divelab/Sys2Bench huggingface dataset:
Question: If the ratio of the sum of the first 6 terms of a G.P. to the sum of the first 3 terms of the G.P. is 65, what is the common ratio of the G.P?
Options:
A)4
B)1/4
C)2
D)9
E)1/9
Rationale: 65=(a1+a2+a3+a4+a5+a6)/(a1+a2+a3)
Factorize the same terms
65=1+(a4+a5+a6)/(a1+a2+a3)
Write every term with respect to r
a1=a1
a2=a1*r^1
a3=a1*r^2
.........
65=1+(a1(r^3+r^4+r^5))/(a1(1+r^1+r^2))
64=(r^3 (1+r^1+r^2))/((1+r^1+r^2))
64=r^3
r=4
A
Answer: A
Question: Three people have $36, $72, and $98, respectively. If they pool their money then redistribute it among them, what is the maximum value for the median amount of money?
Options:
A)$103
B)$85
C)$98
D)$101
E)$202
Rationale: Solution -
Total money distributed is $206. In order to maximize median, one person has to accept $0 and remaining two people share $103 each. Hence median is $103.
ANS A
Answer: A
Question: All the faces of cubes are painted with red colour.It is then cut into 64 equal small cubes.Find How many small cubes have only one face coloured ?
Options:
A)4
B)8
C)16
D)24
E)2
Rationale: There are 64 small cubes,Hence one side side of the big cube is 3√64=4 cm
Number of small cubes having only one face coloured = (x - 2)2 x No. of faces
= (4 - 2)^2 x 6
= 24
Answer:D
Answer: D
Question: If Juan takes 16 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?
Options:
A)16x/y
B)16y/x
C)x/(16y)
D)16/(xy)
E)xy/16
Rationale: This problem is testing us on the Rate x Time = Distance relationship. This relationship also tells us that Rate = Distance/Time and Time = Distance/Rate.
Ultimately, we are looking for how many seconds it will take Juan to run x yards. Thus, the equation we’ll use is: Time = Distance/Rate. We know the distance is x yards, and we need to find Juan’s rate.
We can find Juan’s rate as follows: Rate = Distance/Time = y yards/16 seconds
Using that rate, we need to determine how long it takes him to run x yards at the same rate. So we have:
Time = Distance/Rate
Time = x yards/(y yards/16 seconds)
Time = (x yards) x (16seconds/y yards)
Time = 16x/y seconds
Answer A.
Answer: A
Question: Find the odd man out 2, 3, 6, 15, 52.5, 157.5, 630
Options:
A)6
B)157.5
C)15
D)3
E)52.5
Rationale: 2 x 1.5 = 3
3 x 2 = 6
6 x 2.5 = 15
15 x 3 = 45
ANSWER:E
Answer: E
Question: A man walks at a speed of 5 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?
Options:
A)1 4/5 hours
B)2 hours
C)2 1/6 hours
D)2 1/3 hours
E)2 1/2 hours
Rationale: Required time
= (5 1/4)/5 + (5 1/4)/7
= 1 4/5 hours.
Answer:A
Answer: A
Question: A straight line in the xy- plane has y-intercept of 49 . On this line the x-coordinate of the point is 71 and y-coordinate is 12 then what is the slope of the line?
Options:
A)0.5
B)0.51
C)-0.52
D)0.31
E)-0.49
Rationale: Eq of line = Y = MX +C
C= 49
X=71
Y=12
Substitute given:
M = (Y-C) / X = (12 - 49) / 71 = -37/71 = -0.52
correct option is C
Answer: C
Question: Bob and Sue are building a brick wall. They can each lay fifty bricks per hour. If Bob takes a one hour break after every two hours of working, and Sue takes a one-hour break after every three hours of working, how long will it take them to finish the wall if they need to lay 600 bricks to finish the wall?
Options:
A)6 hours
B)7 hours
C)8 hours
D)9 hours
E)10 hours
Rationale: Bob works 2 hours out of every 3. Sue works 3 hours out of every 4. They can each lay 50 bricks per hour of work. Laying 600 bricks will take a total work of 600/50 = 12 hours. After 6 hours, Bob has done 4 hours of work and Sue has done 5 hours of work, for a total of 9 hours. After 7 hours, Bob has done 5 hours of work and Sue has done 6 hours of work, for a total of 11 hours. After 8 hours, Bob has done 6 hours of work and Sue has done 6 hours of work, for a total of 12 hours. Therefore, the answer is C.
Answer: C
Question: If the side length of Square B is sqrt(5) times that of Square A, the area of Square B is how many times the area of Square A?
Options:
A)1.5
B)2
C)3
D)4
E)5
Rationale: Let x be the side length of Square A.
Then the area of Square A is x^2.
The area of Square B is (sqrt(5)x)^2=5x^2.
The answer is E.
Answer: E
Question: If a clock strikes 12 in 33 seconds, it will strike 6 in how many seconds?
Options:
A)33⁄2
B)15
C)12
D)22
E)None of these
Rationale: In order to strike 12, there are 11 intervals of equal time
= 33⁄11 = 3 seconds each
Therefore, to strike 6 it has 5 equal intervals, it requires 5 × 3 = 15 sec.
Answer B
Answer: B
Question: What is the average (arithmetic mean) of the numbers 5, 6, 7, 7, 8, and 9?
Options:
A) 4.2
B) 6.5
C) 6
D) 7
E) 8
Rationale: {5, 6, 7, 7, 8, 9}={7-2,7-1, 7, 7,7+1,7+2} --> the average = 7.
Answer: D.
Answer: D
Question: (1/2) of a number is 3 more than the (1/6) of the same number?
Options:
A)6
B)7
C)8
D)9
E)10
Rationale: Take a number as x.
(1/2) of a number is 3 more than the (1/6) of the same number.
i.e., x/2 = 3+(x/6)
=> x/3 = 3
=> x = 9
ANSWER:D
Answer: D
Question: A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 4 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold?
Options:
A)480
B)287
C)289
D)270
E)927
Rationale: 1/x - 1/20 = -1/24
x = 120
120 * 4 = 480
Answer: A
Answer: A
Question: A part of certain sum of money is invested at 9% per annum and the rest at 15% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is?
Options:
A)4:2
B)4:8
C)5:3
D)4:0
E)4:9
Rationale: 15:9
= 5:3
Answer: C
Answer: C
Question: A can run 4 times as fast as B and gives B a start of 60 m. How long should the race course be so that A and B might reach in the same time?
Options:
A)70 m
B)60 m
C)80 m
D)65 m
E)75 m
Rationale: Speed of A:Speed of B=4:1
means in a race of 4m A gains 3m.
then in a race of 60m he gains 60*(4/3)
I.e 80m
ANSWER:C
Answer: C
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 250 resolutions?
Options:
A)352 m
B)704 m
C)454 m
D)186 m
E)176 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 250 resolutions.
= 250 * 2 * 22/7 * 22.4
= 35200 cm
= 352 m
Answer: A
Answer: A
Question: If x is the median of the set {9/2, 10/3, 27/9, 21/5, x}, x could be
Options:
A)16/5
B)17/5
C)28/7
D)30/7
E)31/7
Rationale: The median is the middle number once all the numbers are arranged in increasing/decreasing order.
We see that
10/3 = 3.something,
27/9 = 3.something
21/5 = 4.something
9/2 = 4.something
So x should greater than the smallest two numbers and smaller than the greatest two numbers. We can see that x = 4 is possible. (First look at the simplest option or the middle option since options are usually arranged in increasing/decreasing order)
Answer (C)
Answer: C
Question: 12, 38, 116, 350, 1052, ?
Options:
A)5815
B)3815
C)3518
D)3158
E)1538
Rationale: 12
12 × 3 + 2 = 38
38 × 3 + 2 = 116
116 × 3 + 2 = 350
350 × 3 + 2 = 1052
1052 × 3 + 2 = 3158
Answer is D.
Answer: D
Question: A, B and C enter into a partnership. They invest Rs.40,000, Rs.80,000 and Rs.1,20,000 respectively. At the end of the first year, B withdraws Rs.40,000 while at the end of the second year, C withdraws Rs.80,000. In what ratio will the profit be shared at the end of 3 years?
Options:
A)2 : 3 : 5
B)3 : 4 : 7
C)4 : 5 : 9
D)None of these
E)Cannot be determined
Rationale: Solution
A : B: C	=(40000×36) : (80000×12+40000×24) : (120000×24+40000×12)
=144 :192 :336
= 3 : 4 : 7.
Answer B
Answer: B
Question: Taps A and B can fill a bucket in 12 minutes and 15 minutes respectively. If both are opened and B is closed after 3 minutes, how much further time would it take for A to fill the bucket?
Options:
A)5min. 50sec.
B)5min. 30 sec.
C)6 min 36 sec.
D)6mins. 32 sec.
E)6 min. 15 sec.
Rationale: Explanation:
Part filled in 3 minutes =
3∗(1/12+1/15)=3∗9/60=9/20
Remaining part =1−9/20=11/20
=>1/12:11/20=1:X
=>X=6.6 mins.
=>X=6.6 mins.
So it will take further 6 mins 36 seconds to fill the bucket.
Option C
Answer: C
Question: James took a 3-hour bike ride. In the second hour he traveled 6 miles, which was 20 percent farther than he traveled the first hour. If he traveled 25 percent farther in the third hour than he did in the second hour, how many miles did jose travel during the entire ride?
Options:
A)54.0
B)54.9
C)18.5
D)57.0
E)63.0
Rationale: Let the distance travelled in the first hour be x. Thus, 1.2x = 6, x = 5. Now, the distance travelled in the 3rd hour = 6+1/4âˆ—6=7.5 The only option ending with a 0.5 in the decimal place is C.
ANSWER:C
Answer: C
Question: Dimitri weighs x pounds more than Allen weighs. Together, Allen and Dimitri weigh a total of 2y-y pounds. Which of the following represents Allen’s weight?
Options:
A)y - x/2
B)2x - y/2
C)(y - x)/2
D)y - 2x
E)2x - y
Rationale: These type of multi-variable story problems are usually perfect for TESTing VALUES.
Here, we're told that Dimitri weighs X pounds more than Allen weighs and that they weight a combined TOTAL of 2Y-Y or Y pounds.
IF....
Dimitri = 30
Allen = 20
X = 10
Y = 50
We're asked for Allen's weight, so we're looking for an answer that equals 20 when X = 10 and Y = 50.
Answer A: 50 - (10/2) = 45 NOT a match
Answer B: 20 - (50/2) = -5 NOT a match
Answer C: (50-10)/2 = 20 This IS a match
Answer D: 50 - 20 = 30 NOT a match
Answer E: 20 - 50 = -30 NOT a match
Final Answer:
C
Answer: C
Question: 24 oz of juice P and 25 oz of juice V are mixed to make smothies X and Y . The ratio of p to V in smothie X is 4 is to 1 and that in Y is 1is to 5.How many ounces of juice P are contained in the smothie X?
Options:
A)5
B)10
C)15
D)20
E)25
Rationale: Let us now solve for x:
(4/5)X + (1/6)(49-X) = 24
24x + 5(49-x) = (24)(30)
24x + 245-5x = (24)(30)
19x = 720 -245
19x = 475
x=25
ANSWER:E
Answer: E
Question: 895.7 – 573.07 – 95.007 = ?
Options:
A)227.623
B)224.777
C)233.523
D)414.637
E)None of these
Rationale: Solution
Given expression = 895.7 - (573.07 + 95.007) = 895.7 - 668.077 = 227.623. Answer A
Answer: A
Question: Which is smallest prime number?
Options:
A)97
B)109
C)103
D)95
E)163
Rationale: Answer:A
Answer: A
Question: The number of stamps that Kaye and Alberto had were in the ration of 5:3 respectively. After Kaye gave Alberto 10 of her stamps, the ration of the number of Kaye had to the number of Alberto had was 6:4. As a result of the gift, Kaye had how many more stamps than Alberto?
Options:
A)80
B)85
C)65
D)55
E)50
Rationale: C
K1 = 5x
A1 = 3x
K2 = 5x - 10
A2 = 3x + 10
K2/A2 = 6/4
(5x-10)/(3x+10) = 6/4
4*(5x-10) =6*(3x+10)
20x - 40 = 18x + 60
2x = 100
x = 50
K2 = 5*50 - 10 = 240
A2 = 3*50 + 10 = 160
K2 - A2 = 80
Answer : A
Answer: A
Question: What distance will be covered by a bus moving at 54 kmph in 30 seconds?
Options:
A)605
B)450
C)601
D)609
E)604
Rationale: 54 kmph = 54 * 5/18 = 15 mps
D = Speed * time = 15 * 30
= 450 m.
Answer: B
Answer: B
Question: Albert invested an amount of Rs. 8000 in a fixed deposit scheme for 2 years at compound interest rate 5 p.c.p.a. How much amount will Albert get on maturity of the fixed deposit?
Options:
A)Rs. 8600
B)Rs. 8620
C)Rs. 8820
D)Rs. 9820
E)None of these
Rationale: Explanation:
Amount
= Rs.[8000 x	(1 + 5/100)2]	= Rs. 8820.
ANSWER IS C
Answer: C
Question: You have a bag of 9 letters: 3 Xs, 3 Ys and 3 Zs. You are given a box divided into 3 rows and 3 columns for a total of 9 areas. How many different E ways can you place one letter into each area such that there are no rows or columns with 2 or more of the same letter?
Options:
A)5
B)6
C)9
D)12
E)18
Rationale: Consider one particular arrangement of the first row: XYZ, then we can construct only two boxes with so that no rows or columns have 2 or more of the same letter:
XYZ
YZX
ZXY
And:
XYZ
ZXY
YZX
Now, the first row itself can be arranged in 3!=6 ways (since there are three distinct letter), hence the total number of boxes possible E is 2*6=12.
Answer: D.
Answer: D
Question: A store reported total sales of $385 million for February of this year. If the total sales for the same month last year was $320 million, approximately what was the percent increase in sales?
Options:
A)2%
B)17%
C)20%
D)65%
E)83%
Rationale: New Value – Old Value)/Old Value x 100
We are given:
February sales this year = 385 million
February sales last year = 320 million
We need to determine the percent increase between sales from last year to sales this year.
Thus, the new value = 385 million and the old value = 320 million. Let’s plug them into our percent change formula.
(New Value – Old Value)/Old Value x 100
[(385 – 320)/320] x 100
65/320 x 100
13/64 x 100 ≈ 13/65 x 100 ≈ 1/5 x 100 ≈ 20%.
The answer is C.
Answer: C
Question: Fence X is twice as long as fence Y, and fence Y is 2 feet shorter than fence Z. If 3 feet were added to each fence, which of the following must be true?
I) X is twice as long as Y.
II) Y is 2 feet shorter than Z.
III) X is longer than Z.
Options:
A)I only
B)II only
C)III only
D)I and II
E)II and III
Rationale: Length of Z = z
Length of Y = z-2
Length of X = 2z-4
Minimum possible length of fence Z is 2 feet, because if we take the value for length of z below 2, lengths of Z and Y would be negative which is not possible.
If Z = 2
then Y = 0 and X = 0
When we add 3 feet in each fence, we will get
Z= 5
Y=3
X=3
Only Statement II holds true with above values.
ANSWER:B
Answer: B
Question: When Tom works alone he chops 4lb. salad in 3 minutes, and when Tammy works alone she chops 3 lb. salad in 4 minutes. They start working together, and after some time finish chopping 65 lb. of salad. Of those 80 lb., the salad quantity chopped by Tammy is what percent greater than the quantifying chopped by Tom?.
Options:
A)125 %
B)100%
C)25%
D)225%
E)400%
Rationale: Tom chops 8 lbs in 12 minutes
Tammy chopsWhen Tom works alone he chops 2 lb. salad in 3 minutes, and when Tammy works alone she chops 3 lb. salad in 2 minutes. They start working together, and after some time finish chopping 65 lb. of salad. Of those 80 lb., the salad quantity chopped by Tammy is what percent greater than the quantifying chopped by Tom?. 9 lbs in 6 minutes
So in the same amount of time, Tammy chops 125% more than Tom, since 9 is 125% greater than 4. So 125% is the answer.
Note that the actual time doesn't matter. If you multiply the time each work by x, you'll multiply the work each does by x, and 9x is still 125% greater than 4x.
Ans :A
Answer: A
Question: $100 is divided amongst A,B and C so that A may get 1/4 as much as B and C together, B may get 3/5 as much as A and C together, then the share of A is
Options:
A)$15
B)$20
C)$25
D)$18
E)$30
Rationale: A:(B+C) = 1:4
A's share = 100*1/5 = $20
Answer is B
Answer: B
Question: A train 150 meters long completely crosses a 240 meters long bridge in 42 seconds. What is the speed of the train is?
Options:
A)32
B)33
C)88
D)66
E)09
Rationale: S = (150 + 240)/42 = 390/42 * 18/5 = 33
Answer: B
Answer: B
Question: Four of the five parts numbered (a), (b), (c), (d) and (e) are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer.
Options:
A)16.80 × 4.50 + 4.4
B)1600 ÷ 40 + 16 × 2.5
C)5.5 × 8.4 + 34.6
D)1620 ÷ 20 – 1
E)1856.95 – 1680.65 – 96.3
Rationale: Others equal 80 whereas (c) equals 80.8.
Answer C
Answer: C
Question: If a coin is flipped, the probability that the coin will land tails is 1/2. If the coin is flipped 3 times, what is the probability that it will land tails up on the first flip and not on the last 2 flips?
Options:
A)1/8
B)1/4
C)1/3
D)1/2
E)3/4
Rationale: (1/2) * (1/2) * (1/2) = 1/8 Answer: A
Answer: A
Question: A shopkeeper buys mangoes at the rate of 6 a rupee and sells them at 5 a rupee. Find his net profit or loss percent?
Options:
A)34 %
B)33 %
C)20 %
D)35 %
E)30 %
Rationale: The total number of mangoes bought by the shopkeeper be 30.
If he buys 6 a rupee, his CP = 5
He selling at 5 a rupee, his SP = 6
Profit = SP - CP = 6 - 5 = 1
Profit Percent = 1/5 * 100 = 20 %
Answer:C
Answer: C
Question: A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train?
Options:
A)230 m
B)240 m
C)260 m
D)270 m
E)290 m
Rationale: 72 Kmph=72*5/18=20m/s
The train has to cover its length and the length of the platform
so the total distance =250+l
250+l=20*26
250+l=520
l=520-250
=270m
length of the train=270m
ANSWER:D
Answer: D
Question: fill in ht blank:
(a) the point with coordinates (0,0) is called ____ of a rectangular coordinate system,
(b) to find the x-intercept of a line, we let ___ equal 0 and solve for ___; to find y- intercept , we let ____ equal 0 and solve for___
Options:
A)(a) the point with coordinates (0,0) is called axis of a rectangular coordinate system, (b) to find the x-intercept of a line, we let x equal 0 and solve for y ; to find y- intercept , we let y equal 0 and solve for y; to find y- intercept , we let x equal 0 and solve for x
B)(a) the point with coordinates (0,0) is called end of a rectangular coordinate system, (b) to find the x-intercept of a line, we let x equal 0 and solve for x ; to find y- intercept , we let y equal 0 and solve for y
C)(a) the point with coordinates (0,0) is called origin of a rectangular coordinate system, (b) to find the x-intercept of a line, we let y equal 0 and solve for x ; to find y- intercept , we let x equal 0 and solve for y
D)(a) the point with coordinates (0,0) is called end of a rectangular coordinate system, (b) to find the x-intercept of a line, we let x equal 0 and solve for y ; to find y- intercept , we let y equal 0 and solve for x
E)none of the above
Rationale: (a) the point with coordinates (0,0) is called origin of a rectangular coordinate system, (b) to find the x-intercept of a line, we let y equal 0 and solve for x ; to find y- intercept , we let x equal 0 and solve for y
correct answer (C)
Answer: C
Question: Income and expenditure of a person are in the ratio 5:4. If the income of the person is Rs.18000, then find his savings?
Options:
A)Rs.3600
B)Rs.8600
C)Rs.3630
D)Rs.9600
E)Rs.2600
Rationale: Let the income and the expenditure of the person be Rs.5x and Rs.4x respectively.
Income, 5x = 18000 => x = 3600
Savings = Income - expenditure = 5x - 4x = x
So, savings = Rs.3600
Answer: A
Answer: A
Question: The area of a triangle is with base 12m and height 5m?
Options:
A)88 m2
B)30 m2
C)66 m2
D)77 m2
E)31 m2
Rationale: 1/2 * 12 * 5 = 30 m2
Answer: B
Answer: B
Question: The average score of a cricketer in 2 matches is 40 and in other 3 matches is 10. Then find the average score in all the 5 matches?
Options:
A)25
B)22
C)30
D)35
E)42
Rationale: Average in 5 matches = (2*40 + 3*10)/2+3 = 80+30 / 5 = 110/5 = 22
Answer is B
Answer: B
Question: The ages of Patrick and Michael are in the ratio of 3 : 5 and that of Michael and Monica are in the ratio of 3 : 5. If the sum of their ages is 147, what is the difference between the ages of Patrick and Monica?
Options:
A)48
B)47
C)46
D)49
E)52
Rationale: let their ages are 9x,15x and 25x respectively.
difference between the ages of Patrick and Monica = 25x-9x=16x where
49x=147 or x=3
so diff in ages = 16x=16*3=48 yrs
ANSWER:A
Answer: A
Question: The roof of an apartment building is rectangular and its length is 3 times longer than its width. If the area of the roof is 768 feet squared, what is the difference between the length and the width of the roof?
Options:
A)32.
B)40.
C)42.
D)44.
E)46.
Rationale: Answer is A : 42
Let w be the width , so length is 3w. Therefore : w*4w = 768, solving for, w = 16 , so 3w-w = 2w = 2*16 = 32
Answer: A
Question: In a group of 6 boys&4 girls a Committee of 4 persons is to be formed. In how many different ways can it be done so that the committee has at least 1girl?
Options:
A)180
B)185
C)190
D)195
E)200
Rationale: The committee of 4 persons is to be so formed that it has at least 1 woman The different ways that we can choose to form such a committee are:
(i) lw. 3 m in t 6X5X4' x 6C3 = 4x — — 80 3X2X1
x 6c2 =42:: x 26:: = 90 (ii) 2w. 2 m in °C2 (iii) 3w. 1 m in 4C3 x 6C1 = 4 x 6 = 24 (iv) 4w in 6C4 = 1 Total no. of different ways in which a committee of 4 persons can be formed so that it has at least one woman. = 80 + 90 + 24 + 1 = 195
D
Answer: D
Question: The unit digit in the product (124 * 812 * 816 * 467) is:
Options:
A)2
B)7
C)6
D)8
E)1
Rationale: Explanation:
Unit digit in the given product = Unit Digit in (4*2*6*7) = 6
ANSWER: C
Answer: C
Question: A man is 24 years older than his son. In two years, his age will be twice the age of his son. What is the present age of his son?
Options:
A)21
B)20
C)24
D)22
E)23
Rationale: Let present age of the son =x years
Then, present age the man =(x+24) years
Given that, in 2 years, man's age will be twice the age of his son
⇒(x+24)+2=2(x+2)⇒x=22
Answer is D.
Answer: D
Question: A building contractor employs 20 male, 15 female and 5 child workers. To a male worker he pays Rs.25 per day, to a female worker Rs.20 per day and a child worker Rs.8 per day. The average wage per day paid by the contractor is?
Options:
A)24
B)21
C)20
D)22
E)25
Rationale: 20 15 5
25 20 8
500 + 300 + 40 = 840/40 = 21
Answer: B
Answer: B
Question: At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.18000?
Options:
A)6620
B)2888
C)2776
D)2997
E)5958
Rationale: A = 18000(11/10)^3
= 23958
= 18000
----------
5958
Answer: E
Answer: E
Question: I purchased a superb bike and like my bike my number plate is also superb.
The number plate is a five digit number plate and its water image is 78633 more than the number plate.
Also all digits are unique.
Whats is my number plate number ?
Options:
A)10935
B)10968
C)23984
D)13725
E)11332
Rationale: B
10968
Water image is 89601
Answer: B
Question: Two different solutions of alcohol with respective proportions of alcohol to water of 3:1 and 2:3 were combined. What is the concentration of alcohol in the new solution if the first solution was 2.5 times the amount of the second solution?
Options:
A)62
B)65
C)68
D)70
E)72
Rationale: SOL:
Lets assume that 25L of sol1 was mixed with 10L of sol2.
Alcohol in Sol1: 25*3/4 = 18.75L
Alcohol in Sol2: 10*2/5 = 4L
Total Alcohol in the mixed solution of 35L = 18.75 + 4 = 22.75L
Alcohol concentration in the new sol: (22.75/35)*100 = 65%
ANSWER:B
Answer: B
Question: Which of the following is divisible by the first four positive even integer multiples of 31?
(i) 13020
(ii) 123752
(iii) 496496
Options:
A)None
B)iii only
C)ii and iii only
D)i and ii only
E)i, ii and iii
Rationale: A positive integer x is divisible by the first four integer multiples of 31 if and only if it is divisible by their least common multiple, 3*4*31=124.
124*4=496, so (iii)=(4000+4)*124=4004*124, hence (iii) is divisible by 124.
124*(1000-2)=124000-248=123752, so (iii) is divisible by 124.
Finally, 13020-10*124=13020-12400=620=5*124, so (i) is divisible by 124.
Answer E.
Answer: E
Question: A and B can finish a work in 12 days while A alone can do the same work in 20 days. In how many days B alone will complete the work?
Options:
A)76 days
B)30 days
C)98 days
D)31 days
E)22 days
Rationale: B = 1/12 – 1/20 = 2/60 = 1/30=> 30 days
Answer: B
Answer: B
Question: Mitali, a student of VIIIth standard, ranks eighth when put in class VIII A, ranks fifth when put in class VIII B, and ranks sixth when put in class VIII C. What will be Mitali's rank if students of all the three sections are put together?
Options:
A)17th
B)16th
C)15th
D)Cannot be determined
E)None of these
Rationale: 7+4+5=16
16 students have higher rank than her..
So answer is 17th
ANSWER:A
Answer: A
Question: A group of people, cats, and birds has seventy legs, thirty heads, and twenty
tails. How many cats are among this group? (Assume all birds have two legs and a tail.)
Options:
A)0
B)5
C)10
D)15
E)20
Rationale: Write P, C, and B for the number of people, cats, and birds respectively, so that
we have
2P + 4C + 2B = 70; P + C + B = 30; C + B = 20:
Comparing the last two equations we obtain P = 10, and the rst equation simplies to
4C + 2B = 50, or 2C + B = 25. Therefore,
C = (2C + B) / (C + B) = 25 / 5 = 5:
Alternatively,
C = 1
2
2P + 4C + 2B
P + C + B
= 35 - 30 = 5:
correct answer B
Answer: B