divelab/Sys2Bench huggingface dataset:
Question: There are 2 friends Peter and Paul. Peter age is twice as old as Paul when peter was as old as Paul is now. Sum of the present ages of Peter and Paul is 35.What is the present age of Peter?
Options:
A)10
B)15
C)20
D)25
E)30
Rationale: let pauls age be 'a' and peters be 'e'
e+a=35 (given)
e=35-a ------eq1
when peter was as old as paul that is when peter's age was 'a'
pauls age was a-(e-a) =2a-e
now peters age is e=2(2a-e)
e=4a-2e
3e=4a
3(35-a)=4a
105-3a=4a
a=15
hence e=20
ANSWER:C
Answer: C
Question: Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by:
Options:
A)1/7
B)1/8
C)1/9
D)7/8
E)1/5
Rationale: Original share of 1 person = 1/8
New share of 1 person = 1/7
Increase =(1/7-1/8) = 1/56
Required fraction = (1/56)/(1/8)
= (1/56)*8
= 1/7
ANSWER:A
Answer: A
Question: The sequence x1, x2, x3,..., is such that Xn = 1/n - (1/(n+1)). What is the sum of the first 200 terms of the sequence?
Options:
A)201/100
B)99/100
C)100/101
D)1/10000
E)200/201
Rationale: Easy task and accomplish
X1=1-1/2
x2=1/2-1/3
x3=1/3-1/4
.....
x199=1/199-1/200
x200=1/200-1/201
sum=X1+X2+X3+....X200=1-1/2+1/2-1/3+.......1/199-1/200+1/200-1/201=1-1/201=200/201
E is the answer
Answer: E
Question: In a mixture of 60 litres the ratio of milk to water is 5:1. Additional 20 litres of water is added to the mixture. Find the ratio of milk to water in the resulting mixture.
Options:
A)2:3
B)5:3
C)1:4
D)3:2
E)3:1
Rationale: Given that Milk/Water=5x/x and 5x+x=60 --> x=10.
Thus Milk=5x=50 liters and Water=x=10 liters.
New ratio = 50/(20+10) = 50/30 = 5/3.
Answer is B
Answer: B
Question: A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?
Options:
A)2.9 hrs
B)8.9 hrs
C)2.9 hrs
D)7.2 hrs
E)8.6 hrs
Rationale: Net part filled in 1 hour = (1/4 - 1/9)
= 5/36
The cistern will be filled in 36/5 hrs i.e., 7.2 hrs.
Answer:D
Answer: D
Question: If (10^67) – 63 is written as a base 10 integer, which of the following options is the sum of the digits in that integer?
Options:
A)598
B)495
C)590
D)595
E)695
Rationale: We know that (10^67) is ending 00, so (10^67) – 63=9....9937
total number of digits in (10^20) – 63 is 67, or 65 digits of 9 and two digits 3 and 7.
answer choice is 65*9+10=595
Answer is D 595
Answer: D
Question: A relay has a series of 5 circuits in a line. The even-numbered circuits are control circuits; the odd are buffer circuits. If both a control circuit and the buffer circuit immediately following it both fail in that order, then the relay fails. The probability of circuit one failing is 1/8; circuit two, 3/8; circuit three, 3/10; circuit four, 3/4; and circuit five, 2/5 .What is the probability that the relay fails?
Options:
A)9/80
B)3/10
C)35/80
D)303/800
E)497/800
Rationale: The first circuit doesn't matter.
Prob(relay fails) = 1 - Prob(relay succeeds)
Prob(2+3 work) = 1 - 9/80 = 71/80
Prob(4+5 work) = 1 - 3/10 = 7/10
Prob(relay fails) = 1 - Prob(2+3 work AND 4+5 work) = 1 - (71/80)(7/10) = 1 - 497/800 = 303/800
D
Answer: D
Question: Effective annual rate of interest corresponding to nominal rate of 6% per annum compounded half yearly will be
Options:
A)6.09%
B)6.10%
C)6.12%
D)6.14%
E)None of these
Rationale: Explanation:
Let the amount Rs 100 for 1 year when compounded half yearly, n = 2, Rate = 6/2 = 3%
Amount=100(1+3/100)2=106.09
Effective rate = (106.09 - 100)% = 6.09%
Option A
Answer: A
Question: If the average (arithmetic mean) of x + 1, x + 4, and x + 7 is 0, then x =
Options:
A)–4
B)–3
C)–2
D)–1
E)0
Rationale: (x+1 + x+4 + x+7)/3 = 0
=>3x + 12 = 0
=>x = -4
Answer A
Answer: A
Question: Find the average of first 20 natural numbers.
Options:
A)A)11.5
B)B)20.5
C)C)10.5
D)D)15.5
E)E)21.9
Rationale: Sum of first n natural numbers = n(n+1)/2
sum of first 20 natural numbers = 20*21/2 =210
average = 210/20 = 10.5
Answer is C
Answer: C
Question: Difference between the length and breadth of a rectangle is 23 m. Ifits perimeter is 206 m, then its area is??
Options:
A)1220 m^2
B)1520 m^2
C)2520 m^2
D)2600 m^2
E)3420 m^2
Rationale: We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103.
Solving the two equations, we get: l = 63 and b = 40.
Area = (l x b) = (63 x 40) m2 = 2520 m^2
C
Answer: C
Question: A man can row upstream at 12kmph and downstream at 14kmph. Find man's rate in still water ?
Options:
A)5km/hr
B)15km/hr
C)13km/hr
D)20km/hr
E)7.5km/hr
Rationale: Rate in still water = 1/2 (12+14) = 13km/hr
Answer is C
Answer: C
Question: The forth proportional to 5,10,20 is?
Options:
A)20
B)40
C)45
D)80
E)35
Rationale: Let the fourth proportional to 5,10,20 be x
then 5:10::20:x
5x = 10*20
x = 40
Answer is B
Answer: B
Question: 6 private companies bought a share of 2 million dollars. If the all companies have to pay the same amount and none of them have bills smaller than $1, how much money would they have to pay?
Options:
Options:
A)$2,000,000
B)$2,000,001
C)$2,000,004
D)$2,000,007
E)$2,000,009
Rationale: In order to divide the sum in 6 shares, the amount must be divisible by 6
Divisibility rule of 6: The sum of the digits must be divisible by 6
Sum of digits of 2,000,000 = 2 and 6 is divisible by 6.
Hence, we need to add 4 to this number for it to be divisible by 6
Correct Option: c
Correct Option:	$2,000,004
Answer: C
Question: The average (arithmetic mean) of four numbers is 4x + 6. If one of the numbers is x, what is the average of the other three numbers?
Options:
A)x + 1
B)3x + 3
C)5x + 8
D)5x + 4
E)15x + 12
Rationale: The sum of all four numbers is 4 * (4x + 6) = 16x + 24.
If one of the numbers is x, the sum of the other 3 numbers is 15x+24.
The average of the remaining three numbers is (15x+24)/3 = 5x+8.
The answer is C.
Answer: C
Question: Tavid has d books, which is 3 times as many as Jeff and 1/2 as many as Paula. How many books do the three of them have altogether, in terms of d?
Options:
A) 5/6*d
B) 7/3*d
C) 10/3*d
D) 7/2*d
E) 9/2*d
Rationale: Tavid has d books;
Jeff has d/3 books;
Paula has 2d books;
Total = d+d/3+2d=10d/3.
Answer: C.
Answer: C
Question: A man purchased 3 blankets @ Rs.100 each, 1 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets?
Options:
A)1050
B)2770
C)1550
D)5102
E)5000
Rationale: 10 * 150 = 1500
3 * 100 + 1 * 150 = 450
1500 – 450= 1050
Answer:A
Answer: A
Question: The side of a square is increased by 30% then how much % does its area increases?
Options:
A)52.65
B)69
C)50.75
D)42.75
E)52.75
Rationale: a = 100 a2 = 10000
a = 130 a2 = 16900
----------------
10000 --------- 6900
100 -------? => 69 %
ANSWER: B
Answer: B
Question: Some pens are divided among A, B, C and D. A gets twice the number of pens that B gets. C gets the same number of pens as D gets. If A gets 25 pens more than D and the ratio of the number of pens that B and C get is 2 : 3, then find the number of pens that D gets ?
Options:
A)56 pens
B)76 pens
C)75 pens
D)87 pens
E)12 pens
Rationale: Let the number of pens that A, B, C and D get be a, b, c and d respectively.
a : b = 2 : 1
a = c + 25
b : c = 2 : 3
a : b : c : d = 4 : 2 : 3 : 3
a,d get 4p, 3p pens
=> 4p - 3p = 25 (given)
p = 25
=> D gets 3p = 3 * 25 = 75 pens.
Answer:C
Answer: C
Question: A train 160 metres long passes a standing man in 18 seconds. The speed of the train is
Options:
A)35 kmph
B)45 kmph
C)32 kmph
D)42 kmph
E)None of these
Rationale: From formula Speed = Distance / Time
Thus, Speed = 160 / 18 => 8.88 sec
or, Speed = 8.88 x 18/5 kmph
or, Speed = 32 kmph
ANSWER:C
Answer: C
Question: How many multiples of 2 are there between 1 and 54, exclusive?
Options:
A)21
B)22
C)24
D)26
E)28
Rationale: 26
multiples of 2 between 1 and 54 exclusive.
from 2 * 1 upto 2*26, (1,2,3,4,...,26). Hence, 26 multiples !
correct option is D
Answer: D
Question: find the terms which do not contain 7 between 1000 and 9999
Options:
A)3168
B)3169
C)3170
D)3172
E)3174
Rationale: Total number of four digit numbers =9000 (i.e 1000 to 9999 )
We try to find the number of numbers not having digit 2 in them.
Now consider the units place it can be selected in 9 ways (i.e 0,1,2,3,4,5,6,8,9)
Tens place it can be selected in 9 ways (i.e 0,1,2,3,4,5,6,8,9)
Hundreds place it can be selected in 9 ways (i.e 0,1,2,3,4,5,6,8,9)
Thousands place can be selected in 8 ways (i.e 1,2,3,4,5,6,,8,9) here '0' cannot be taken
Total number of numbers not having digit 7 in it =9 x 9 x 9 x 8 =5832
Also,Total number of numbers having digit 7 in it = 9000-5832 =3168
ANSWER:A
Answer: A
Question: Find the value for x from below equation: x/3=-2?
Options:
A)-6
B)7
C)-3
D)4
E)-5
Rationale: 1. Multiply both sides by 3:
x*3/3= -2/3
2. Simplify both sides:
x = -6
A
Answer: A
Question: How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
Options:
A)20 sec
B)10 sec
C)5 sec
D)30 sec
E)60 sec
Rationale: Explanation:
Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 500 * 3/50 = 30 sec.
Answer:D
Answer: D
Question: The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and 15 as remainder. What is the smaller number?
Options:
A)240
B)270
C)295
D)360
E)365
Rationale: Let the smallest number be x.
Then larger number = (x + 1365)
x + 1365 = 6x + 15
= 5x = 1350
x = 270
Smaller number = 270.
ANSWER:B
Answer: B
Question: How many odd integers Q between 200 and 600 are there such that their tens digit is even?
Options:
A)20
B)25
C)100
D)150
E)200
Rationale: The hundreds digit can take 4 values: 2, 3, 4 and 5;
The tens digit can take 5 values: 0, 2, 4, 6 and 8;
The units digit can take 5 values: 1, 3, 5, 7 and 9;
Total Q: 4*5*5=100.
Answer: C.
Answer: C
Question: A can copy 50 papers in 10 hrs, while A & B can copy 70 papers in 10 hrs. How many hours are required for B to copy 26 papers?
Options:
A)11 hours
B)12 hours
C)13 hours
D)14 hours
E)18 hours
Rationale: A can copy 50 papers in 10 hrs, while A & B can copy 70 papers in 10 hrs.
It means B can copy 20 papers in 10 hrs.
Then time taken by B to copy 26 papers = 26*10/20 = 13 hours
ANSWER:C
Answer: C
Question: The three digits of a number add up to 23. The number is divisible by 5. The leftmost digit is double the middle digit. What is the product of the three digits?
Options:
A)350
B)720
C)360
D)380
E)425
Rationale: Say the three-digit number is abc.
The leftmost digit is double the middle digit --> a=2b;
The number is divisible by 5 --> c is either 0 or 5;
The three digits of a number add up to 23 --> a+b+c=23
So, either a+b+c=2b+b+0=23 or a+b+c=2b+b+5=23. The first equation does not give an integer value of b, so it's not the case. From the second we get that b=6 --> a=12 and c=5 --> a*b*c=360.
Answer: C.
Answer: C
Question: 34 people attend a party. 4 men are single and the rest are there with their wives. There are no children in the party. In all 22 women are present. Then the number of married men at the party is ?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: Total people = number of men + number of women
34 = 4 + number of married men + 22
number of married men = 34 - 22-4 = 8 men
ANSWER:D
Answer: D
Question: A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did A get in a profit of Rs.2460?
Options:
A)750
B)888
C)261
D)787
E)17`
Rationale: 1/2:1/3:1/4 = 6:4:3
Ram = 6/13 * 3250 = 1500
Shyam = 4/13 * 3250 = 1000
Mohan = 3/13 * 3250 = 750
Answer: A
Answer: A
Question: John bought 2 shares and sold them for $96 each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares John had
Options:
A)a profit of $10
B)a profit of $8
C)a loss of $8
D)a loss of $10
E)neither a profit nor a loss
Rationale: Loss% = (%age Profit or loss / 10)^2 = (20/10)^2 = 4% loss
Total Selling Price = 96*2 = $192
Total Cost Price = 196/(0.96) = $200
Loss = 200-192 = $8
Answer: Option C
Answer: C
Question: A student chose a number, multiplied it by 2, then subtracted 180 from the result and got 104. What was the number he chose?
Options:
A)90
B)100
C)120
D)142
E)200
Rationale: Solution:
Let x be the number he chose, then
2*x*180=104
2x=284
x=142
correct answer D
Answer: D
Question: Bhanu spends 30% of his income on petrol on scooter 20% of the remaining on house rent and the balance on food. If he spends Rs.300 on petrol then what is the expenditure on house rent?
Options:
A)2287
B)140
C)128
D)797
E)123
Rationale: Given 30% (Income ) = 300 ⇒⇒ Income = 1000
After having spent Rs.300 on petrol, he left with Rs.700.
His spending on house rent = 20% (700) = Rs.140
Answer:B
Answer: B
Question: The average of 5 quantities is 12. The average of 3 of them is 4. What is the average of remaining 2 numbers?
Options:
A)24
B)10
C)8
D)9.5
E)None of these
Rationale: ANSWER: A
(5x12-3x4)/2=24
Answer: A
Question: For every positive integer n, the nth term of a sequence is the total sum of three consecutive integers starting at n. What is the total sum of terms 1 through 50 of this series?
Options:
A)3975
B)4125
C)4375
D)4525
E)4775
Rationale: Each term of the series has the form (n+n+1+n+2) = 3n+3
Since the series goes from 1 to 50, the sum of the series is:
3(1+2+...+50) + 50(3) =
3(50)(51)/2 + 50(3) =
75*51 + 150 = 3975
The answer is A.
Answer: A
Question: Harry started a 6-mile hike with a full 7-cup canteen of water and finished the hike in 2 hours with 1 cup of water remaining in the canteen. If the canteen leaked at the rate of 1 cup per hour and Harry drank 1 cups of water during the last mile, how many cups did he drink per mile during the first 5 miles of the hike?
Options:
A)1/5
B)2/3
C)1/3
D)3/5
E)4/5
Rationale: A.
No of cups leaked during the trip = 2 cups.
No of cups Harry drank = 4 cups.
No of cups harry drank during the first 5 miles = 4.
drink / mile = 4/5
Answer: E
Answer: E
Question: Consider the word RMTMR. Whichever way you read it, from left to right or from right to left, you get the same word. Such a word is known as palindrome. Find the maximum possible number of 5 letter palindromes.
Options:
A)16500
B)17568
C)17576
D)13454
E)18776
Rationale: The first letter from the right can be chosen in 26 ways because there are 26 alphabets.
Having chosen this, the second letter can be chosen in 26 ways
The first two letters can chosen in 26 x 26 = 676 ways
Having chosen the first two letters, the third letter can be chosen in 26 ways.
All the three letters can be chosen in 676 x 26 =17576 ways.
It implies that the maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter.
C
Answer: C
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train.
Options:
A)150 meter
B)299 meter
C)278 meter
D)208 meter
E)277 meter
Rationale: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 9
= 150 meter
Answer:A
Answer: A
Question: If the sum of n consecutive positive integers is 33, what of the following could be the value of n?
I. 3
II. 6
III. 11
Options:
A)I only
B)II only
C)III only
D)I and II
E)I, II and III
Rationale: solved it the way bunuel explained, although took some time to arrive to the answer choice.
3 -> 10+11+12=33.
6 ->3+4+5+6+7+8=33.
11 -> since we are told that we have a set of n consecutive POSITIVE numbers, we can have the smallest possible numbers:
1+2+3+4+5+6+7+8+9+10+11 - the sum is way over 33, it is actually 11*12/2 = 11*6=66.
thus, only I and II works. the answer is D
Answer: D
Question: A trained covered x km at 40 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 3x km.
Options:
A)22
B)99
C)24
D)77
E)898
Rationale: Total time taken = x/40 + 2x/20 hours
= 5x/40 = x/8 hours
Average speed = 3x/(x/8) = 24 kmph.Answer: C
Answer: C
Question: Look at this series: 53, 53, 40, 40, 27, 27, ... What number should come next?
Options:
A)12
B)15
C)14
D)18
E)17
Rationale: In this series, each number is repeated, then 13 is subtracted to arrive at the next number.
ANSWER C
Answer: C
Question: A certain school principal must choose 5 students to attend a field trip out of a group of 10 students. In addition, out of the 5 chosen students, the principal must select a note-taker and a treasurer. How many different ways are there for the principal to select the 5 students and then select the treasurer and the note-taker?
Options:
A)1,260
B)2,520
C)5,040
D)6,020
E)10,080
Rationale: Out of 10 students, 5 students can be chosen in 10C5 ways.
Out of the 5 chosen students, note taker role can be taken in 5 ways
Since the note taker role is already taken by 1 student, the treasure role can be taken in 4 ways
Total number of ways = 10C5 * 5 * 4 = 5040
Answer: C
Answer: C
Question: What is the remainder when 3990990900032 is divided by 32 ?
Options:
A)0
B)8
C)4
D)2
E)3
Rationale: Though i was unaware of the divisibility test for 32 but i guessed the pattern!!
divisibility rule for 4- last two digits must be divisible by 4
divisibility rule for 8- last three digits must be divisible by 8
similarly, divisibility rule for 32 - last five digits must be divisible by 32
Hence, Ans A
Answer: A
Question: From the below series find the remainder?
1201 × 1203 ×1205 × 1207 is divided by 6
Options:
A)3
B)6
C)8
D)4
E)9
Rationale: If you don't know the above rule, this problem is really calculation intensive.
But by applying the above rule, when 1201, 1201, 1203, 1204 divided by 6, leaves remainders 1, 3, 5, 1. The product of these remainders = 15.
When 15 is divided by 6, Remainder is 3
A
Answer: A
Question: Using all the letters of the word "NOKIA", how many words can be formed, which begin with N and end with A?
Options:
A)8
B)6
C)9
D)3
E)1
Rationale: There are five letters in the given word.
Consider 5 blanks ....
The first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 3! ways.
The number of words = 3! = 6.
Answer:B
Answer: B
Question: The price of a jacket is reduced by 25%. During a special sale the price of the jacket is reduced another 30%. By approximately what percent must the price of the jacket now be increased in order to restore it to its original amount?
Options:
A)100
B)125
C)122.2
D)105.5
E)65
Rationale: 1) Let the price of jacket initially be $100.
2) Then it is decreased by 25% , therefore bringing down the price to $75.
3) Again it is further discounted by 30%, therefore bringing down the price to $45.
4) Now 67.5 has to be added byX %in order to equal the original price.
45 + ( X% ) 45 = 100.
Solving this eq for X, we get X = 122.2
Ans is C.
Answer: C
Question: If x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year, the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $38. If $2,000 is the total amount invested, how much is invested at 8 percent?
Options:
A)$700
B)$800
C)$900
D)$1100
E)$1200
Rationale: 0.1x = 0.08(2000-x)+38
0.18x = 198
x = 1100
Then the amount invested at 8% is $2000 - $1100 = $900
The answer is C.
Answer: C
Question: a is a positive integer and multiple of 2; p = 4^a, what is the remainder when p is divided by 10?
Options:
A)10
B)6
C)4
D)0
E)It Cannot Be Determined
Rationale: It is essential to recognize that the remainder when an integer is divided by 10 is simply the units digit of that integer. To help see this, consider the following examples:
4/10 is 0 with a remainder of 4
14/10 is 1 with a remainder of 4
5/10 is 0 with a remainder of 5
105/10 is 10 with a remainder of 5
It is also essential to remember that the a is a positive integer and multiple of 2. Any integer that is a multiple of 2 is an even number. So, a must be a positive even integer.
With these two observations, the question can be simplified to:what is the units digit of 4 raised to an even positive integer?
The units digit of 4 raised to an integer follows a specific repeating pattern:
4^1 = 4
4^2 = 16
4^3 = 64
4^4 = 256
4^(odd number) --> units digit of 4
4^(even number) --> units digit of 6
There is a clear pattern regarding the units digit. 4 raised to any odd integer has a units digit of 4 while 4 raised to any even integer has a units digit of 6.
Since a must be an even integer, the units digit of p=4^a will always be 6. Consequently, the remainder when p=4^a is divided by 10 will always be 6.
In case this is too theoretical, consider the following examples:
a=2 --> p=4^a=16 --> p/10 = 1 with a remainder of 6
a=4 --> p=4^a=256 --> p/10 = 25 with a remainder of 6
a=6 --> p=4^a=4096 --> p/10 = 409 with a remainder of 6
a=8 --> p=4^a=65536 --> p/10 = 6553 with a remainder of 6
Answer: B.
Answer: B
Question: A room 8 m 47 cm long and 7m 77 cm broad is to be paved with square tiles. Find the least number of square tiles required to cover the floor.
Options:
A)13636
B)13440
C)13647
D)13431
E)13675
Rationale: Explanation:
Area of the room = (847 x 777) cm2.
Size of largest square tile = H.C.F. of 847 cm and 777 cm = 7 cm.
Area of 1 tile = (7 x 7) cm2.
Number of tiles required =(847×777)/(7×7)=13431
Answer: Option D
Answer: D
Question: A large delicatessen purchased Q pounds of cheese for c dollars per pound. If d pounds of the cheese had to be discarded due to spoilage and the delicatessen sold the rest for s dollars per pound, which of the following represents the gross profit on the sale of the purchase? (gross profitequalssales revenueminusproduct cost)
Options:
A)(p − d)(s − c)
B)s(p − d) − pc
C)c(p − d) − ds
D)d(s − c) − pc
E)pc − ds
Rationale: Total cost price = c*Q ............... (1)
Wastage = d pounds
Quantity sold = p-d
Selling price per pound = s
Total selling price = s(Q-d) ........... (2)
Profit = (2) - (1)
= s(Q-d) - cQ
E
Answer: E
Question: What is the sum of all the composite numbers up to 12?
Options:
A)21
B)20
C)36
D)40
E)49
Rationale: Explanation:
4 + 6 + 8 + 9 + 10 +12 = 37
Answer: E
Answer: E
Question: If n is the product of 3 consecutive integers, which of the following must be true about n?
I. n is a multiple of 2
II. n is a multiple of 3
III. n is a multiple of 4
Options:
A)I only
B)II only
C)III only
D)I and II
E)II and III
Rationale: n is the product of 3 consecutive integers.
So, according to the rule, n must be divisible by 3, 2 and 1
So, we already know that statements I and II must be true.
Do we need to check statement III? No.
Notice that NONE of the answer choices include all 3 statements. Since we've already concluded that statements I and II are true, the correct answer is D.
Answer: D
Question: How many positive even integers less than 100 contain digits 7 or 9?
Options:
A)16
B)17
C)18
D)19
E)10
Rationale: Two digit numbers:
7 at tens place: 70,72,74,76,78
9 at tens place: 90,92,94,96,98
If 7 and 9 is at units place, the number cant be even
Total:5+5= 10
Answer E
Answer: E
Question: 36 men can complete a piece of work in 18 days. In how many days will 72 men complete the same work ?
Options:
A)24
B)17
C)18
D)9
E)11
Rationale: Explanation:
Less Men, means more Days {Indirect Proportion}
Let the number of days be x
then,
72 : 36 :: 18 : x
x = 9
Answer: D) 9 days
Answer: D
Question: If x is a positive integer, which of the following must be odd?
Options:
A)x+1
B)x^2+x
C)x^2+x+7
D)x^2−1
E)3x^2−3
Rationale: A. X+1 = can be odd or even. Since O + O =E or E + O = O
B. X^2 + X = X(X+1). Since from the above derivation we already know the term X+1 can be Odd or Even, directly substitute here. X(ODD) = Even (When X is Even) or X(EVEN) = EVEN [When X is ODD]
C. Here's the answer. Since we know the term x^2 + X can always take a EVEN number, EVEN + 7 = ODD
Hence C.
Answer: C