divelab/Sys2Bench huggingface dataset:
Question: In a card game, a combination of three queens beats all others. If Jose is the first to draw from a standard deck of 52 cards, what is the probability that he wins the game with the best possible combination?
Options:
A)1/5425
B)1/5550
C)1/5600
D)1/5555
E)1/5525
Rationale: he best possible combination is the case when he wins in his first two draws
There are 52 cards in a deck of cards with 4 queens in it.
Probability of first card to be queen = 4/52
Probability of Second card to be queen = 3/51
Probability of third card to be queen = 2/50
Probability of Best possible case = (4/52)*(3/51)*(2/50) = 1/5525
E
Answer: E
Question: The probability that a number selected at random from first 50 natural numbers is a composite number is
Options:
A)21/25
B)17/25
C)4/25
D)8/25
E)10/25
Rationale: The number of exhaustive events = 50C1 = 50. We have 15 primes from 1 to 50.
Number of favourable cases are 34.
Therefore, Required probability = 34/50 = 17/25.
ANSWER:B
Answer: B
Question: If x^4 + y^4 = 20, then the greatest possible value of x is between:
Options:
A)0 to 2
B)2 to 4
C)4 to 6
D)6 to 8
E)8 to 10
Rationale: The answers to this question provide a great 'hint' as to how to go about solving it; since they're all essentially 'ranges', you can use them to figure out which solution contains the maximum value of X.
We're told that X^4 + Y^4 = 20. To maximize the value of X, we need to minimize the value of Y^4. The smallest that Y^4 could be is 0 (when Y = 0), so we'll have....
X^4 = 20
Looking at the answers, it makes sense to see what 2^4 equals....
2^4 = 16
Since that is BELOW 20, and 3^4 will clearly be MORE than 20, we have the correct answer.
Final Answer:
A
Answer: A
Question: Find the value of 1.5 x [(3.6 x 0.48 x 2.50) / (0.12 x 0.09 x 0.5)]
Options:
A)800
B)500
C)900
D)1200
E)None
Rationale: Answer
1.5 x [(3.6 x 0.48 x 2.50) / (0.12 x 0.09 x 0.5)]
= 1.5 x [(36 x 48 x 250) / (12 x 9 x 5)]
= 1.5 x 4 x 4 x 50 = 1200
Correct Option: D
Answer: D
Question: Sahil purchased a machine at Rs 11000, then got it repaired at Rs 5000, then gave its transportation charges Rs 1000. Then he sold it with 50% of profit. At what price he actually sold it.
Options:
A)Rs. 22500
B)Rs. 25500
C)Rs. 26000
D)Rs. 28000
E)None of these
Rationale: Explanation:
Question seems a bit tricky, but it is very simple.
Just calculate all Cost price, then get 150% of CP.
C.P. = 11000 + 5000 + 1000 = 17000
150% of 17000 = 150/100 * 17000 = 25500
Option B
Answer: B
Question: A sum of Rs.1550 was lent partly at 8% p.a. simple interest. The total interest received after 3 years was Rs.300. The ratio of the money lent at 5% to that lent at 8% is :
Options:
A)16:18
B)16:10
C)16:15
D)16:11
E)16:12
Rationale: let the sum lent at 5% be Rs.x and that lent at 8% be Rs.(1550-x). then,
Interest on x at 5% for 3 years + interest on (1550-x) at 8% for 3 years = 300
Required ratio = x : (1550-x) = 800 : (1550-800) = 800 : 750 = 16 : 15
Answer: C) 16:15
Answer: C
Question: A number is doubled and 5 is added. If the resultant is trebled, it becomes 105. What is that number?
Options:
A)9
B)15
C)18
D)None of these
E)Cannot be determined
Rationale: Explanation:
Let the number be x.
Therefore,
3(2x + 5) = 105
6x + 15 = 105
6x = 90
x = 15
ANSWER: B
Answer: B
Question: A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
Options:
A)253m
B)239m
C)236m
D)240m
E)230m
Rationale: Relative speed = (120 + 80) km/hr
200 x5/18= 500/9 m/sec
Let the length of the other train be x metres.
Then,x + 270/9	=500/9
x + 270 = 500
x = 230m
Answer E
Answer: E
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 25%. What quantity of whisky is replaced ?
Options:
A)1/3
B)2/3
C)2/5
D)3/5
E)4/5
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 = 0.26 ---> x = 20/3 ml.
Per the question, you need to find the x ml removed as a ratio of the initial volume ---> (20/3)/10 = 2/5.
Hence, C is the correct answer.
Answer: C
Question: Two trains start from two opposite directions towards each other. The stations from which they start are 50 miles apart. Both the trains start at the same time on a single track. A falcon which is sitting on one train. starts at the same time towards the other train. as soon as it reaches the second one, it flies back to the first train and so on and so forth. It continues to do so, flying backwards and forwards from one train to the other until the trains meet.
Both the trains travel at a speed of 25 miles per hour, and the bird flies at 100 miles per hour.
How many miles will the falcon have flown before the trains meet?
Options:
A)100 miles
B)140 miles
C)107 miles
D)230 miles
E)321 miles
Rationale: A
100 miles
The train travel at 25 miles per hour. Therefore, they will meet after travelling for one hour and the falcon also must have been flying for one hour. Since it travel at 100 miles per hour, the bird must have flown 100 miles.
Answer: A
Question: The ratio of the area of a square mirror to its frame is 16 to 33. If the frame has a uniform width (a) around the mirror, which of the following could be the value, in inches, of a ?
I. 2
II. 3 1/2
III. 5
Options:
A)I only
B)III only
C)I and II only
D)I and III only
E)I, II, and III
Rationale: Area of picture = 16x Area of frame = 33x
Area of picture / (Area of picture + area of frame) = 16x / 49x = 4x/7x.
This results in a value to be a multiple of 1.5 = multiple of 3/2 and since a is not constrained to be only integer all the three choices are possible
For i) the multiple of a is 4/3
For ii) the multiple of a is 7/3
For iii) the multiple of a is 10/3
The key is a can be any real positive number... very tricky problem.. took me > 15 minutes.
Answer is E
Answer: E
Question: The edges of a cuboid are 2 cm, 5 cm and 8 cm. Find the volume of the cuboid?
Options:
A)90
B)80
C)40
D)120
E)70
Rationale: 2*5*8
= 80
Answer: B
Answer: B
Question: There are x numbers in list L, where x is a positive integer, and there are y numbers in list M, where y is a positive integer. The average (arithmetic mean) of the numbers in list L is p, and the average of all the numbers in both lists L and M is q. Which of the following expressions is the average of the numbers in list M?
Options:
A)(qy - px) / x
B)(qy - px) / y
C)(p + q)x / y
D)[(q - p)x - py] / (x + y)
E)[(q - p)x + qy] / y
Rationale: You can eliminate Answer A (it divides by 2)
Answer B: (QY-PX)/Y = (7.8 - 4)/3 = 3.8/3 This is clearly too small. Eliminate B.
Answer C: (P+Q)X/Y = (4.6)(2)/3 = 9.2/3 This is too big. Eliminate C.
Answer E is all that's left, but I'll check it just to be sure....
Answer E: [(Q-P)X +QY]/Y = [(0.6)(2) +7.8]/3 = 9/3 = 3. This is a MATCH.
Final Answer:E
Answer: E
Question: In the xy-plane, the line y = k is the perpendicular bisector of the line segment PQ and the line x = g is the perpendicular bisector of the line segment RQ. If the coordinates of the point R are (-g, -k), then what are the coordinates of the point P?
Options:
A)(-5g, -5k)
B)(-3g, -3k)
C)(2g, 2k)
D)(3g, 3k)
E)(5g, 5k)
Rationale: firstly the Question tells us that RQ and PQ are perpendicular at Q..
Now the coordinates of the point R are (-g, -k), so R is at a distance of 2g from line x and at dist of 2k from line Y..
as line X bisect RQ .... length of RQ =4g and coord (3g,-k)..
as line Y bisect PQ .... length of PQ =4k and coord (3g,3k).ans D
Answer: D
Question: If a rectangular billboard has an area of 104 square feet and a perimeter of 42 feet, what is the length of each of the longer sides?
Options:
A)4
B)7
C)8
D)13
E)26
Rationale: This question can be solved algebraically or by TESTing THE ANSWERS.
We're told that a rectangle has an area of 104 and a perimeter of 42. We're asked for the length of one of the LONGER sides of the rectangle.
Since the answers are all INTEGERS, and the area is 104, the shorter side will almost certainly be less than 10 (since 10x10 = 100, but we're NOT dealing with a square). Answer B (7) does NOT divide evenly into 104, so the correct answer is probably A or C.
Let's TEST Answer C: 8
IF...
The shorter side = 8...
The area = 104....104/8 = 13 = the longer side
Perimeter = 8+8+13+13 = 42
D
Answer: D
Question: If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 2 years the amount to be paid is?
Options:
A)81288
B)2776
C)3777
D)8112
E)2887
Rationale: A = 7500(26/25)2 = 8112.Answer: D
Answer: D
Question: A computer system uses alphanumeric case sensitive characters for its passwords. When the system was created it required users to create passwords having 6 characters in length. This year, it added the option of creating passwords having 5 characters in length. Which of the following gives the expression for the total number of passwords the new computer system can accept?
Assume there are 62 unique alphanumeric case sensitive characters.
Options:
A)63^4
B)62^5
C)62(62^4)
D)63(62^5)
E)63(62^6)
Rationale: Total number of passwords = number of 6 character password +number of 5 character password
= 62^6 + 62^5 (Since there is no limitation on repetition , each character can be chosen in 62 ways )
=62^5(1+ 62)
=62^5 * 63
Answer D
Answer: D
Question: What will come in place of the x in the following Number series? 12, 38, 116, x,
Options:
A)2643
B)350
C)3456
D)7554
E)3158
Rationale: 12
12 Ã— 3 + 2 = 38
38 Ã— 3 + 2 = 116
116 Ã— 3 + 2 = 350
B
Answer: B
Question: Two persons A and B take a field on rent. A puts on it 21 horses for 3 months and 15 cows for 2 months; B puts 15 cows for 6months and 40 sheep for 7 1/2 months. If one day, 3 horses eat as much as 5 cows and 6 cows as much as 10 sheep, what part of the rent should A pay?
Options:
A)1/7
B)1/9
C)1/8
D)1/4
E)2/1
Rationale: 3h = 5c
6c = 10s
A = 21h*3 + 15c*2
= 63h + 30c
= 105c + 30c = 135c
B = 15c*6 + 40s*7 1/2
= 90c + 300s
= 90c + 180c = 270c
A:B = 135:270
27:52
A = 27/79 = 1/3.Answer:A
Answer: A
Question: How many numbers between 300 and 500 begin or end with 3?
Options:
A)20
B)60
C)100
D)110
E)120
Rationale: How many numbers between 300 and 500 begin or end with 3?
Just think that those numbers are:
i) The ones ending in 3: 303, 313, 323, ... , 493 --> 20 numbers
ii) The ones beginning in 3: 300, 301, 302, 303, ... , 393, ... , 399 --> 100 numbers
BUT 10 out of the first 20 numbers are repeated in the second set.
THEREFORE, the solution is 110 numbers.
Answer: D
Answer: D
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue?
Options:
A)1/455
B)1/452
C)1/412
D)1/129
E)1/410
Rationale: Explanation:
Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that all the three marbles picked at random are blue = Â³Câ‚ƒ/Â¹âµCâ‚ƒ = (1 * 3 * 2 * 1)/(15 * 14 * 13) = 1/455
Answer: A
Answer: A
Question: 6 In covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay's speed is:
Options:
A)5 kmph
B)6 kmph
C)6.25 kmph
D)7.5 kmph
E)7.8 kmph
Rationale: Let Abhay's speed be x km/hr.
Then,	30/X	-	30/2X	= 3
6x = 30
x = 5 km/hr. Answer: Option A
Answer: A
Question: How much does a watch lose per day, if its hands coincide every 64 minutes?
Options:
A)32 8⁄11 min.
B)36 5⁄11 min.
C)90 min.
D)96 min.
E)None of these
Rationale: 55 min. spaces are covered in 60 min.
60 min. spaces are covered in (60⁄55 × 60) min.
= 655⁄11 min.
Loss in 64 min. = (655⁄11 - 64) = 16⁄11 min.
Loss in 24 hrs. = (16⁄11 × 1⁄64 × 24 × 60) min = 328⁄11 min.
Answer A
Answer: A
Question: The milk level in a rectangular box measuring 60 feet by 25 feet is to be lowered by 6 inches. How many gallons of milk must be removed? (1 cu ft = 7.5 gallons)
Options:
A)100
B)250
C)750
D)5625
E)5635
Rationale: 6 inches = 1/2 feet (there are 12 inches in a foot.), so 60*25*1/2=750 feet^3 of milk must be removed, which equals to 750*7.5=5625 gallons.
Answer: D.
Answer: D
Question: If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be?
Options:
A)4 days
B)7 days
C)8 days
D)5 days
E)43 days
Rationale: Let 1 men's 1 day work = x and 1 boy's 1 day work = y.
Then, 6x + 8y = 1/10 and 26x + 48y = 1/2
Solving these two equations, we get:
x = 1/100 and y = 1/200
(15 men + 20 boys)'s 1 day work = (15/100 + 20/200) = 1/4
15 men and 20 boys can do the work in 4 days.
Answer: A
Answer: A
Question: The population of 6 villages is 803,900,1100,1023,945 and 980.what is the population of the seventh village if the average population of the seven villages is 1000?
Options:
A)1134
B)1238
C)1348
D)1500
E)1249
Rationale: Population of seventh village =7*1000-(803+900+1100+1023+945+980)=1249
Answer is E
Answer: E
Question: a, b, c, d are positive integers such that exactly one of the following inequalities is false. Which inequality is false?
Options:
A) a<b
B) c<d
C) a+c<b+c
D) a+c<b+d
E) a<b+c+d
Rationale: Essentially, we need to find the statement thatcouldbe false if all the other statements are true.
The first thing that jumps out to me is statements A and C:
(A) a < b
(C) a+c < b+c
Regardless of the value of c, these statement are either both false or both true. Since only statement CAN be false, we can eliminate these two.
(E) a < b+c+d
Since c and d are both positive integers, and we have determined that statement A is true, statement E must be true as well. This leaves us with:
(B) c < d
(D) a+c < b+d
Since we know statement A (a < b) to be true, if statement B is true, statement D MUST be true. However, if statement D is true, as long as c-d < b-a, statement B does NOT have to be true.
Therefore, the answer isB: c < d. Good question, +1.
Answer: B
Question: Tourist purchased a total of 30 travelers checks in $50 and $100 denominations. The total worth of the travelers checks is $1800. How many checks of $50 denominations can he spend so that average amount (arithmetic mean) of the remaining travelers checks is $100?
Options:
A)4
B)12
C)15
D)22
E)24
Rationale: you could set-up a quick table and brute force the answer.
A	4	*	50	200 1800	-200 1600	26 61.54
B	12	*	50	600 1800	-600 1200	18 66.67
C	15	*	50	750 1800	-750 1050	15 70.00
D	22	*	50	1000 1800	-1000	800	8 100.00
E	24	*	50	1200 1800	-1200	600	6 100.00
Answer is D
Answer: D
Question: A starts business with a capital of Rs.1200 B and C join with some investments after 3 and 6 months respectively. If the end of a year, the profit is divided in the ratio 2:3:5 respectively. What is B's investment in the business?
Options:
A)Rs.2400
B)Rs.1800
C)Rs.3600
D)Rs.6000
E)Rs.7000
Rationale: 1200 * 12: x * 9 = 2:3
x = 2400
ANSWER:A
Answer: A
Question: If {x} is the product of all even integers from 1 to x inclusive, what is the greatest prime factor of {12} + {10}?
Options:
A)23
B)20
C)13
D)5
E)2
Rationale: Soln:
{12} + {10} = 12*{10} +{10} = 13*{10}
ANSWER:C
Answer: C
Question: The length of a rectangle is twice its breadth. If its lengthis decreased by 5cm & breadth is increased by 5cm, the area of the rectangle is increased by 75sq.cm. What is the length of the rectangle?
Options:
A)25 cm
B)30 cm
C)40 cm
D)45 cm
E)60 cm
Rationale: Let breadth =x cm
Then, length =2x cm
Area =x×2x=2x2 sq.cm.
New length =(2x−5) cm
New breadth =(x+5) cm
New area =(2x−5)(x+5) sq.cm.
Given that, new area = initial area +75 sq.cm.
⇒(2x−5)(x+5)=2x2+75⇒2x2+10x−5x−25=2x2+75⇒5x−25=75⇒5x=75+25=100⇒x=1005=20 cm
Length =2x=2×20=40 cm
C
Answer: C
Question: A batsman scored 120 runs which included 5 boundaries and 5 sixes. What percent of his total score did he make by running between the wickets?
Options:
A)45
B)58.33%
C)600/11
D)55
E)35
Rationale: Explanation :
Number of runs made by running,
=>120−(5×4+5×6).
=>120−(50).
=>70.
Hence, the required percentage is:-
=>70/120 * 100
=>58.33%
Answer : B
Answer: B
Question: If |x^2 − 2| = x, which of the following could be the value of x?
Options:
A)-2
B)-1
C)0
D)1
E)4
Rationale: The LHS is not negative, so the RHS is also not negative. Thus x >= 0.
First, let's assume that x^2-2 is negative.
-(x^2 - 2) = x
x^2 + x - 2 = 0
(x+2)(x-1) = 0
x = 1 or x = -2 (However, x can not be negative.)
Then x = 1 is a possible value for x.
The answer is D.
Answer: D
Question: If 2^z is a factor of 24!, which of the following could be the value of z?
I. 22
II. 23
III. 24
Options:
A)I ​only
B)II only
C)I​ and II
D)I, II, and III
E)None
Rationale: 24! contains all numbers from 1 to 24. To find the factor with the highest power of 2, we count the number of multiples of 2, 4, 8 and 16.
Multiples of 2 = 12
Multiples of 4 = 6
Multiples of 8 = 3
Multiples of 16 = 1
Total count = 22
The answer is A.
Answer: A
Question: How many liters of water must be evaporated from 50 liters of a 6-percent sugar solution to get a 10-percent solution?
Options:
A)20
B)22
C)24
D)26
E)28
Rationale: 6% of a 50 liter solution is 3L which is 10% of the solution at the end.
The solution at the end must be 30 L.
We need to evaporate 20 liters.
The answer is A.
Answer: A
Question: log3 N+log12 N what is 3 digit number N that will be whole number
Options:
A)6291
B)7292
C)1728
D)1929
E)1727
Rationale: No of values N can take is 1
12^3=1728
ANSWER:C
Answer: C
Question: Set X consists of all two-digit primes and set Y consists of all positive multiples of 4 less than 100. If the two sets are combined into one, what will be the range of the new set?
Options:
A) 84
B) 93
C) 90
D) 92
E) 95
Rationale: Set X = {11, 13, 17,............., 83, 89, 97}
Set Y = {4, 8, 12,..............., 88, 92, 96}
Combining two sets, say Set Z
Set Z = {4,8, 11, 12,13, 17, ..................., 83, 88, 89, 92, 96, 97}
Range = Max Value - Min Value
Range (Z) = 97 - 4 = 93
OA B is the answer.
Answer: B
Question: A baker sold all of his donuts for a total amount of 216 pounds. If on each donut the baker made a profit of 8% of the cost, how much did it cost the baker to make all the donuts?
Options:
A)210.
B)200.
C)190.
D)180.
E)170.
Rationale: THE CORRECT ANSWER IS B
Cost of donuts = X
Profit on one donut = 8%
Profit on all donuts is also =8% (Well, you must know why it is so !! IF you don't know then please revisist percentage chapter again.. ok ok.. i have given the explanation at the end of the solution.... understand it , if you are confused)
X+8% of X =216
1.08X=218
X=218/1.08
X=200
answer is B
Answer: B
Question: A man purchases the milk at Rs. x per liter and sells it at Rs. 2x/liter stillhe mixes 2liters water with every 6liters of pure milk. Whatis the profit %?
Options:
A)145%
B)150%
C)155.7%
D)166.6%
E)176.5%
Rationale: Let the cost price of 1 litre pure milk be Re.1, then
\inline{6litres(milk)→CP=Rs.62litres(water)→CP=Rs.0}{6litres(milk)→CP=Rs.62litres(water)→CP=Rs.0}\rightarrow CP=Rs.6 only
and 8 litre mixture \rightarrow SP \rightarrow 8 x 2 = Rs.16
Profit %= 166.66%
D
Answer: D
Question: In how many different number of ways 7 men and 3 women can sit on a shopa which can accommodate persons?
Options:
A)200
B)230
C)240
D)250
E)5040
Rationale: 10p4 = 10 X 9 X 8 X 7 = 5040
E
Answer: E
Question: A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent?
Options:
A)27%
B)20%
C)80%
D)30%
E)24%
Rationale: 900 ---- 180
100 ---- ? => 20%
Answer: B
Answer: B
Question: Lisa and Robert have taken the same number of photos on their school trip. Lisa has taken 3 times as many photos as Claire and Robert has taken 24 more photos than Claire. How many photos has Claire taken?
Options:
A)6
B)8
C)10
D)12
E)14
Rationale: L = R
L = 3C
R = C + 24
3C = C + 24
C = 12
The answer is D.
Answer: D
Question: If r = 2^4 * 5^2 * 7 and s = 2^2 * 3^2 * 5, which of the following is equal to the greatest common divisor of r and s?
Options:
A)2 * 5
B)2^2 * 5
C)2^3 * 5^2
D)2*3*5*7
E)2^3 * 3^2 * 5^2 * 7
Rationale: GCD = product of prime factors raised to the least power = 2^2 * 5
The answer is B.
Answer: B
Question: Find the total number of four digit numbers that can be formed using the digits 1,2,5,6.
Options:
A)253
B)256
C)258
D)260
E)265
Rationale: no. will be formed by taking all at a time with repititon allowed
total=4*4*4*4=256
ANSWER:B
Answer: B
Question: How many different ways can you select a pilot and a co pilot if you have 75 people to choose from?
Options:
A)199
B)200
C)398
D)4950
E)5550
Rationale: 1) PERMUTATION:-
since it is selection, we have to find permutation..
75P2= 75!/(75-2)!=5550
ANS:E
Answer: E
Question: A train speeds past a pole in 25 seconds and a platform 200 m long in 30 seconds. Its length is:
Options:
A)1200 m
B)2000 m
C)1500 m
D)1000 m
E)4000 m
Rationale: Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 25 => y = x/25
x + 200 / 30 = x / 25
x = 1000 m.
Answer: Option D
Answer: D
Question: Eight cubes, each with a volume of 512 cm^3, are joined to form one large cube. What is the surface area of the large cube?
Options:
A)4096 sq cm
B)1536 sq cm
C)1024 sq cm
D)2048 sq cm
E)512 sq cm
Rationale: volume = a x a x a = a ^3
volume of cube = 8 x 512 = 4096 cm^3
4096 = a^3
a = 16
surface area of cube = 6 a^2 = 6 x 16^2 = 1536
Answer is B
Answer: B
Question: What amount does Kiran get if he invests Rs.9800 at 12% p.a. compound interest for three years, compounding done annually?
Options:
A)13456
B)13487
C)18978
D)13456
E)12308
Rationale: A= P{1 + R/100}n
=> 9600{1 + 12/100}3
= Rs.13487
Answer: B
Answer: B
Question: Having received his weekly allowance, a student spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $1.20 at the candy store. What is this student’s weekly allowance?
Options:
A)$3.50
B)$4.00
C)$4.25
D)$4.50
E)$5.00
Rationale: Let x be the value of the weekly allowance.
(2/3)(2/5)x = 120 cents
(4/15)x = 120
x = $4.50
The answer is D.
Answer: D
Question: Of the 30 employees of a certain company, 10 are accountants. 2 employees of the company will be selected at random. Which of the following is closest to the probability that neither of the employees selected will be an accountant?
Options:
A)P(E)=0.43
B)0.36
C)0.31
D)0.52
E)0.63
Rationale: We can Solve this by two ways:
either find the probability by = 1-(both accountant+atleast one accountant)
or direct from = P(both non accountant)
second is easier but requires calculation if don't do the approximation.
So probability= (20/30)*(19/29) = 0.43
so the answer is A
Answer: A
Question: One night 17 percent of the female officers on a police force were on duty. If 170 police officers were on duty that night and half of these were female officers, how many female officers were on the police force?
Options:
A)400
B)420
C)450
D)480
E)500
Rationale: Let x be the number of female police officers on the police force.
The number of female police officers on duty was 85.
0.17x = 85
x = 500
The answer is E.
Answer: E
Question: A and B together can do a work in 3 days. If A alone can do it in 6 days. In how many days can B alone do it?
Options:
A)10
B)99
C)77
D)55
E)6
Rationale: 1/3 – 1/6 = 1/6
=> 6
Answer: E
Answer: E
Question: w, q, and r are positive integers. If w, q, and r are assembled into the six-digit number wqrwqr, which one of the following must be a factor of wqrwqr?
Options:
A) 23
B) 19
C) 17
D) 7
E) none of the above
Rationale: One short way -
wqrwqr = 1000wqr + wqr = (1000+1)wqr = 1001wqr
Therefore any factor of 1001 is a factor of wqrwqr
7 is a factor of 1001
So D
Answer: D
Question: Express a speed of 84 kmph in meters per second?
Options:
A)13.33 mps
B)23.33 mps
C)33.33 mps
D)25.33 mps
E)43.33 mps
Rationale: 84 * 5/18 = 23.33 mps
ANSWER:B
Answer: B
Question: Calculate the fourth proportional to 1.8, 2.9 and 5.2?
Options:
A)7.38
B)8.38
C)8.19
D)20.38
E)12.38
Rationale: Explanation:
Formula = Fourth propotional = (b × c)/a
A = 1.8 , B = 2.9 and C = 5.2
(2.9 × 5.2)/1.8 = 8.38
Answer: Option B
Answer: B