbers be 2(x - 2), 2(x - 1), 2x, 2(x + 1)
Their sum = 8x - 4 = 292 => x = 37
Smallest number is: 2(x - 2) = 70.
Answer: C
Answer: C
Question: The sum R of the arithmetic sequence a, a+d, a+2d,..., a+(n-1)d is give by Rn = (n/2)*(2a + n-1)d. What is the sum of the integers 1 to 100 inclusive, with the even integers between 25 and 63 omitted.
Options:
A)4345
B)4302
C)4258
D)4214
E)4170
Rationale: a method to do it under one minutes is to take advantage of the choices given...
lets work on the last digit aswe have different units digit in each choice...
total sum of 1 to 100 inclusive will have 0 as the last digit..
this is so because the resultant will be 10*(sum of all single digits)... and since we are multiplying by 10,units digit will be 0...
now for single digit in sum R of even number from 25 to 63..
25 to 65 will have 4 times sum of single digit even int, 4*(2+4+6+8+0)=4*20..
here too the units digit is 0, but 64 has to be excluded from the total..
two ways from here on..
1) we are subtracting 0 from 0
so units digit should be 0, but we have to add 64..
so last/units digit =4..
2)we subtract 64 from sum of even int..
so units digit=80-4=76..
or units digit =6...
so our answer should have units digit as 10-6=4..
only D has 4 as units digit..
ans D
Answer: D
Question: A batsman scored 140 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?
Options:
A)45(4/11) %
B)45 %
C)45(5/11) %
D)57(1/7) %
E)None of these
Rationale: Explanation :
Total runs scored = 140
Total runs scored from boundaries and sixes = 3 x 4 + 8 x 6 = 60
Total runs scored by running between the wickets = 140 - 60 = 80
Required % = (80/140) × 100 = 400/7 = 57(1/7)%
Answer : Option D
Answer: D