divelab/Sys2Bench huggingface dataset:
Question: If W is the set of all the integers between 10 and 332, inclusive, that are either multiples of 3 or multiples of 2 or multiples of both, then W contains how many numbers?
Options:
A)111
B)28
C)160
D)213
E)107
Rationale: Official Solution:
Number of multiples of 3
Step 1. Subtract the extreme multiples of 3 within the range (The greatest is 330, the smallest is 12): 330 - 12 = 318
Step 2. Divide by 3: 318 / 3 = 106
Step 3. Add 1: 106 + 1 = 107.
So there are 107 multiples of 3 within the range: examples are 51, 54, 57, 60, etc.
Number of multiples of 2
Step 1. Subtract the extreme multiples of 2 within the range (The greatest is 330, the smallest is 12): 330 - 12 = 318
Step 2. Divide by 2: 318 / 2 = 159
Step 3. Add 1: 159 + 1 = 160.
So there are 160 multiples of 2 within the range: examples are 50, 52, 54, 56, 58, 60 etc.
Add the 107 multiples of 3 and the 160 multiples of 2: 107+160=267.However, by adding the multiples of 2 and the multiples of 3, we are effectively counting several numbers twice: for example, 54 and 60 are parts of both the lists above. So we can't just take 107+160=267. Find the Number of multiples of 6 (which are the double counted, as 6 is divisible by both 2 and 3), and subtract it from 25:
Step 1. Subtract the extreme multiples of 6 within the range (The greatest is 72, the smallest is 54): 330 - 12 = 318
Step 2. Divide by 6: 318 / 6 = 53
Step 3. Add 1: 53 + 1 =54.
So there are 54 multiples of 6 within the range: we counted 54 numbers twice.
Subtract the 54 multiples of 6 from the sum of the multiples of 2 and 3:
= 107+160 - 54
= 267 - 54
= 213
Therefore, the final number of multiples of 2, 3 or 6 is 213.
Hence, this is the correct answer. (D)
Answer: D
Question: For any positive integer N, the sum of the first N positive integers equals N(N+1)/2 . If M and N are positive integers and M > N, what is the sum of all the integers between M and N, inclusive?
Options:
A) M(M+1)/2 + N(N+1)/2
B) M(M+1)/2 - N(N-1)/2
C) M(M+1)/2 - N(N+1)/2
D) M(M+1)/2 + N(N-1)/2
E) M(N+1)/2 - N(M-1)/2
Rationale: The sum of all the integers between M and N,inclusiveis the sum of the first M positive integersminusthe sum of the first N-1 positive integers.
The sum of the first M positive integers is M(M+1)/2;
The sum of the first N-1 positive integers is (N-1)N/2;
Therefore the answer is M(M+1)/2 - (N-1)N/2.
Answer: B.
Answer: B
Question: A women purchased 3 towels @ Rs.100 each, 5 towels @ Rs.150 each and two towels at a certain rate which is now slipped off from his memory. But she remembers that the average price of the towels was Rs.155. Find the unknown rate of two towels?
Options:
A)A)400
B)B)450
C)C)500
D)D)550
E)E)600
Rationale: 10 * 155 = 1550
3 * 100 + 5 * 150 = 1050
1550 – 1050 = 500
C
Answer: C
Question: A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used?
Options:
A)5
B)6
C)8
D)7
E)4
Rationale: 7 * 8 : 9 * x
= 8:9 => x= 7
Answer:D
Answer: D
Question: Which of the following describes all values of x for which 1–x^2 = 0?
Options:
A) x >= 1
B) x <= –1
C) x=1; x=–1
D) x =2
E) x=-2
Rationale: Which of the following describes all values of x for which 1–x^2 = 0?
(A) x >= 1
Plugged in 2. 1–(2)^2 >= 0 -3>=0? NO. Wrong
(B) x <= –1
Plugged in -2. 1–(-2)^2 >= 0 -3>=0? NO. Wrong
(C) x=1; x=–1
Plugged in 1. 1–1^2 = 0. Also -1. 1–(-1)^2 = 0. Since both are correct, answer is c.
(D) x =2
1–(2)^2 = -3. Wrong.
(E) –1 <= x <= 1
1–(-2)^2 = -3. Wrong
Answer is C.
Answer: C
Question: 5005 - 5000 ÷ 10.00 = ?
Options:
A)0.5
B)50
C)5000
D)4505
E)None
Rationale: Answer
Given expression = 5005 - 5000 ÷ 10.00
= 5005 - 500
= 4505
Correct Option: D
Answer: D
Question: The ratio of the radius of two circles is 1: 3, and then the ratio of their areas is?
Options:
A)1:6
B)1:0
C)1:9
D)1:2
E)1:1
Rationale: r1: r2 = 1: 3
Πr12: Πr22
r12: r22 = 1:9
Answer:C
Answer: C
Question: What is the greater of the two numbers whose product is 1280, given that the sum of the two numbers exceeds their difference by 32?
Options:
A)A)90
B)B)100
C)C)110
D)D)70
E)80
Rationale: Let the greater and the smaller number be g and s respectively.
g*s = 1288
g + s exceeds g - s by 32 i.e., g + s - (g - s) = 32
i.e., 2s = 32 => s = 16.
g = 1280/s = 80.
ANSWER:E
Answer: E
Question: Find the fraction which has the same ratio to 2/3 that 3/5 has to 6/7
Options:
A)1/5
B)2/22
C)3/4
D)7/15
E)5/6
Rationale: P : 2/3 = 3/5 : 6/7
As the product of the means is equal to the product of the extremes.
P*6/7 = 2/3 * 3/5
P*6/7 = 6/15
P = 7/15 => P = 7/15
ANSWER:D
Answer: D
Question: An amount of Rs. 3000 becomes Rs. 3600 in four years at simple interest. If the rate of interest was 1% more, then what was be the total amount?
Options:
A)3728
B)3726
C)3720
D)3722
E)3721
Rationale: A = P(1 + TR/100)
=> 3600 = 3000[1 + (4 * R)/100] => R = 5%
Now R = 6%
=> A = 3000[1 + (4 * 6)/100] = Rs. 3720.
Answer: C
Answer: C
Question: If a quarter Kg of potato costs 60 paise, How many paise will 200 gm cost?
Options:
A)48 Paise
B)26 Paise
C)28 Paise
D)11 Paise
E)12 Paise
Rationale: Explanation:
Let the Required cost be X paise. Less Weight , Less cost (Direct Proportion)
\inline \fn_jvn \therefore \inline \fn_jvn 250:200:: 60:x \inline \fn_jvn \Leftrightarrow \inline \fn_jvn 250\times X =(200\times 60) \inline \fn_jvn \Leftrightarrow \inline \fn_jvn x=\frac{(200\times 60)}{250} \inline \fn_jvn \Leftrightarrow x= 48
Answer: A
Answer: A
Question: In the set of positive integers from 1 to 80, what is the sum of all the odd multiples of 5?
Options:
A)180
B)245
C)320
D)260
E)270
Rationale: reduce to 1 - 80
5 - 15 - 25 - 35 - 45--55--65--75 are valid multiples. Add them --> 320
C
Answer: C
Question: The difference between the two numbers is 1/3 of the larger number. If the smaller one is 48 the larger one is
Options:
A)72
B)60
C)32
D)96
E)65
Rationale: Explanation:
Let the larger number be x. Then,
x - 48 = 1/3 x
x - x/3 = 48
=> 2x/3 = 48 => x = 72
Answer: Option A
Answer: A
Question: Jerry and john play a card game. In the beginning of the game they have an equal number of cards. Each player, at her turn, gives the other a third of her cards. john plays first, giving Jerry a third of her cards. Jerry plays next, and john follows. Then the game ends. jerry ended up with 14 more cards than Michelle. How many cards did each player have originally?
Options:
A)28
B)27
C)29
D)30
E)31
Rationale: Game john jerry
Initially2727
After game 1 1836
After game 2 3024
After game 3 2034
Now Merry has 14 cards more than Michelle. This option gives us exactly what number of cards they had initially.
So the answer is B
Answer: B
Question: The ratio of two numbers is 5 to 1. The sum is 18. What are the two numbers?
Options:
A)17
B)18
C)19
D)20
E)21
Rationale: Solution
Let x be the first number. Let y be the second number
x / y = 5 / 1
x + y = 18
Using x / y = 5 / 1, we get x = 5y after doing cross multiplication
Replacing x = 5y into x + y = 18, we get 5y + y = 18
6y = 18
y = 3
x = 5y = 5 × 3 = 15
As you can see, 15/3 = 5, so ratio is correct and 3 + 15 = 18, so the sum is correct.
Answer B
Answer: B
Question: A drawer holds 5 red hats and 5 blue hats. What is the probability of getting exactly three red hats or exactly three blue hats when taking out 5 hats randomly out of the drawer and returning each hat before taking out the next one?
Options:
A)1/8
B)1/4
C)1/2
D)5/8
E)7/12
Rationale: Let's find the probability of getting exactly 3 red hats.
One possible case is red-red-red-blue-blue.
The probability of this is 1/2*1/2*1/2*1/2*1/2 = 1/32
There are 5C3 = 10 such cases so we need to multiply this by 10.
P(exactly 3 red hats) = 10*1/32 = 5/16
Clearly the probability of getting exactly 3 blue hats will also be 5/16.
The sum of the probabilities is 5/16+5/16 = 5/8
The answer is D.
Answer: D
Question: From group of 15 cricket players a team of 11 players is to be chosen. How many ways this can be done?
Options:
A)3252
B)1365
C)5325
D)1432
E)1324
Rationale: 11 players are to be chosen from 15 players. This can be done in 15C11 ways. ie) 15!/11!x4! = 1365 ways. Ans: B
Answer: B
Question: How many 3/4 foot pieces of cable can be cut out of a piece that is 30 feet long?
Options:
A)a.30
B)b.36
C)c.37
D)d.38
E)e. 40
Rationale: Pretty Simple..the answer is choice (E) 40.
All that one has to do is :
1: Convert 3/4 into an improper fraction (3/4) or a decimal (0.75)
2: Divide 30 by 3/4 (or 0.75)
Answer =40 (E)
Answer: E
Question: The ratio of the area of a square mirror to its frame is 16 to 33. If the frame has a uniform width (s) around the mirror, which of the following could be the value, in inches, of s ?
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 s value to be a multiple of 1.5 = multiple of 3/2 and since s is not constrained to be only integer all the three choices are possible
For i) the multiple of s is 4/3
For ii) the multiple of s is 7/3
For iii) the multiple of s is 10/3
The key is s can be any real positive number... very tricky problem.. took me > 15 minutes.
Answer is E
Answer: E
Question: The diagonals of a rhombus are 22 cm and 30 cm. Find its area?
Options:
A)358
B)329
C)350
D)330
E)317
Rationale: 1/2 * 22 * 30 = 330
Answer:D
Answer: D
Question: Two women can do a work in 4 days. Six men can complete the same work in 3 days. What is the ratio between the capacity of a man and a woman?
Options:
A)1:2
B)2:1
C)4:9
D)3:2
E)None of these
Rationale: Explanation:
(2 Ã— 4 ) women can complete the work in 1 day.
âˆ´ 1 woman's 1 day's work = 1/8
(6 Ã— 3) men can complete the work in 1 day.
âˆ´ 1 man's 1 day's work = 1/18
so, required ratio =1/8 : 1/18= 4:9
Answer: C
Answer: C
Question: 85% of a number is added to 24, the result is the same number. Find the number?
Options:
A)13√5
B)13√2
C)13√9
D)12√9
E)13√1
Rationale: 4a = 48 4a = 20
a = 12 a = 5
a2 = 144 a2 = 25
Combined area = a2 = 169 => a = 13
d = 13√2
Answer:B
Answer: B
Question: Kamal obtained 96, 65, 82, 67 and 85 marks(out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
Options:
A)65
B)69
C)72
D)79
E)NOne
Rationale: Sol.
Average
= 96 + 65 + 82 + 67 + 85 / 5)
= (395 / 5)
= 79.
Answer D
Answer: D
Question: The sum of two numbers is 25 and their difference is 13. Find their product.
Options:
A)104
B)108
C)114
D)325
E)None
Rationale: Sol.
Let the numbers be x and y.
Then, x + y = 25 and x - y = 13.
4xy = (x+y)2 - (x-y)2
= (25)2 - (13)2 = 625 - 169 = 456
⇒ xy = 114.
Answer C
Answer: C
Question: For each of her sales, a saleswoman receives a commission equal to 20 percent of the first $500 of the total amount of the sale, plus 35 percent of the total amount in excess of $500. If the total amount of one of her sales was $800, the saleswoman’s commission was approximately what percent of the total amount of the sale?
Options:
A)22%
B)24%
C)25%
D)26%
E)28%
Rationale: Total sales =800
Comission = (20/100)*500+ (35/100)*300
=100 + 105
=205
%Comission =(205/800)*100=25.6~ 26%
Answer is D
Answer: D
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 50 years now, the son's age five years back was?
Options:
A)18years
B)19years
C)20years
D)21years
E)22years
Rationale: Let the son's present age be x years. Then, (50 - x) = x
2x = 50.
x = 25.
Son's age 5 years back (25 - 5) = 20 years.
C)
Answer: C
Question: 1, 8, 27, 64, 125, 216, (....)
Options:
A)354
B)343
C)245
D)392
E)400
Rationale: The pattern is 1^3, 2^3, 3^3, 4^3, 5^3, 6^3, etc
Hence, next number is 7^3 = 343
Answer is B
Answer: B
Question: A shipment of 1500 heads of cabbage, each of which was approximately the same size was purchased for $600.The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head.The following day the rest were sold at a price per head equal to 12% less than the price each head sold for the day before.what was the gross profit on this shipment?
Options:
A)$100
B)$115
C)$120
D)$130
E)$135
Rationale: Sol:
1500 heads -> $600
1 head -> $600/1500
1 head -> $(2/5)
25% more of (2/5) -> 125/100 * 2/5 = $(1/2)
He sold 2/3*1500 = 1000 heads for $(1/2) per head
Total revenue by selling 1000 heads = 1000 * 1/2 = $500
Heads left: 500
Cost per head: 88% of the previous price: 88/100 * 1/2 = $(11/25)
Total revenue by selling 500 heads = 11/25 * 500 = 220
Total revenue after selling 1500 cabbage heads - 220+500 = $720
Money spent on the purchase: $600
Profit = 720-600 = $120
Ans: "C
Answer: C
Question: A train running at the speed of 60 km/hr crosses a pole in 15 sec. What is the length of the train?
Options:
A)250
B)279
C)277
D)272
E)150
Rationale: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 15
= 250 m
Answer: A
Answer: A
Question: An escalator moves towards the top level at the rate of 10 ft.sec and its length is 112 feet. If a person walks on the moving escalator at the rate of 4 feet per second towards the top level, how much time does he take to cover the entire length.
Options:
A)14 sec
B)10 sec
C)12 sec
D)8 sec
E)9 sec
Rationale: Time taken to cover the entire length = tot.dist/resultant speed
= 112/ (10+4)
= 8 sec
ANSWER:D
Answer: D
Question: If FRIEND is coded as HUMJTK, how is CANDLE written in that code ?
Options:
A)EDRIRL
B)FFIIIUU
C)WDFDD
D)DRFED
E)E8U8W
Rationale: Explanation:
The first, second, third, fourth, fifth and sixth letters of th word are respectively moved two, three, four, five, six and seven steps forward to obtain the corresponding letters of the code.
Answer: A
Answer: A
Question: The average of 10 numbers is calculated as 16. It is discovered later on that while calculating the average, the number 35 was incorrectly read as 25, and this incorrect number was used in the calculation. What is the correct average?
Options:
A)16
B)17
C)19
D)22
E)26
Rationale: The total sum of the numbers should be increased by 10.
Then the average will increase by 10/10 = 1.
The correct average is 17.
The answer is B.
Answer: B
Question: After 10% of the inhabitants of a village disappeared, a panic set in during which 25% of the remaining inhabitants left the village. At that time, the population was reduced to 5265. What was the number of original inhabitants?
Options:
A)7500
B)7800
C)8100
D)8400
E)8700
Rationale: Let the total number of original inhabitants be x.
(75/100) * (90/100) * x = 5265
(27/40) * x = 5265
x = 5265 * 40 / 27 = 7800
The answer is B.
Answer: B
Question: A BAG CONTAINS 6 WHITE AND 4 BLACK BALLS .2 BALLS ARE DRAWN AT RANDOM. FIND THE PROBABILITY THAT THEY ARE OF SAME COLOUR.
Options:
A)8/9
B)75/4
C)7/15
D)3/7
E)4/3
Rationale: LET S BE THE SAMPLE SPACE
THEN N(S)=NO OF WAYS OF DRAWING 2 BALLS OUT OF (6+4)=10C2=(10*9)/(2*1)=45
LET E=EVENT OF GETTING BOTH BALLS OF SAME COLOUR
THEN N(E)=NO OF WAYS(2 BALLS OUT OF SIX) OR(2 BALLS OUT OF 4)
=(6C2+4C2)=(6*5)/(2*1)+(4*3)/(2*1)=15+6=21
P(E)=N(E)/N(S)=21/45=7/15
Ans: C
Answer: C
Question: A certain company had a total annual expenditure of 1.47∗10^7 on employee salaries last year. If the company employed 420 people, what was the average employee salary?
Options:
A)$20,000
B)$25,000
C)$35,000
D)$40,000
E)$45,000
Rationale: Given: Total annual expenditure of 1.47∗10^7 on employee salaries
Total employees = 420
Observe that 420*3.5 = 1470
Therefore try to bring the numerator in terms of 1470
Average salary = (1470*10^4) /420 = 3.5*10^4 = 35,000
Option C
Answer: C
Question: which number need to add to 859622 to get a number exactly divisible by 456?
Options:
A)544365
B)465674
C)345465
D)675644
E)859622
Rationale: Dividend = Quotient * Divisor + Reminder
859622 / 456 gives quotient = 1885 and reminder = 62.
So, the next number divisible by 456 is 456 places infront of 456 * 1885
Which means 456 – 62 = 394 should be added to 859622.
E
Answer: E
Question: A rectangular with dimensions 16 inches by 20 inches is to be divided into squares of equal size. Which of the following could be a length of a side of the squares?
Options:
A)a) 4 inches
B)b) 6 inches
C)c) 7 inches
D)d) 8 inches
E)e) 10 inches
Rationale: you need to divide the width and length of the rectangular to equal pieces where L = W
you can solve this using GCF
16=2*2*2*2
20=2*2*5
GCF = 2*2= 4
P.S you can make squares with side of 2,4 and we choose 4 because 2 is not in the answers
Answer : A
Answer: A
Question: A woman invested $1,000, part at 5% and the rest at 6%. Her total investment with interest at the end of the year was $1,054. How much did she invest at 5%?
Options:
A)$500
B)$600
C)$700
D)$900
E)$950
Rationale: et x be the portion invested at 5% and
Let (1-x) be the rest which is invested at 6%
The question states that the return after 1 year is (1054/1000)-1 = 0.054 = 5.4%
We want to find the dollar amount invested in X
Using our defined variables, put together the equation and solve for x (the percentage of 1000 invested at 5%)
0.05x+0.06(1-x)= 0.054
(0.05)x +0.06 - (0.06)x = 0.054
-0.01x = -0.006
x= -0.006/-0.01 = 6/10 = 60%
So X = 60% of the 1000 which is 600
ANSWER:B
Answer: B
Question: CX, EV, GT, IR, ?
Options:
A)JH
B)UU
C)KP
D)UY
E)IS
Rationale: ANSWER:C
Answer: C
Question: The figure shown can be folded into the shape of a cube. In the resulting cube, which of the lettered faces is opposite the face marked x?
Options:
A)D
B)H
C)J
D)H
E)W
Rationale: Explanation: If you fold the above picture at the dotted lines, X and C are opposite to each other.
Answer:A
Answer: A
Question: A cylinder and a cone have the same height and same radius of base. The ratio between the volumes of the cylinder and the cone is:
Options:
A)4:1
B)2:1
C)7:1
D)5:1
E)3:1
Rationale: Volume of the cylinder = πr(power2)h
Volume of the cone = 1/3 πr(power2)h
(πr(power2)h)/(1/3 πr(power2)h) = 3/1 = 3 : 1
Answer is E.
Answer: E
Question: A 10-by-5 inch piece of paper is used to form the lateral surface of a cylinder. If the entire piece of paper is used to make the lateral surface, which of the following must be true of the two possible cylinders that can be formed?
Options:
A)The volume of the cylinder with height 10 is 50/pi cubic inches greater than the volume of the cylinder with height 6.
B)The volume of the cylinder with height 5 is 50/pi cubic inches greater than the volume of the cylinder with height 10.
C)The volume of the cylinder with height 10 is 50pi cubic inches greater than the volume of the cylinder with height 6.
D)The volume of the cylinder with height 5 is 50pi cubic inches greater than the volume of the cylinder with height 10.
E)The volume of the cylinder with height 5 is 250/pi cubic inches greater than the volume of the cylinder with height 10.
Rationale: Pretty straightforward. Plug in the values to compute the volume of the cylinder. Keep in mind 5 and 10 are the circumference of the base and not the radius. B is the right answer.
Answer: B
Question: A BUS is running at a speed of 40 km/hr and it crosses a post in 18 seconds. What is the length of the BUS ?
Options:
A)metres
B)metres
C)metres
D)metres
E)metres
Rationale: Explanation:
Speed of the BUS, v = 40 km/hr = 40000/3600 m/s = 400/36 m/s
Time taken to cross, t = 18 s
Distance Covered, d = vt = (400/36)× 18 = 200 m
Distance covered is equal to the length of the BUS= 200 m
Answer: Option C
Answer: C
Question: The average age of the mother and her six children is 8 years which is reduced by 5 years if the age of the mother is excluded. How old is the mother?
Options:
A)38
B)41
C)42
D)43
E)44
Rationale: Total age of mother and 6 children = avg x n = 8 x (6+1)= 56
If mother is excluded new average is (8 - 5) = 3
so for 6 children = 6 x 3 =18
so mother's age is 56 - 18 =38
Answer: Option A
Answer: A
Question: If a and b are positive real numbers, and a^3 + b^3 = 25, then the greatest possible value of a is between:
Options:
A)0 and 3
B)3 and 4
C)4 and 5
D)5 and 7
E)7 and 9
Rationale: If a > 3, then a^3 + b^3 > 25.
The answer is A.
Answer: A
Question: The “length of integer x” refers to the number of prime factors, not necessarily distinct, that x has. (If x = 60, the length of x would be 4 because 60 = 2 × 2 × 3 × 5.) What is the greatest possible length of integer z if z < 1,080?
Options:
A)13
B)10
C)9
D)7
E)6
Rationale: To maximize the length of z we should minimize its prime base. The smallest prime is 2 and since 2^10=1,024<1,080 then the greatest possible length of integer z is 10.
Answer: B.
Answer: B
Question: How many distinct integer values of n satisfy the inequality||n-3| + 2| ≤ 12?
Options:
A)15
B)16
C)12
D)18
E)19
Rationale: so i can write this as In-3I+2<=12
or In-3I<=10
so n can have -7 to 13 = 12 true values....
C
Answer: C
Question: How is 2% expressed as a decimal fraction?
Options:
A)0.2
B)0.02
C)0.002
D)0.0002
E)2
Rationale: 2/100= 0.02
ANSWER:B
Answer: B
Question: There are 1200 jelly beans divided between two jars, Jar X and Jar Y. If there are 400 fewer jelly beans in jar X than three times the number of beans in jar Y, how many beans are in jar X?
Options:
A)650
B)700
C)750
D)800
E)850
Rationale: X+Y=1200 so Y=1200-X
X=3Y-400
X=3(1200-X)-400
4X=3200
X=800
The answer is D.
Answer: D
Question: f n = 3^4 - 2^4, which of the following is NOT a factor of n?
Options:
A)13
B)22
C)65
D)169
E)130
Rationale: ( 3^2+2^2)(3^2-2^2) = 13*5*1 . 13 and 5 prime number and factor any thing not having 13 and 5 as factor will not be a factor.
B
Answer: B
Question: The banker's discount on a bill due 4 months hence at 15% is $6.20. The true discount is:
Options:
A)$5.90
B)$6.80
C)$6.60
D)$6.70
E)$6.10
Rationale: T.D.	=	B.D. x 100/100 + (R x T)
= $ [6.20 x 100/100 +15 x 1/3]
= $	[6.20 x 100/105]
= $ 5.90
ANSWER:A
Answer: A
Question: Find the area of the quadrilateral of one of its diagonals is 10 cm and its off sets 7 cm and 3 cm?
Options:
A)50 cm2
B)100 cm2
C)150 cm2
D)200 cm2
E)250 cm2
Rationale: 1/2 * 10(7 + 3)
= 50 cm2
Answer: A
Answer: A
Question: If ab > 0, which of the following must be negative?
Options:
A)a + b
B)|a| + b
C)b - a
D)a/b
E)-a/b
Rationale: If ab > 0 the we Infer that a and b both have same sign i.e. either both a and b are Positive or Both a and b are Negative
Now Checking Options:
(A) a + b will be positive for both a and b to be positive hence INCORRECT OPTION
(B) |a| + b will be positive for both a and b to be positive hence INCORRECT OPTION
(C) b - a May be positive for both a and b to be positive (e.g. b=3 and a=2) henceINCORRECT OPTION
(D) a/b will be positive for both a and b to be positive or Negative hence INCORRECT OPTION
(E) -a/b will always be Negative because an and b have same sign so a/b will be positive therefore -a/b will be Negative hence CORRECT
Answer: Option E
Answer: E
Question: Anand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak's share is :
Options:
A)Rs. 5400
B)Rs. 700
C)Rs. 8400
D)2Rs. 9600
E)Rs. 8000
Rationale: Explanation:
Ratio of their shares = 22500 : 35000 = 9 : 14.
Deepak's share = Rs.
(13800âˆ—14/23)
= Rs. 8400.
ANSWER IS C
Answer: C
Question: Some persons can do a piece of work in 12 days. Two times the number of these people will do half of that work in?
Options:
A)2 days
B)3 days
C)1 days
D)5 days
E)7 days
Rationale: B
3 days
12/ (2 * 2) = 3 days
Answer: B
Question: Find the value of x: 2x² + 9x − 5.
Options:
A)1/2
B)1/3
C)2/3
D)2/5
E)3/5
Rationale: That quadratic is factored as follows:
2x² + 9x − 5 = (2x − 1)(x + 5).
Lesson 17.
Now, it is easy to see that the second factor will be 0 when x = −5.
As for the value of x that will make
2x − 1	=	0,
we must solve that little equation. (Lesson 9.)
We have:
2x	=	1
x	=	1
2
The solutions are:
x	=	1/2 or −5
A
Answer: A
Question: Ram's age and Shyam's age are in the ratio 3:4. Seven years ago the ratio of their ages was 2:3. Find the ratio of their ages five years hence?
Options:
A)26/73
B)26/39
C)26/93
D)26/33
E)26/13
Rationale: Let ages of Ramu and Shyam be x and y respectively.
x/y = 3/4 => x = 3/4 y
(x- 7)/(y - 7) = 2/3
=> 3x - 21 = 2y - 14 => 3x = 2y + 7
But x = 3/4 y
3 * 3/4 y = 2y + 7
9y = 8y + 28 => y = 28years
=> x = 21 years
Ratio of their ages five years hence, (21 + 5)/(28 + 5) = 26/33.
Answer: D
Answer: D