divelab/Sys2Bench huggingface dataset:
Question: From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first is a red card and the second is a king is?
Options:
A)1/26
B)1/27
C)1/87
D)1/67
E)1/21
Rationale: Let E1 be the event of drawing a red card.
Let E2 be the event of drawing a king .
P(E1 ∩ E2) = P(E1) . P(E2)
(As E1 and E2 are independent)
= 1/2 * 1/13 = 1/26
Answer:A
Answer: A
Question: The Average of six numbers is 8. The average of the first two is 11 and the average of the last three is 4. What is the middle number?
Options:
A)A)15
B)B)8
C)C)6
D)D)14
E)E)9
Rationale: The total of six numbers = 6X8 = 48
The total of first 2 and last 3 numbers is = 2 X 11+3 X 4 = 34
So, the middle number is (48 - 34 ) = 14
D
Answer: D
Question: If 5^23 * 4^12 = 2 * 10^n, what is the value of n?
Options:
A)11
B)21
C)22
D)23
E)32
Rationale: My attempt:
5^(23) * 4^(12) = 2*10^p
5^(23) * 2 ^ (24) = 2 * (2*5)^p
5^(23) * 2 ^ (24) = 2 * 2^(p) * 5^(p)
5^(23) * 2 ^ (24) = 2^(p+1) * 5^(p)
=> (p+1) = 24
=> p = 23
Answer: 23 (D)
Answer: D
Question: Ravi purchased a refrigerator and a mobile phone for Rs. 15000 and Rs. 8000 respectively. He sold the refrigerator at a loss of 5 percent and the mobile phone at a profit of 10 percent. Overall he make a.
Options:
A)50
B)288
C)27
D)200
E)881
Rationale: Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively.
r = 15000(1 - 5/100) = 15000 - 750
m = 8000(1 + 10/100) = 8000 + 800
Total SP - Total CP = r + m - (15000 + 8000) = -750 + 800 = Rs. 50
As this is positive, an overall profit of Rs. 50 was made.Answer:A
Answer: A
Question: A began business with 45,000 and was later joined by B with 54,000. When did B join if the profit at the end of the year were divided in the ratio 2 : 1?
Options:
A)5 months after
B)10 months after
C)7 months after
D)12 months after
E)None of these
Rationale: Let B join after ‘x’ month of the start of the business.
⇒ (45,000 × 12) : 54,000 × (12 – x) = 2 : 1
∴ (45,000 × 12) × 1 = 54,000 × (12 – x) × 2
⇒ x = 7
Answer C
Answer: C
Question: A military commander has to choose 6 soldiers out of a company of 9 for guarding the headquarters. How many different group combinations of 6 does he have to choose from?
Options:
A)84
B)15
C)16
D)27
E)35
Rationale: A military commander has to choose 6 soldiers out of a company of 9.
different group combinations of 6
He can do this in 9C6 ways
9*8*7*6*5*4/6*5*4*3*2*1= 84 ways
ANSWER:A
Answer: A
Question: Of all the students in a certain dormitory, 1/2 are first-year students and the rest are second-year students. If 4/5 of the first-year students have not declared a major and if the fraction of second-year students who have declared a major is 1/3 times the fraction of first-year students who have declared a major, what fraction of all the students in the dormitory are second-year students who have not declared a major?
Options:
A)7/15
B)1/5
C)4/15
D)1/3
E)2/5
Rationale: tot students=x
1st year student=x/2----> non majaor=4/5(x/2)-----> maj=1/5(x/2)
2nd year student=x/2---->maj=1/3(1/5(x/2))=1/30(x)--->non major=x/2-1/30(x)=7/15(x)
hence 7/15
A
Answer: A
Question: 45 workers work 8 hours to dig a hole 30 meters deep. How many extra workers should be hired to dig another hole 55 meters deep by working for 6 hours?
Options:
A)50
B)55
C)60
D)65
E)70
Rationale: 45 workers * 8 hours / 30 meters = x * 6 / 55
x = 110 total workers
110 - 45 = 65 new workers
The answer is D.
Answer: D
Question: The product of all the prime numbers less than 22 is closest to which of the following powers of 10?
Options:
A)a) 10^9
B)b) 10^7
C)c) 10^8
D)d) 10^6
E)e) 10^5
Rationale: Group these numbers so as to get product close to a multiple of 10, so they can be rewritten as (2*5)(3*7)(11*19)(13*17) or 10*21*209*221
Now take out power of 10 from each number and rewrite
10*10*100*100*(1*2.1*2.09*2.21) or 10^6*(1*2.1*2.09*2.21)
=9.69*10^6=10^7
B
Answer: B
Question: If r = ||s – 3| – 2|, for how many values of s is r = 7?
Options:
A)4
B)5
C)2
D)1
E)3
Rationale: r = ||s – 3| – 2| can be 4 only and only when s-3= +/-9. so there are 2 values of s
Answer : C
Answer: C
Question: What is the place value of 1 in the numeral 1259
Options:
A)A)1000
B)B)2800
C)C)2900
D)D)2980
E)E)3000
Rationale: 1 * 1000 = 1000
A
Answer: A
Question: A grocer buys apples for 81¢ per pound. If 10% of the apples goes bad and he still wants to make a 20% profit over his purchase price, what should be the sales price?
Options:
A)100¢
B)108¢
C)110¢
D)95¢
E)99¢
Rationale: for making calculation simple let us consider he buys 10pounds @ 81/pound=810¢ in total .
10% apples lost...means 9 pounds left.
further he wants 20% profit on 810 ¢
means he wants to earn 972¢
sales price should be 972/9=¢ 108
Ans B
Answer: B
Question: In a graduating class of 242 students, 144 took geometry and 119 took biology. What is the difference between the greatest possible number and the smallest possible number of students that could have taken both geometry and biology?
Options:
A)144
B)119
C)113
D)88
E)123
Rationale: Greatest Possible Number taken both should be 144 (As it is maximum for One)
Smallest Possible Number taken both should be given by
Total - Neither = A + B - Both
Both = A+B+Neither - Total (Neither must be 0 to minimize the both)
So 144 + 119 + 0 - 242 = 21
Greatest - Smallest is 144-21 = 123
So answer must be E. 123
Answer: E
Question: Ram professes to sell his goods at the cost price but he made use of 975 grms instead of a kg, what is the gain percent?
Options:
A)3 22/39%
B)4 22/39%
C)2 22/39%
D)7 22/39%
E)9 22/39%
Rationale: 975 --- 25
25 --- ? =>
25/975 *100
= 2 22/39%
Answer: C
Answer: C
Question: If the probability that Stock A will increase in value during the next month is 0.54, and the probability that Stock B will increase in value during the next month is 0.68. What is the greatest value for the probability that neither of these two events will occur?
A.
B.
C.
D.
E.
Options:
A)0.22
B)0.32
C)0.37
D)0.46
E)0.63
Rationale: This would be a different question if we knew the probabilities were independent --- that is, any increase in Stock A would tell you nothing about whether or not Stock B increased, and vice versa. If the question guaranteed that, then probability P(not A *and* not B) = P(not A)*P(not B) = (1 - 0.54)*(1 - 0.68) = (0.46)*(0.32) = 0.1472 We can't do that here, because the question does not specify that A and B are independent, but I share that because that's also a common type of question on the GMAT.
The best way to think about this particular question is this. Visualize a big circle: that's the space of everything that could happen with these two stocks next year, what statisticians call the "sample space." That represents 100%. The "B space", the area of that space where Stock B increases is 68% of that space, so only 32% is outside the "B space". We don't know the relationship of Stock A & Stock B, but we'd like to know where to put Stock A on the diagram to maximize the area that's outside of both the "A space" and the "B space." Well, with just the "B space" in the big circle, already 68% is taken up, and only 32% is free. If any of the "A space" is outside of the "B space", then it will eat up some of that free 32%. The only way to maximize that free space, to keep all 32% free, would be to put the entirety of "A space" inside "B space", that is, overlapping with "B space." That would be the real world situation in which Stock A rises *only if* Stock B rises: Stock B could go up without Stock A going up, but the the only way that Stock A can go up is if Stock B goes up too. That configuration would leave the maximum amount, 32%, in the region that overlaps with neither "A space" or "B space". Thus, the greatest value for the probability that neither of these two events will occur is 32%, or 0.32. Answer choice = B.
Answer: B
Question: A tradesman fixed his selling price of goods at 30% above the cost price. He sells half the stock at this price, one-quarter of his stock at a discount of 15% on the original selling price and rest at a discount of 30% on the original selling price. Find the gain percentage altogether?
Options:
A)14.875%
B)15.375%
C)15.575%
D)16.375%
E)16.5%
Rationale: Solution: Let CP = 100; then, marked price=130;
Now,
revenue = [(1/2)*130+(1/4)*0.85*130+(1/4)*0.7*130]
= 65+27.65+22.5 = 115.4;
% profit = 15.4*100/100 = 15.4%.
Answer: Option B
Answer: B
Question: An article is bought for Rs.600 and sold for Rs.500, find the loss percent?
Options:
A)18 2/3%
B)16 7/3%
C)16 2/8%
D)16 2/3%
E)76 2/3%
Rationale: 600 ---- 100
100 ---- ? => 16 2/3%
Answer:D
Answer: D
Question: 5 liters of a 20 percent solution of alcohol in water are mixed with 3 liters of a 12 percent alcohol in water solution. What is the percentage of alcohol in the new solution?
Options:
A)16.7%
B)17.0%
C)17.3%
D)17.6%
E)17.9%
Rationale: The total amount of alcohol is 0.2(5) + 0.12(3) = 1.36 liters.
The percentage is 1.36 / 8 = 136 / 800 = 17 / 100 which is 17%
The answer is B.
Answer: B
Question: The length, breadth and height of a room are in the ratio 12 : 4 : 4. If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will
Options:
A)(a) remain the same
B)(b) decrease by 13.64%
C)(c) decrease by 15%
D)(d) decrease by 18.75%
E)(e) decrease by 30%
Rationale: Length (L) = 12
Breadth (B) = 4
Height (H) = 4
Total Area of Walls = 2(BH + LH) = 2*(4*4 + 12*4) = 2*(16+48) = 128
Then, Finally
Length (L) = 2*12 = 24
Breadth (B) = 4/2 = 2
Height (H) = 4/2 = 2
Total Area of Walls = 2(BH + LH) = 2*(2*2 + 24*2) = 2*(4+48) = 104
% change in Area of four walls = (Final Area-Initial Area)*100 /Initial Area
i.e. % change in Area of four walls = (104-128)*100 /128=- 18.75% (Decrease)
Answer: Option D
Answer: D
Question: A certain number of men complete a piece of work in 60 days. If there were 8 men more, the work could be finished in 10 days less. How many men were originally there?
Options:
A)30
B)32
C)36
D)40
E)45
Rationale: Originally 1et there be x men.
More men, Less days
(x + 8) : x ∷ 60:50
So, x + 8 / x = 60/50 or x = 40.
ANSWER:D
Answer: D
Question: How many 2's are there between the terms 112 to 375?
Options:
A)A)156
B)B)157
C)C)158
D)D)159
E)E)160
Rationale: Let us calculate total 2's in the units place. (122, 132, 142 ... 192), (201, 212, 222, ... 292), (302, 312, ... 372) = 8 + 10 + 8 = 26
Total 2's in tenth's place, (120, 121, 122, ..., 129) + (220, 221, ..., 229) + (320, 321, ..., 329) = 30
Total 2's in hundred's place = (200, 201, ... 299) = 100.
Total 2's between 112 and 375 = 26 + 30 + 100 = 156
Answer:A
Answer: A
Question: What is greatest positive integer n such that 2^n is a factor of 12^11?
Options:
A)a)10
B)b)12
C)c)22
D)d)20
E)e)60
Rationale: The given number is 12^11
=(2*2*3)^11
=(2^22)*(3^11)
So the greatest possible value for n such that 2^n can be factor of given number is 22.
Answer C
Answer: C
Question: Find the amount on Rs.8000 in 9 months at 20% per annum, if the interest being compounded quarterly?
Options:
A)9269
B)9261
C)9262
D)9231
E)9263
Rationale: A = 8000(21/20)3 = 9261
Answer:B
Answer: B
Question: How many liters of water must be evaporated from 50 liters of a 1-percent sugar solution to get a 10-percent solution?
Options:
A)35
B)40
C)42
D)45
E)48
Rationale: 1% of a 50 liter solution is 0.5L which is 10% of the solution at the end.
The solution at the end must be 5 L.
We need to evaporate 45 liters.
The answer is D.
Answer: D
Question: A fair coin is tossed 13 times. What is the probability of getting more heads than tails in 13 tosses?
Options:
A)1/2
B)63/128
C)4/7
D)61/256
E)63/64
Rationale: On each toss, the probability of getting a head is 1/2 and the probability of getting a tail is 1/2.
There is no way to get the same number of heads and tails on an odd number of tosses.
There will either be more heads or more tails.
Then there must be more heads on half of the possible outcomes and more tails on half of the possible outcomes.
P(more heads) = 1/2
The answer is A.
Answer: A
Question: N is a positive integer. When N + 1 is divided by 6, the remainder is 4. What is the remainder when N is divided by 2?
Options:
A)6
B)5
C)1
D)3
E)2
Rationale: N+1 = 6a+4
i.e. N+1 = 10, 16, 22, 28, ... etc.
i.e. N = 9, 15, 21, 27, ... etc.
When N is divided by 2 Remainder is always 1
Answer: C
Answer: C
Question: A man sitting in a train which is traveling at 70 kmph observes that a goods train, traveling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed.?
Options:
A)50 kmph
B)58 kmph
C)62 kmph
D)65 kmph
E)42 kmph
Rationale: Relative speed = 280/9 m / sec = ((280/9)*(18/5)) kmph = 112 kmph.
Speed of goods train = (112 - 70) kmph = 42 kmph.
Answer : E
Answer: E
Question: The radius of a circular wheel is 1.75 m, how many revolutions will it make in traveling 1 km?
Options:
A)100
B)277
C)288
D)267
E)281
Rationale: 2 * 22/7 * 1.75 * x = 11000
x = 1000
Answer: A
Answer: A
Question: A man bought 20 shares of Rs. 50 at 5 discount, the rate of dividend being 13. The rate of interest obtained is:
Options:
A)12	1/2	%
B)13 1/2%
C)15%
D)16 2/3%
E)None of these
Rationale: Explanation:
Investment = Rs. [20 x (50 - 5)] = Rs. 900.
Face value = Rs. (50 x 20) = Rs. 1000.
Dividend = Rs.27/2 * 1000/100 =Rs. 135.
Interest obtained =(135/900 *100)%= 15%
ANSWER IS C
Answer: C
Question: The variables a and b are non-zero integers F. If a = 2b^3/c, what happens to c when a is halved and b is doubled?
Options:
A)c is not changed.
B)c is halved.
C)c is doubled.
D)c is multiplied by 4.
E)c is multiplied by 16.
Rationale: a =2b^3/c
c =2b^3/a
when a is halved and b is doubled
c=2(2b)^3/(a/2)
c=16*2b^3/a
Ans. E c is multiplied by 16.
Answer: E
Question: In the coordinate plane, points (x, 1) and (4, y) are on line k. If line k passes through the origin and has slope 1/4, then x + y =
Options:
A)1
B)2
C)4
D)5
E)7
Rationale: Line k passes through the origin and has slope 1/4 means that its equation is y=1/4*x.
Thus: (x, 1)=(4, 1) and (4, y) = (4,1) --> x+y=4+1=5.
Answer: D
Answer: D
Question: If 76 is divided into four parts proportional to 7, 5, 3, 4, then the smallest part is:
Options:
A)12
B)15
C)16
D)19
E)None of these
Rationale: Explanation:
Given ratio = 7 : 5 : 3 : 4, Sum of ratio terms = 19.
Smallest part =(76 x 3/19) = 12
Answer: A
Answer: A
Question: If 1/(m – 2) = 1/(m + 2) + 1/(m – 1), which of the following is a possible value of m?
Options:
A)0
B)-1
C)-2
D)1
E)2
Rationale: Multiply by (m-2)*(m+2)*(m-1) throughout to get:
(m+2)*(m-1) = (m-2)*(m-1) + (m+2)(m-2)
Of the given options, only m=0 satisfies this.
Answer : A
Answer: A
Question: The sum of squares of three numbers is 764 and sum of their products taken two at a time is 500. What is their sum?
Options:
A)48
B)42
C)52
D)32
E)33
Rationale: Description :
Let the numbers be x,y,z.
=> x2+y2+z2=764
=> 2(xy+yz+xz)=2*500=1000
=> (x+y+z)2=(x2+y2+z2)+2(xy+yz+xz)=1764
=> (x+y+z)=sqrt(1764)=42
Answer B
Answer: B
Question: A, B and C enter into a partnership by investing $7000, $11000 and $18000 respectively. At the end of 8 months, B receives $880 as his share. Find the share of A.
Options:
A)$320
B)$440
C)$560
D)$670
E)$780
Rationale: The ratio of capital of A, B and C = 7000 : 11000 : 18000 = 7 : 11 : 18
A's share = (7/11)*880 = $560
The answer is C.
Answer: C
Question: A man rows 750 m in 675 seconds against the stream and returns in 7 and half minutes. His rowing speed in still water is
Options:
A)4 kmph
B)5 kmph
C)6 kmph
D)7 kmph
E)None of these
Rationale: Explanation:
Rate upstream = (750/675) = 10/9 m/sec
Rate downstream (750/450) m/sec = 5/3 m/sec
Rate in still water = (1/2)*[(10/9) + (5/3)] m/sec.
= 25/18 m/sec
= (25/18)*(18/5) kmph
= 5 kmph
Option B
Answer: B
Question: The sale price of an article including the sales tax is Rs. 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 16%, then the cost price of the article is:
Options:
A)500
B)334
C)531
D)664
E)5598
Rationale: 110% of S.P. = 616
S.P. = (616 * 100)/110 = Rs. 560
C.P = (110 * 560)/116 = Rs. 531
Answer: Option C
Answer: C
Question: Find the value of e from (14)^2 x 5^3 Ã· 568 = e.
Options:
A)13.1
B)43.1
C)40.1
D)23.1
E)45.1
Rationale: Given Exp. =(14)^2 x 5^3 Ã· 568 = e
= 196 x 125 Ã· 568
43.1
B
Answer: B
Question: In how many ways can the letters of the word 'LEADER' be arranged?
Options:
A)28 ways
B)35 ways
C)670 ways
D)230 ways
E)360 ways
Rationale: The word 'LEADER' contains 6 letters, namely 1L, 2E, 1A, 1D and 1R.
Required number of ways =6!/(1!)(2!)(1!)(1!)(1!)= 360
=360 ways.
Answer:E
Answer: E
Question: Evaluate:58- 12*3*2 =?
Options:
A)42
B)50
C)62
D)72
E)82
Rationale: According to order of operations, 12?3?2 (division and multiplication) is done first from left to right
12**2 = 4* 2 = 8
Hence
58- 12*3*2 = 58- 8 = 50
correct answer B
Answer: B
Question: A spike is hammered into a train rail. You are standing at the other end of the rail. You hear the sound of the hammer strike both through the air and through the rail itself. These sounds arrive at your point six seconds apart. You know that sound travels through air at 1100 feet per second and through steel at 16,500 feet per second. How far away is that spike?
Options:
A)7070.25 ft
B)7080.25
C)6070.25
D)8070.25
E)7170.25
Rationale: d = 1100(t + 6 ), d = 16500t, so 1100(t + 6) = 16500t
1100t + 6600 = 16500t, 1100t - 1100t + 6600 = 16500t-1100t, 6600 = 15400t
6600/15400 = 15400t/15400, 0.4285 = t, 1100(.4285 + 6) = 7071.35, 16500(.4285) = 7070.25
ANSWER:A
Answer: A
Question: How many positive factors of 42 are not factors of 56?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: 42=2*3*7.
So, total number of factors for 42 = 2*2*2 = 8
factors for 42 = 1,2,3,6,7,14,21 and 42
56=2*2*2*7
So, total number of factors for 56 = 4*2 = 8
factors of 56 = 1,2,4,7,8,14,28 and 56.
Factors same in 42 and 56 are 1,2,7 and 14.
Hence, answer will be D.
Answer: D
Question: The total of 334 of 20 paise and 25 paise make a sum of Rs. 71. The no of 20 paise coins is
Options:
A)250
B)277
C)278
D)200
E)288
Rationale: Explanation:
Let the number of 20 paise coins be x. Then the no of 25 paise coins = (334 - x).
0.20 * (x) + 0.25 (334 - x) = 71 => x = 250..
Answer: A) 250
Answer: A
Question: The least number which should be added to 2497 so that the sum is exactly divisible by 5, 6, 4 and 3 is:
Options:
A)3
B)13
C)23
D)33
E)43
Rationale: L.C.M of 5, 6, 4 and 3 = 60.
On dividing 2496 by 60, the remainder is 37. Number to be added = 60 - 37 = 23.
ANSWER:C
Answer: C
Question: The average (arithmetic mean) of four different positive integers is 15. If the first of these integers in 3 times the second integer and the second integer is 2 less than the third integer, what is the least possible value of the fourth integer?
Options:
A)8
B)4
C)3
D)2
E)1
Rationale: Let the second integer be x and the fourth be a.
Then [3x + x + (x+2) + a]/4 =15
=> 5x + 2 + a = 60
=> 5x + a = 58
=> a = 58 - 5x
From the above equation we can see that a is minimum when x is maximum, provided both are positive
The maximum value that x can take in the above equation while still keeping a positive is x=10
This gives us a= 58 - 50 =8
Therefore the minimum value that the fourth integer can have is 8. Option A.
Answer: A
Question: Country X imported approximately $1.20 billion of goods in 1996. If Country X imported $288 million of goods in the first two months of 1997 and continued to import goods at the same rate for the rest of the year, by how much would Country Xs 1997 imports exceed those of 1996?
Options:
A) $24 million
B) $120 million
C) $144 million
D) $240 million
E) $528 million
Rationale: Convert units to millions as answer is in millions
1996 Imports = $1.20 bill = $1200 mill
i.e. 1200/12 = $100 mill/month
1997 Imports = $288 mill/2 month
i.e. $144 mill/month
Difference/month = 144-100 = 44
Difference/year = $44 mill * 12 = $528 mill
ANSWER: E
Answer: E
Question: What is the maximum number of pieces of birthday cake of size 2” by 2” that can be cut from a cake 20” by 20”?
Options:
A)5
B)100
C)16
D)20
E)25
Rationale: The prompt is essentially asking for the maximum number of 2 x 2 squares that can be cut from a larger 20 by 20 square. Since each 'row' and each 'column' of the larger square can be sub-divided into 10 'pieces' each, we have (10)(10) = 100 total smaller squares (at maximum).
B
Answer: B
Question: How many litres of pure salt are there in 12 litres of a 25% solution?
Options:
A)1.14 litres
B)1.41 litres
C)2.56 litres
D)3 litres
E)34litres
Rationale: Explanation :
Quantity of pure salt = 25% of 12 litres
= (25/10012)litres
= 3 litres
Answer : D
Answer: D
Question: A fair price shopkeeper takes 10% profit on his goods. He lost 20% goods during theft. His loss percent is:
Options:
A)10%
B)45%
C)12%
D)17%
E)42%
Rationale: C
Suppose he has 100 items. Let C.P. of each item be Re. 1.
Total cost = Rs. 100. Number of items left after theft = 80.
S.P. of each item = Rs. 1.10
Total sale = 1.10 * 80 = Rs. 88
Hence, loss % = 12/100 * 100 = 12%
Answer: C
Question: present ages of A and B are in the ratio of 5:4 respectively. 5 years ago, the ratio of their ages was 4:3 respectively . what A's age in 5 year ago in years?
Options:
A)27
B)24
C)40
D)32
E)20
Rationale: A and B be 5x years and 4x years respectively
(5x-5)/(4x-5)=4/3
3(5x-5)= 4(4x-5), 15x-15=16x-20
x=5, therefore A's present age : 5x=25 years
A's age in 5 years ago = 25 - 5 = 20
correct answer(E)
Answer: E
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
Options:
A)298 m
B)277 m
C)245 m
D)256 m
E)267 m
Rationale: Speed = [45 X 5/18] m/sec
= [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30
= 25/2 => 2(130 + x) = 750 => x
= 245 m.
Answer: C
Answer: C
Question: In the formula V = (2r)^4, if r is halved, then V is multiplied by?
Options:
A)64
B)8
C)1
D)1/8
E)1/16
Rationale: Say r=2 => V1 = 256
when r=1; V2 = 16
V2 = 1/16*V1.
Answer : E
Answer: E
Question: A mixture of 180 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture?
Options:
A)4 liters
B)8 liters
C)10 liters
D)12 liters
E)12.5 liters
Rationale: Number of liters of water in180 liters of the mixture = 20% of 120 = 20/100 * 180 = 36 liters.
P liters of water added to the mixture to make water 25% of the new mixture.
Total amount of water becomes (36 + P) and total volume of mixture is (180 + P).
(36 + P) = 25/100 * (180 + P)
96+4P = 180+P
P = 12 liters.
Answer:D
Answer: D
Question: If equation |x/2| + |y/2| = 2 encloses a certain region on the coordinate plane, what is the area of this region?
Options:
A)20
B)32
C)100
D)200
E)400
Rationale: The equation can be reduced to intercept form as |x/4| + |y/4| = 1, so these are lines in four quadrants with x and y intercept as 14, so it is a rhombus with diagonals of 8 each and hence area = 1/2*d1*d2 = 1/2*8*8 = 32. Answer B.
Answer: B
Question: If two positive numbers are in the ratio 1/7 : 1/5, then by what percent is the second number more than the first?
Options:
A)70%
B)90%
C)60%
D)40%
E)65%
Rationale: Given ratio = 1/7 : 1/5 = 5 : 7
Let first number be 5x and the second number be 7x.
The second number is more than first number by 2x.
Required percentage = 2x/5x * 100 = 40%.
Answer:D
Answer: D
Question: A, B and C have Rs.500 between them, A and C together have Rs.200 and B and C Rs.350. How much does C have?
Options:
A)50
B)99
C)88
D)65
E)21
Rationale: A+B+C = 500
A+C = 200
B+C = 350
--------------
A+B+2C = 550
A+B+C = 500
----------------
C = 50
Answer: A
Answer: A
Question: The difference between the place value and the face value of 4 in the numeral 854973 is
Options:
A)973
B)6973
C)3996
D)6084
E)None of these
Rationale: (Place value of 4) - (Face value of 4) = (4000 - 4) = 3996
Answer: Option C
Answer: C
Question: What is the probability of rolling three six-sided dice, and getting a different number on each die?
Options:
A)1/12
B)1/3
C)4/9
D)5/9
E)7/18
Rationale: three dices were rolled
total outcome 6x6x6
different number should appear on each
favorable outcome= 6c1*5c1*4c1
probability= favorable/total
ans=(6*5*4)/(6*6*6)= 5/9
ans= D
Answer: D