divelab/Sys2Bench huggingface dataset:
Question: x is the product of each integer from 1 to 50, inclusive and y=100^k, where k is an integer . What is the greatest value of k for which y is a factor of x?
Options:
A)0
B)5
C)6
D)10
E)12
Rationale: x = 1*2*3*4*5*......*49*50 = 50!
y = 100^k
100 = 10^2 = 2^2 * 5^2
On prime factorization of x, power of 5 will always be greater than power of 2
CONCEPT: In every Factorial value (x!), On prime factorization, the power of Bigger Prime number > the power of Smaller Prime number
Also, Power of any Prime Number in any factorial can be calculated by following understanding
Power of prime x in n! = [n/x] + [n/x^2] + [n/x^3] + [n/x^4] + ... and so on
Where,
[x] = Greatest Integer less than or equal to x and the explanation of terms is as follows
[n/x] = No. of Integers that are multiple of x from 1 to n
[n/x^2] = No. of Integers that are multiple of x^2 from 1 to n whose first power has been counted in previous step and second is being counted at this step
[n/x^3] = No. of Integers that are multiple of x^3 from 1 to n whose first two powers have been counted in previous two step and third power is counted at this step
And so on.....
Where [n/x] is greatest Integer value of (n/x) less than or equal to (n/x)
i.e. [100/3] = [33.33] = 33
i.e. [100/9] = [11.11] = 11 etc.
Power of 5 in x = [50/5] + [50/5^2] + [50/5^3]... = 10 + 2 + 0 = 12
Power of 2 in x = [50/2] + [50/2^2] + [50/2^3]... = 25 + 12 + 6 + 3 + 1 = 47
i.e. x = 50! = 2^47 * 5^12 * ... = 10^12 * ... = 100^6 * ...
i.e. x is divisible by a 6th power of 100 at the most
i.e. y = 100^k = 100^6
i.e. k = 6
Answer: option C
Answer: C
Question: The least number which should be added to 3218 so that the sum is exactly divisible by 5, 6, 4 and 3 is?
Options:
A)10
B)20
C)30
D)40
E)50
Rationale: L.C.M. of 5, 6, 4 and 3 = 60.
On dividing 3220 by 60, the remainder is 40.
Number to be added = (60 - 40) = 20
B)
Answer: B
Question: A professional athlete was offered a three-year contract to play with Team K that provided for an annual salary of $100,000 in the first year, an increase in annual salary of 20% over the previous year for the next two years, and a bonus of $50,000 on signing. Team L offered a three-year contract providing for an annual salary of $120,000 in the first year, an increase in annual salary of 10% over the previous year for the next two years, and no signing bonus. If he accepts the offer of Team L and fulfills the three-year contract terms, the athlete will receive how much more money by choosing Team L over Team K ?
Options:
A)$16,800
B)$50,000
C)$82,500
D)$92,000
E)$100,000
Rationale: Team K's contract = $100,000 + $100,000*1.2 + $100,000*1.2*1.2 + $50,000 = $414,000
Team L's contract = $120,000 + $120,000*1.1 + $120,000*1.1*1.1 = $397,200
The difference = $16,800.
Answer: A.
Answer: A
Question: 385, 462, 572, 396, 424, 671, 264
Options:
A)385
B)424
C)671
D)264
E)None of these
Rationale: Solution
In each number except 424,the middle digit is the sum of the other two. Answer B
Answer: B
Question: Three coworkers P , H , R meet for Dinner. P had 5 sandwiches, H had 3 and R had none. Both PH share their sandwiches with R such that each one got the same amount. If R paid $ 8 to PH, how much of $ 8 should P get? Assume both sandwiches and Dollars can be split.
Options:
A)a) 5$
B)b) 3 $
C)c) 7 $
D)d) 4 $
E)e) 5.5 $
Rationale: we got total 8 sandwiches ....we are dividing equally in 3 people.
per person: 8/3
initially
p:8
H:3
r:0
now since r ate 8/3 so he is paying 8 dollars for 8/3 sandwiches.
now p also ate 8/3 of his 5 sandwiches = so he gave 5-8/3 to r ==>7/3 to r
ok we have 8 dollars for 8/3 sandwich
therefore for 7/3 sandwich we will get 7 dollars.
hence p should get 7 dollars.
hence C
Answer: C
Question: A paint store mixes 3/4 pint of red paint and 2/3 pint of white paint to make a new paint color called Perfect Pink. How many pints of red paint would be needed to make 30 pints of Perfect Pink paint?
Options:
A)9
B)16
C)15
D)25 1/3
E)28 1/2
Rationale: 3/4 pint is required to make 3/4 + 2/3 = 17/12 pint of perfect pink
so 17/12 pint requires 3/4 pint of red..
1 pint will require 3/4 * 12/17=9/17..
30 pints will require 9/17 * 30= 15 pints..
C
Answer: C
Question: Awordis defined as a sequence of Four dots arranged in a row. Each dot is colored either yellow or blue. How many distinct words can be formed?
Options:
A)13
B)15
C)16
D)18
E)19
Rationale: Each dot can be either yellow or blue, so 2 options for each dot: 2*2*2*2 = 16.
Answer: C
Answer: C
Question: Find the total no. of distinct bike no.'s that can be formedusing 2 letters followed by 2 no.'s. How manyletters need to be distinct?
Options:
A)45789
B)49653
C)57900
D)65000
E)70046
Rationale: Out of 26 alphabets two distinct letters can be chosen in \inline {\color{Black}26P_2{}} ways. Coming to numbers part, there are 10 ways.(any number from 0 to 9 can be chosen) to choose the first digit and similarly another 10ways to choose the second digit. Hence there are totally 10X10 = 100 ways.
Combined with letters there are \inline {\color{Black}6P_2{}} X 100 ways = 65000 ways to choose vehicle numbers.
D
Answer: D
Question: During a special promotion, a certain filling station is offering a 10 percent discount on gas purchased after the first 5 gallons. If Kim purchased 20 gallons of gas, and Isabella purchased 25 gallons of gas, then Isabella‟s total per-gallon discount is what percent of Kim‟s total per-gallon discount?
Options:
A)80%
B)107%
C)116.7%
D)120%
E)140%
Rationale: Kim purchased 20 gallons of gas. She paid for 5 + 0.9*15 = 18.5 gallons, so the overall discount she got was 1.5/20 = 7.5%.
Isabella purchased 25 gallons of gas. She paid for 5 + 0.9*20 = 23 gallons, so the overall discount she got was .5/25 = 8%.
8 is 8/7.5*100 = 107% of 7.5.
Answer: B.
Answer: B
Question: One-third of Rahul’s savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 2,50,000 as total savings, how much has he saved in Public Provident Fund ?
Options:
A)Rs. 30,000
B)Rs. 50,000
C)Rs. 60,000
D)Rs. 100,000
E)None
Rationale: EXPLANATION
Let savings in N.S.C and P.P.F. be Rs. x and Rs. (250000 – x) respectively. Then,
1/3x=1/2(250000-x)
=> x/3 + x/2 = 125000
=> 5x/6 = 125000
=> x= 125000 x 6 /5= 150000
Savings in Public Provident Fund = Rs. (250000 – 150000) = Rs. 100000
Answer D
Answer: D
Question: A shopkeeper sold an article at $1050 and gained a 20% profit. What was the cost price?
Options:
A)$835
B)$845
C)$855
D)$865
E)$875
Rationale: Let x be the cost price.
1.2x = 1050
x = 1050/1.2 = 875
The answer is E.
Answer: E
Question: In how many different number of ways 6 men and 2 women can sit on a shopa which can accommodate persons?
Options:
A)200
B)1680
C)240
D)250
E)260
Rationale: 8p4 = 8 X 7 Ã— 6 Ã— 5 = 1680
B
Answer: B
Question: One-third of Rahul's savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,50,000 as total savings, how much has he saved in Public Provident Fund ?
Options:
A)90000
B)85000
C)50000
D)75000
E)60000
Rationale: Let savings in N.S.C and P.P.F. be Rs. x and Rs. (150000 - x) respectively. Then,
=1/3 x = 1/2 (150000 - x)
=x/3 + x/2 = 75000
=5x/6 = 75000
=x = 75000 x 6 /5	= 90000
Savings in Public Provident Fund = Rs. (150000 - 90000) = Rs. 60000
Answer is E.
Answer: E
Question: 5 cats can catch 5 mice in 5 minutes. How many cats does it take to catch 100 mice in 100 minutes?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: let x be no. of cat
5 cat catch 5 mice in 5 min
5 cat catch 1 mice in (5/5=1 min)
1 cat catch 1 mice in 1*5=5 min
1 cat catch 100 mice in 5*100 min
x cat catch 100 mice in (5*100)/x min
A/Q (5*100)/x = 100
=> 5*100=x*100
=> x=5
ANSWER:E
Answer: E
Question: Arjun started a business with Rs. 20,000 and is joined afterwards by Anoop with Rs.80, 000. After how many months did Anoop join if the profits at the end of the year are divided equally?
Options:
A)3
B)9
C)5
D)6
E)7
Rationale: Suppose Anoop joined after 3 months.
Then, 20000 * 12 = 80000 * (12 – x)
=> x = 9.
ANSWER:B
Answer: B
Question: If n ≠ 0, which of the following could be less than n?
I. 2n
II. n^2
III. 2 - n
Options:
A)I only
B)II only
C)I and II only
D)I and III only
E)None
Rationale: n ≠ 0 => n = negative or n = positive
if n = negative:
2n < n (n = -1 then 2n = -2 => -2 < -1)
n^2 > n (n =-1 then n^2 = 1 => n^2 > n)
2 - n > n (n = -1 then 2--1 = 2+1=3 => 2-n > n)
but if n = positive:
n^2 > n (n = 2 then n^2 = 4 => n^2 > n) => II
2 - n < n(n =2 then 2-2 = 0)
=>answer is D
Answer: D
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 $0.40 at the candy store. What is this student’s weekly allowance?
Options:
A)$1.20
B)$1.50
C)$1.80
D)$2.00
E)$2.50
Rationale: Let x be the value of the weekly allowance.
(2/3)(2/5)x = 40 cents
(4/15)x = 40
x = $1.50
The answer is B.
Answer: B
Question: Due to construction, the speed limit along an 15-mile section of highway is reduced from 55 miles per hour to 35 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options:
A) 5
B) 8
C) 9.36
D) 15
E) 24
Rationale: Old time in minutes to cross 15 miles stretch = 15*60/55 = 15*12/11 = 16.36
New time in minutes to cross 15 miles stretch = 15*60/35 = 15*12/7 = 25.71
Time difference = 9.36
Answer C)
Answer: C
Question: A certain function f satisfies the equation f(x)+2*f(6-x)=x for all real numbers x. The value of f(1) is
Options:
A)3
B)1
C)2
D)5
E)6
Rationale: Put x =1 ⇒ f(1)+2*f(6-1) = 1 ⇒ f(1) + 2*f(5) = 1
Put x = 5 ⇒ f(5)+2*f(6-5) = 5 ⇒ f(5) + 2*f(1) = 5
Put f(5) = 5 - 2*f(1) in the first equation
⇒ f(1) + 2*(5 - 2*f(1)) = 1
⇒ f(1) + 10 - 4f(1) = 1
⇒ f(1) = 3
Answer: A
Answer: A
Question: In a group of cows and hens, the number of legs are 14 more than twice the number of heads. The number of cows is
Options:
A)22
B)7
C)8
D)6
E)51
Rationale: Let the number of cows be x and the number of hens be y. Then, 4x + 2y = 2 (x + y) + 14 4x + 2y = 2x + 2y + 14 2x = 14 x = 7.
Answer: B
Answer: B
Question: Find the value of 3/11 × [(1 + 1/3) (1 + 1/4) …………. (1 + 1/120)] is
Options:
A)10
B)13
C)11
D)15
E)17
Rationale: =3/11 × [(1 + 1/3) (1 + 1/4) ....... (1 + 1/120)]
=3/11 × [4/3 + 5/4 × ........ 121/120]
=3/11 × 4/3 × 5/4 × .... 121/120
=121/11 = 11.
Answer is C.
Answer: C
Question: If 4 men working 10 hours a day earn Rs. 800 per week, then 9 men working 6 hours a day will earn how much per week?
Options:
A)Rs 840
B)Rs 1320
C)Rs 1080
D)Rs 1680
E)None of these
Rationale: Explanation :
(Men 4:9) : (Hrs/Day 10:6) :: 800 : x
hence 4 * 10 *x = 9 * 6 * 800
or x = 9*6*800/ 4*10 = 1080
Answer : C
Answer: C
Question: Three pipes of same capacity A,B,C can fill a tank in 14 hours. If there are only two pipes C and A of same capacity, the tank can be filled in?
Options:
A)6
B)12
C)28
D)42
E)21
Rationale: The part of the tank filled by three pipes in one hour
= 1/14
=> The part of the tank filled by two pipes in 1 hour
= 2/3 * 1/14= 1/21.
The tank can be filled in 21 hours.
Answer:E
Answer: E
Question: In one hour, a boat goes 4 km/hr along the stream and 2 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
Options:
A)3 km/hr
B)4 km/hr
C)5 km/hr
D)6 km/hr
E)8 km/hr
Rationale: Upstream relative speed is u + v=4km/hr
Downstream speed is u-v = 2
Where u = speed of boat in still water and v is speed of stream
Then adding two equations u+v + u-v =4+2
2u=6
Finally, u=3.
ANSWER : A
Answer: A
Question: It is required to fix a pipe such that water flowing through it at a speed of 7 metres per minute fills a tank of capacity 220 cubic metres in 10 minutes. The inner radius of the pipe should be :
Options:
A)√2 m
B)2 m
C)1 m
D)1⁄√2 m
E)None of these
Rationale: Let inner radius of the pipe be r.
Then, 220 = 22⁄7 × r2 × 7 × 10
or r2=220/22×10=1
or r = √1=1 m
Answer C
Answer: C
Question: A = {2, 3, 5, 7, 15}
B = {2, 4, 6, 13}
Two integers will be randomly selected from sets A and B, one integer from set A and one from set B, and then multiplied together. How many different products can be obtained?
Options:
A)15
B)16
C)19
D)20
E)36
Rationale: Step 1: Find out the number of products you get.
5 distinct numbers in set A and 4 distinct in set B so number of products = 5*4 = 20
Step 2: Remove the products that appear more than once.
Notice that 5, 7, 11 and 13 are primes and none of their multiples are in either set. So ignore them. We just need to focus on 2 and 3 of set A and 2, 4 and 6 of set B.
2, 3
2, 4, 6
The only product repeated when you take a number from each set is 12. (3*4 and 2*6) Rest all are distinct.
Answer = 20 - 1 = 16
Note here that the second step will involve manual calculation since it will depend on the specific numbers you have in the two sets.
B
Answer: B
Question: I bought two books; for Rs.480. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?
Options:
A)276
B)280
C)287
D)267
E)270
Rationale: x*(85/100)
= (480 - x)119/100
x = 280
Answer:B
Answer: B
Question: n what time will a railway train 60 m long moving at the rate of 36 kmph pass a telegraph post on its way?
Options:
A)2
B)7
C)8
D)6
E)9
Rationale: T = 60/36 * 18/5 = 6 sec
Answer: D
Answer: D
Question: If the product of the integers w, x, y and z is 840, and if 1 < w < x < y < z, what is the value of w + z?
Options:
A)10
B)11
C)16
D)18
E)21
Rationale: 840= 4* 5 * 6* 7
So w = 4, x = 5, y = 6, z = 7
w + z = 4+ 7= 11
Answer - B
Answer: B
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 44, the dividend is:
Options:
A)4884
B)5340
C)5342
D)5345
E)5356
Rationale: Divisor = (5 * 44) = 220
= 10 * Quotient = Divisor
=> Quotient = 220/10 = 22
Dividend = (Divisor * Quotient) + Remainder
Dividend = (220 * 22) + 44 = 4884.
A
Answer: A
Question: Bullock likes to keep a spare tyre in his car every time. On a certain day, he travels 1, 20,000 km and just to make the most of all the tyres, he changes the tyres between his journey such that each tyre runs the same distance.
What is the distance traveled by each tyre?
Options:
A)70,000
B)60,000
C)80,000
D)96,000
E)10,000
Rationale: The distance traveled by each tyre:
4/5 * 1, 20, 000km = 96,000 km. D
Answer: D
Question: If a person walks at 20 km/hr instead of 10 km/hr, he would have walked 40 km more. The actual distance traveled by him is?
Options:
A)40 km
B)76 km
C)18 km
D)16 km
E)97 km
Rationale: Let the actual distance traveled be x km. Then,
x/10 = (x + 40)/20
10x - 400 =>x = 40 km.
Answer: A
Answer: A
Question: If a man lost 10% by selling oranges at the rate of 10 a rupee at how many a rupee must he sell them to gain 50%?
Options:
A)6
B)8
C)7
D)4
E)2
Rationale: 90% ---- 10
150% ---- ?
90/150* 10 = 6
Answer: A
Answer: A
Question: Marge has 3 pumps for filling her swimming pool. When all 3 pumps work at their maximum rates, the swimming pool is filled in 56 minutes. Pump 1's maximum rate is twice the maximum rate of pump 2 and four times the maximum rate of pump 3. How long would it take Marge to fill the pool if she used only pump 2 at its maximum rate ?
Options:
A)3hrs, 16mins
B)6hrs, 32mins
C)7hrs, 12mins
D)13hrs, 4mins
E)14hrs, 24mins
Rationale: The rate of pump 1 = 4x job/minute.
The rate of pump 2 = 2x job/minute.
The rate of pump 3 = x job/minute.
Given that x+2x+4x=1/56 --> x=1/392 --> (time) = (reciprocal of rate) = 392 minutes x/2= 196 = 3 hrs 16 minutes.
Answer: A
Answer: A
Question: A watch which gains uniformly, is 6 min. slow at 8 o'clock in the morning Sunday and it is 6 min. 48 sec. fast at 8 p.m. on following Sunday. When was it correct?
Options:
A)20 min past 7 pm on Tuesday
B)20 min. past 7 p.m.on Wednesday
C)20 min. past 7 p.m. on Thursday
D)20 min. past 7 p.m. on Friday
E)None of these
Rationale: Explanation :
Time from 8 a.m. on Sunday to 8 p.m. on following Sunday = 7 days 12 hours = 180 hours
The watch gains (5 + 29/5) min. or 54/5 min. in 180 hrs.
Now 54/5 min. are gained in 180 hrs.
5 min. are gained in (180 x 5/54 x 5) hrs = 83 hrs 20 min. = 3 days 11 hrs 20 min.
Watch is correct 3 days 11 hrs 20 min. after 8 a.m. of Sunday.
It will be correct at 20 min. past 7 p.m. on Wednesday.
Answer : B
Answer: B
Question: At a certain stage of a soccer tournament, the score ratio of teams A, B and C was 3:4:5. Eventually, the score ratio of A to B has doubled while the score ratio of A to C has halved. If the final score of team C was 40, what was the final score Q of team B?
Options:
A)1)8
B)2)10
C)3)20
D)4)40
E)5)80
Rationale: A to B = 3 : 4
So, on doubling we get 6 : 4
A to C = 3 : 5
So, on halving we get 1.5 : 5 or 3 : 10 or 6 : 20
So final ratio = 6 : 4 : 20.
If 20x = 40
4x = 8
Hence, answer is A
Answer: A
Question: If a bus moving at the speed of y km/hr travels a distance of x km, which of the following cannot be equal to the distance traveled?
Options:
A)y-x km
B)y/2 km
C)(y-x)/2 km
D)x/y km
E)x-y km
Rationale: This question can be solved by TESTing VALUES, but there's a particular pattern that you have to recognize to make the workeasy.
We're not really limited by anything in this question, so X and Y can be anything. Under normal circumstances, I won't TEST the number 1 in PS questions (as it often leads to duplicate answers), but here it's a great option (since we're looking to eliminate 4 answers, multiple TESTs are going to be likely anyway).
We're given information on speed (y km/hour) and distance (x km). We're asked which of the 5 answer choices CANNOT be the distance traveled.
IF....
Y = 2 and X = 1
Answers A (2-1 = 1) and B (2/2 = 1) are POSSIBLE. Eliminate A and B.
IF....
Y = 3 and X = 1
Answer C ([3-1]/2 = 1) is POSSIBLE. Eliminate C.
IF....
Y = 1 and X = 1
Answer D (1/1 = 1) is POSSIBLE. Eliminate D.
Final Answer:
E
Answer: E
Question: What is the measure of the radius of the circle that circumscribes a triangle whose sides measure 9, 40 and 41?
Options:
A)6
B)4
C)24.5
D)20.5
E)12.5
Rationale: Explanatory Answer
9, 40 and 41 is Pythagorean triplet. So, the triangle is right angled.
Key property about right triangles
In a right angled triangle, the radius of the circle that circumscribes the triangle is half the hypotenuse.
In the given triangle, the hypotenuse = 41.
Therefore, the radius of the circle that circumscribes the triangle = 41/2 = 20.5 units.
Choice D
Answer: D
Question: When is |x-7| = 7-x?
Options:
A)x>7
B)x<7
C)x=7
D)x<0
E)x<=7
Rationale: When is |x-7| = 7-x?
Choice A: X=7, it is true but X cannot be always 7
Choice B: X=0, it is also true, but X cannot be always 0
Choice C: X>7, it is false, for e.g. X=6, then one side of equation is 2 and the other side is -2
Choice D: X<=7, this choice encapsulate Choice A, Choice B and for all other conditions and is true for above said equation. Hence the answer choice is E.
Answer: E
Question: A machine, working at a constant rate, manufactures 72 staplers in 28 minutes. How many staplers does it make in 1 hr 52 min?
Options:
A)268
B)262
C)300
D)288
E)250
Rationale: Change 1 hr 52 min to 112 min. For this, we need to set up a simple proportion of staplers per time 72/28= S/112.
The absolutely worst thing you could do at this point in the problem is to cross-multiply. That would be a supremely unstrategic move. We can cancel the common factor of 28 in the two denominators.
72/28*28 = S/112*28
72/1 = S/4
S = 4* 72
S = 288
The machine would be 288 staplers in 1 hr 52 min.
Answer:D
Answer: D
Question: Virat buys an old car for Rs. 50000 and spends Rs. 2000 on its repairs. If he sells the car for Rs. 62000, his gain percent is:
Options:
A)19.23%
B)11 (1/9) %
C)12.1 %
D)12%
E)None of these
Rationale: Explanation:
C.P. = Rs. (50000 + 2000) = Rs. 52000
S.P. = Rs. 62000.
Gain% = ( (10000 / 52000) * 100 ) % = 19.23%
ANSWER A
Answer: A
Question: If a, r, and c are consecutive even integers and a < r < c, all of the following must be divisible by 4 EXCEPT
Options:
A)a + c
B)r + c
C)ac
D)(bc)/2
E)(abc)/4
Rationale: I did get the correct answer within 80 seconds and it was not by luck either. I did not pick numbers but just used the concept stated by Ian.
The 3 numbers can be written as
a, (a + 2)(a + 4).
If 'a' is divisible by 4, then even 'c' or 'a + 4' is divisible by 4. However, is 'b' is divisible by 4, then both 'a' and 'a + 4' are still divisible by 2.
A - (a + c) = a + (a + 4) = 2a + 4 = 2(a + 2) = 2b. 2b will always be divisible by 4 even if 'b' is not divisible by 4. Reason: 'b' already has a prime factorization of at least a '2'. Hence '2b' has two 2s.
C - ac = a(a+4). If, as stated above, one of them is divisible by 4, then the product is divisible. If both of them are not divisible by 4, then the product is still divisible by 4 because of the presence of two 2s again in the prime factorization.
D - bc/2 = (a + 2)(a + 4)/2. Either b or c is divisible by 2. Hence, if we assume that b is divisible by 2 and not divisible by 4, then it leaves us just one possibility. Is c divisible by 4? It has to be because c is the next consecutive even integer.
E - abc/4 = a(a + 2)(a + 4)/4. One of these integers is divisible by 4 already. If we again assume 'b' to be that integer divisible by 4, then we are left with the question - Is a(a + 4) divisible by 4? This is the same as option C.
B - r + c = (a + 2) + (a + 4) = 2a + 6 = 2(a + 3). (a + 3) will never be divisible by 2 because it is an odd integer. Hence, 2(a + 3), although divisible by 2, will not be divisible by 4 because it has just one 2 in its prime factorization.
As a whole, whether you choose numbers (2, 46 being the easiest) or solve conceptually, the answer is still easily obtainable within 2 minutes.B
Answer: B
Question: An investor bought 200 shares of stock in ABCD company in 1990. By 1992, the investment was worth only 2/3 of its original value. By 1995, the 200 shares were worth only 2/5 of their value in 1990. By what percent did the value of the investment drop from 1992 to 1995?
Options:
A)16 2/3%
B)25%
C)40%
D)50%
E)66 2/3%
Rationale: Let price of each share in 1990 = X.
Total cost in 1990 = 200X
Now Price in 1992 = 2/3 * 200X = 400/3 * X
Now price in 1995 = 2/5 *200X= 80X
%Change in 1995 from 1992 = [(400/3* X -80X) / (400/3 *X) ] *100 = 40%
Answer C
Answer: C
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)110
B)130
C)145
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: What are the number of ways to select 3 men and 2 women such that one man and one woman are always selected?
Options:
A)26 ways
B)19 ways
C)30 ways
D)76 ways
E)15 ways
Rationale: The number of ways to select three men and two women such that one man and one woman are always selected = Number of ways selecting two men and one woman from men and five women
= ⁴C₂ * ⁵C₁ = (4 * 3)/(2 * 1) * 5
= 30 ways.
Answer: C
Answer: C
Question: we have two cubes which are joined to each other covering one face of each. and remaining faces of both are colored with the different colors.then the first cube is cut into 8 smaller cubes and another in 27 smaller cubes. what is the total number of faces having no color?
Options:
A)141
B)142
C)143
D)144
E)145
Rationale: each cube having 6 faces
for each cube 5 faces has color and one face for each has not
1st cube divided into 8 smaller cubes so num of faces = 8*6 = 48
in this 48 faces 5*4 = 20 faces having the color and 28 don't
because if we divided a cube into 2^n smaller cubes (2^3 = 8) then each face of original cube is divided into 2^(n-1) smaller faces (2^2 = 4) [and inner faces also there]
similarly 2nd cube divided into 27 smaller cubes so num of faces = 27*6 = 162
in tiis 162 faces 5*9 = 45 faces having color and 117 don't
total no of faces having no color = 28+117 = 145
ANSWER:E
Answer: E