divelab/Sys2Bench huggingface dataset:
Question: X and Y started a business with capitals Rs. 20000 and Rs. 25000. After few months Z joined them with a capital of Rs. 30000. If the share of Z in the annual profit of Rs. 50000 is Rs. 14000, then after how many months from the beginning did Z join?
Options:
A)3
B)4
C)6
D)9
E)5
Rationale: Investments of X, Y and Z respectively are Rs. 20000, Rs. 25000 and Rs. 30000
Let investment period of Z be x months.
Ratio of annual investments of X, Y and Z is (20000 * 12) : (25000 * 12) : (30000 * x)
= 240 : 300 : 30x = 8 : 10 : x
The share of Z in the annual profit of Rs. 50000 is Rs. 14000.
=> [x/ (18 + x)] 50000 = 14000 => [x/ (18 + x)] 25 = 7
=> 25x = 7x + (18 * 7) => x = 7 months.
Z joined the business after (12 - 7) months. i.e., 5 months.
Answer:E
Answer: E
Question: Two members of a certain club are selected to speak at the next club meeting. If there are 15 different possible selections of the 2 club members, how many members does the club have?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: Method-1
Total No. of Selection of r out of n objects are defined by nCr = n! / [(r!)(n-r)!]
i.e. If total member = n
then nC2 = n! / [(2!)(n-2)!] = 15
i.e. n*(n-1)*n-2!/ [(2!)n-2!] = 15
i.e. n*(n-1) = 30
(for Positive Values of n)
therefore, n*(n-1) = 30
i.e. n= 6
Answer: Option B
Answer: B
Question: Mr X, a businessman, had income in the year 1995 such that he earned a profit of 20% on his investment in the business. In the year 1996 his investment was less by 2000 but still had the same income (Income = Investment + Profit) as that in 1995. Thus the per cent profit earned in 1996 increased by 6%. What was his investment in 1995?
Options:
A)100000
B)12500
C)42000
D)Data inadequate
E)None of these
Rationale: Let the investment of X in 1995 be x.
∴ Profit = x⁄5
∴ Income = (x + x⁄5) = 6⁄5x
Investment of company X in 1996 would be (x – 2000) From the question,
(x - 2000) × 126⁄100 = 6⁄5x ⇒ x = 42000
Answer C
Answer: C
Question: If 2 cards are selected at random from the deck of 52 cards then What is the probability of one of the selected cards will be King and other will be 10?
A deck of cards has a total of 52 cards, consisting of 4 suits; (spades(Black), hearts(Red), diamond(Red)s, and clubs(Black)); and 13 cards including 1 king, 1 queen and 1 jack in each suit
Options:
A)8/2652
B)18/2652
C)1/2652
D)12/2652
E)16/2652
Rationale: 2 possible cases:
King - 10 or 10 -King (4 kings and 4 10).
Either way,
the total probability = 2( King -10) = 2 (4/52 * 4/51) = 18/2652. B is the correct answer.
Answer: B
Question: Ayesha's father was 35 years of age when she was born while her mother was 30 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
Options:
A)2 years
B)4 years
C)6 years
D)8 years
E)9 years
Rationale: Mother's age when Ayesha's brother was born = 30 years.
Father's age when Ayesha's brother was born = (35 + 4) years = 39 years.
Required difference = (39 - 30) years = 9 years. Answer: Option E
Answer: E
Question: sale of Rs 6835, Rs. 9927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs, 6700 ?
Options:
A)4966
B)6191
C)2877
D)2676
E)1881
Rationale: Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.
Required sale = Rs.[(6700 x 6) - 34009]
= Rs. (40200 - 34009)
= Rs. 6191
Answer: B
Answer: B
Question: In one can of mixed nuts, 10% is peanuts. In another can of mixed nuts that is one-half the size of the first one, 40% is peanuts. If both cans are emptied into the same bowl, what percentage of the mixed nuts in the bowl is peanuts?
Options:
A)16 2/3%
B)20%
C)25%
D)33 1/3%
E)35%
Rationale: Can 1: size 1; 10% nuts
Can 2: size 0.5 and 40% nuts
(1x0.1+0.5x0.4)/1.5=33.33
D
Answer: D
Question: There is a lot of speculation that the economy of a country depends on how fast people spend their money in addition to how much they save. Auggie was very curious to test this theory.
Auggie spent all of his money in 5 stores. In each store, he spent Rs.4 more than one-half of what he had when he went in. How many rupees did Auggie have when he entered the first store?
Options:
A)248
B)120
C)252
D)250
E)350
Rationale: Amount left = 0.5x−4
For fifth store this is zero. So x = 8. That means he entered fifth store with 8.
Now for fourth store, amount left = 8 so 0.5x−4=8⇒ x = 24
For third store, amount left = 24 so 12x−4=24⇒ x = 56
For Second store, amount left = 56 so 0.5x−4=56⇒ x = 120
For first store, amount left = 120 so 0.5x−4=120⇒ x = 248
So he entered first store with 248.
ANSWER:A
Answer: A
Question: What is the sum of the odd integers from 25 to 55, inclusive?
Options:
A)495
B)550
C)555
D)600
E)640
Rationale: The mean is 40.
Sum=Mean(# of elements)
There are 16 odd numbers between 25-55 inclusive. 16*40=640
E
Answer: E
Question: A farmer is having a total of 20 fruits (apples or oranges). He made two type packets with these fruits. All the fruits are in either apple packets of orange packets. Apple Packets contain 3 apples each and Orange packets contain 2 oranges each.
If |apple packets| < 4
Then How many packets of apples the farmer can have. When number of apple and orange packets are both positive integers above zero.
Options:
A)2
B)3
C)4
D)7
E)6
Rationale: Let us start by understand the meaning of 4 > |Number of Apples|
1) when we write |-x| this means the same as |x|.
2) Mod is very easy concept if you solve mod question by considering as a distance. when a mod is written as |x-(a)| = b, this means the distance from point 'a' (both side left and right of 'a' on number line) is b. |x-(a)| < b means the distance is between the two extreme distance(left and right side of 'a' on number line, considering the max distance is 'b' from 'a' - as per this scenario.....hence the value of 'a' must be between these two extremes. |x-(a)| > b means the distance is greater than the distance of 'b'..i.e the value of a could be anywhere more than 'b'.
Now come to the question. Let number of apple packets be ‘a’ and number of oranges packets be ‘b’. First its given |a| < 4 ==> |a-0| < 4 ==> the distance from zero is less than 4. So the point ‘a’ will be -3,-2,-1,0,1,2,3 as distance from 0 to these values is less than 4. Number of apple packets is above zero so possible values of ‘a’ left are 1,2,3.
As per the given information there are total of 20 fruits and they are in packets (3 per packet for apples and 2 per packets for oranges) so we can write it as follows:
3a + 2b = 20 ==> b = 10 – (3*a)/2. If b is an integer then ‘a’ must be divisible by 2. If we take only those values of ‘a’ that are divisible by 2 then we are left with 2 only. So there are two packets of apples. If there are two packets of apples then b = 10 – (3*2)/2 ==> b = 7. So we have 7 packets of oranges and 2 packets of apples. So A is the answer. 7 packets (2 orange each) and 2 packets of apples (3 apples each) make 20 fruits in total.
Answer: A
Question: A class average mark in an exam is 70. The average of students who scored below 60 is 50. The average of students who scored 60 or more is 75. If the total number of students in this class is 20, how many students scored below 60?
Options:
A)20
B)10
C)60
D)50
E)40
Rationale: Let n the number of students who scored below 60 and N the number of students who scored 60 or more. Xi the grades below 60 and Yi the grades 60 or above.
[sum(Xi) + sum(Yi)] / 20 = 70 : class average
sum(Xi) / n = 50 : average for less that 60
sum(Yi) / N = 75 : average for 60 or more
50n + 75N = 1400 : combine the above equations
n + N = 20 : total number of students
n = 4 and N = 16 : solve the above system
correct answer A
Answer: A
Question: The average (arithmetic mean)R of the four distinct positive integers p, q, s and t is x. If p and q are odd, and s and t are even, which of the following must be true?
I. x is an integer
II. (x−0.5) is an integer.
III. 2x is an odd integer.
Options:
A)I only
B)II only
C)III only
D)II and III only
E)None of the above
Rationale: Given :
p + q = EVEN (odd + odd =even)
p + q + s + t = EVEN (even + even = even) nothing more....
(p + q + s + t) / 4 = x
I.
x may or may not be integer, we only know sum of 4 variables is even not necessarily multiple of 4. I is out.
II.
Similarly, x an integer if sum of 4 variables is multiple of 4 but not an integer if it is not multiple of 4, we only know it is even. II is out.
III.
As in II, if X is integer 2x is Even, if X has decimal part (a.5), 2x is odd. III is out.
Answer E, None.
Answer: E
Question: A grocer stacked oranges in a pile. The bottom layer was rectangular with 4 rows of 5 oranges each. In the second layer from the bottom, each orange rested on 4 oranges from the bottom layer, and in the third layer, each orange rested on 4 oranges from the second layer. Which of the following is the maximum number of oranges that could have been in the third layer?
Options:
A) 6
B) 4
C) 3
D) 2
E) 1
Rationale: Bottom Layer = 5 x 4 = 20
IInd Layer = (5-1) x (4-1) = 12
IIIrd Layer = (4-1) x (3-1) = 6
Answer = 6 = A
Answer: A
Question: A person walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 8 minutes earlier. How far is the office from his house?
Options:
A)3 1/5 Km
B)4 Km
C)4 1/5 Km
D)3 2/5 Km
E)3 3/5 Km
Rationale: Formula = S1*S2/S2-S1 * T1+T2/60
= 4*6/2 * 16/6
= 24/2 * 16/60
= 8 * 2/5
= 16/5 = 3 1/5 Km
A
Answer: A
Question: Cubes with each side one inch long are glued together to form a larger cube. The larger cube's face is painted with red color and the entire assembly is taken apart. 23 small cubes are found with no paints on them . How many of unit cubes have at least one face that is painted red?
Options:
A)64
B)72
C)86
D)98
E)102
Rationale: Use the options.
The options which after getting added to 23 shows a cube of a number could be right.
Here
64+23 = 87
72+23= 95
86+23= 109
98+23 = 121
102+23=125 ---(5*5*5)
So we have 102 as the answer!
E
Answer: E
Question: A train sets off at 2 p.m. at the speed of 70 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet?
Options:
A)10.36
B)10.39
C)10.3
D)10.34
E)10.31
Rationale: D = 70 * 1 ½ = 105 km
RS = 85 – 70 = 15
T = 105/15 = 7 h
3.30 + 7 h = 10.30 p.m.
Answer:C
Answer: C
Question: An entry in an unshaded square is obtained by adding the entries connected to it from the row above (11 is one such number). Write the value of n ?
Options:
A)10
B)11
C)12
D)9
E)8
Rationale: see the values row wise
5 6 n 7
11 6+n 7+n
11+6+n 6+n+7+n
60
hence 11+6+n+6+n+7+n =60
n= 10
ANSWER:A
Answer: A
Question: The population of a town is 10000. It increases annually at the rate of 40% p.a. What will be its population after 2 years?
Options:
A)14000
B)14400
C)19600
D)14600
E)14700
Rationale: Formula :
10000 × 140/100 × 140/100 = 19600
Answer : C
Answer: C
Question: Length of a rectangular plot is 20mtr more than its breadth. If the cost of fencing theplot at 26.50 per meter is Rs.5300, what is the length of the plot in mtr?
Options:
A)40 m
B)60 m
C)70 m
D)77 m
E)80 m
Rationale: Let breadth = x metres.
Then, length = (x + 20) metres.
Perimeter = 5300 m = 200 m.
26.50
2[(x + 20) + x] = 200
2x + 20 = 100
2x = 80
x = 40.
Hence, length = x + 20 = 60 m
B
Answer: B
Question: How much interest will $10,000 earn in 9 months at an annual rate of 4%?
Options:
A)$300
B)$350
C)$450
D)$550
E)$650
Rationale: Soln:-
9 months = 3/4 of year;
4% = 4/100=1/25;
$10,000(principal)*1/25(interest rate)*3/4(time)=$300.
ANSWER:A
Answer: A
Question: What is the remainder when 8^714 is divided by 5 ?
Options:
A)2
B)3
C)1
D)0
E)4
Rationale: 8^0 = 1
8^1 = 8
8^2 = 64
8^3 = 512
8^4 = 4096
8^5 = .....8
and so on after ignoring the first last-digit of 8^0 = 1, in a recurring last-digit pattern of 8,4,2,6,8,4,2,6....
715/4 = 178 (with a remainder 2) so the last number is a 4.
so when 8^714 is divided by 5 the remainder is 4, ANS = E
Answer: E
Question: A small table has a length of 12 inches and a breadth of b inches. Cubes are placed on the surface of the table so as to cover the entire surface. The maximum side of such cubes is found to be 4 inches. Also, a few such tables are arranged to form a square. The minimum length of side possible for such a square is 40 inches. Find b.
Options:
A)8
B)6
C)24
D)32
E)48
Rationale: From the info that the maximum sides of the cubes is 4, we know that the GCF of 12 (=2^2*3) andbis 4 (=2^2), sob=2^x, where x>=2.
From the second premise, we know that the LCM of 12 (2^2*3) andbis 40 (2^3*5), sob=2^3 or 2^3*5 (8 or 40).
Combining 2 premises shows the answer is B(6).
Answer: B
Question: The edge of a cube is 5a cm. Find its surface?
Options:
A)150a2 cm2
B)170a2 cm2
C)125a2 cm2
D)175a2 cm2
E)120a2 cm2
Rationale: 6a2 = 6 * 5a * 5a = 150a2
Answer:A
Answer: A
Question: Of the 65 cars on a car lot, 45 have power steering, 25 have power windows, and 17 have both power steering and power windows. How many of the cars on the lot have neither power steering nor power windows?
Options:
A) 2
B) 8
C) 12
D) 15
E) 18
Rationale: Total -Neither = All power steering + All Power Windows - Both
or 65 - Neither = 45 + 25 -17 = 53.
=> Neither = 12, hence C.
Answer : C
Answer: C
Question: If x, y, and z are negative integers and 3x - 3y = -3z, then which of the following statements must be true?
I.	x > y>z
II.	x > y
III. x = z
Options:
A)I and II
B)I only
C)II only
D)III only
E)None
Rationale: 3x-3y=-3z
x-y=-z
Since z<0; -z>0
x-y>0
x>y
II correct.
We can't say much about z though;
x=-5; y=-100; z=-95
I and III incorrect.
Ans:C
Answer: C
Question: To create paint with a certain shade of gray, one must combine 2.116 liters of black paint with every one liter of white paint. Approximately how many liters of white paint must be combined with 350 liters of black paint to create the certain shade of gray?
Options:
A)165.4
B)176.4
C)347.1
D)694.4
E)705.6
Rationale: Since the ratio of Black to White is 2.016 to 1 this implies that Amount of Black is going to be more than (approximately double) the amount of White. This implies Option C, D and E can not be correct.
Now between A and B:
Black:White = 2.116:1 Since the ratio is more than double, the amount of White Paint should be less than half of Black Paint. B is more than half so can not be the answer, A fits the criteria hence should be the correct answer. No calculation needed whatsoever.
Answer: A
Question: Statements: The old order changed yielding place to new.
Assumption:
1) Change is the law of nature.
2) Discard old ideas because they are old.
Options:
A)Only conclusion I follows
B)Only conclusion II follows
C)Either I or II follows
D)Neither I nor II follows
E)Both I and II follow
Rationale: Clearly, I directly follows from the given statement. Also, it is mentioned that old ideas are replaced by new ones, as thinking changes with the progressing time. So, II does not follow.
A
Answer: A
Question: A man is 24 years older than his son.In two years, his age will be twice the age of his son.The present age of the son is :
Options:
A)22
B)25
C)45
D)32
E)15
Rationale: Let the son's present age be x years. Then, man's present age =(x+24) years.
(x+24)+2=2(x+2)
x+26=2x+4
x=22.
Answer is A
Answer: A
Question: The numbers in which of the following pairs do NOT have a pair of distinct prime divisors in common?
Options:
A)10 and 20
B)12 and 18
C)30 and 16
D)21 and 63
E)22 and 44
Rationale: 16 has only the prime 2 (16=2^4) in its prime factorization, so it can not have a PAIR of distinct prime divisors in common with ANY of the numbers.
The answer is C.
Answer: C
Question: In how many R ways can 4 white and 3 black chess pieces be arranged in a row such that they occupy alternate places? Assume that the pieces are distinct.
Options:
A)288
B)R=144
C)R=12
D)R=48
E)96
Rationale: 4 white chess pieces can be arranged in 4! ways and 4 black pieces can be arranged in 3 ! ways.
W_ W_W_W
Number of ways = 4!*3! = 24 * 6 = 144
Answer B
Answer: B
Question: If 25% of x is 20 less than 15% of 1500, then x is?
Options:
A)872
B)820
C)837
D)840
E)83
Rationale: 25% of x = x/4 ; 15% of 1500
= 15/100 * 1500 = 225
Given that, x/4 = 225 - 20
=> x/4 = 205 => x = 820.
Answer:B
Answer: B
Question: Compound interest earned on a sum for the second and the third years are Rs.1200 and Rs.1440 respectively. Find the rate of interest?
Options:
A)29%p.a
B)28%p.a
C)20%p.a
D)24%p.a
E)26%p.a
Rationale: Rs.1440 - 1200
= Rs.240 is the interest on Rs.1200 for one year.
Rate of interest
= (100 * 240) / (100 * 1) = 20%p.a
Answer:C
Answer: C
Question: Which of the following functions does not intersect with E = 3x^2 + 2x + 1
Options:
A)E = 3x^2 + 3x + 1
B)E = 2x^2 + 3x + 1
C)E = 3x^2 + 2x + 3
D)E = 4x^2 + 2x - 3
E)E = x^2 + 2x + 3
Rationale: Let’s find the actual intersecting point of given function and each choice E.
A. 3x^2 + 2x + 1 = 3x^2 + 3x + 1 --> x=0
B. 3x^2 + 2x + 1 = 2x^2 + 3x + 1 --> x^2 – x =0 --> x=0 or 1
C. 3x^2 + 2x + 1 = 3x^2 + 2x + 3 --> 1=3(X) --> they don’t have any intersect.
D. 3x^2 + 2x + 1 = 4x^2 + 2x - 3 --> x^2 –4=0 --> x= 2 or -2
E. 3x^2 + 2x + 1 = x^2 + 2x + 3 --> 2x^2 –2 =0 --> x= 1 or –1.
So only choice (C) has no intersecting point. The answer is (C).
Answer: C
Question: Look at this series: 53, 53, 40, 40, 27, 27, ... What number should come next?
Options:
A)12
B)14
C)27
D)53
E)86
Rationale: In this series, each number is repeated, then 13 is subtracted to arrive at the next number.
Answer: B
Answer: B
Question: A fast food truck spends one third of its monthly budget for truck rent and half of the rest for food and beverages. What percentage of the budget does the fast food truck spend for food and beverages?
Options:
A)23.5%
B)32.5%
C)33.33%
D)30%
E)75%
Rationale: Spend on rent = 1/3
Spend on food and beverage= 1/2 of remaining = 1/2*2/3= 2/6=1/3
So 1/3= 33.33%
C is the answer
Answer: C
Question: In a apartment, 30% of the people speak English, 20% speak Hindi and 12% speak both. If a people is selected at random, what is the probability that he has speak English or Hindi?
Options:
A)1/30
B)2/30
C)19/50
D)12/90
E)3/70
Rationale: P (E) = 30 / 100 , P (H) = 20 / 100 and P (E âˆ© H) = 12 / 100 =
P (E or H) = P (E U H)
= P (E) + P (H) - P (E âˆ© H)
= (30 / 100) + (20/100 - (12 / 100) = 38/100 = 19/50
C
Answer: C
Question: Difference of two numbers is 1760. If 7.5% of the number is 12.5% of the other number , find the number ?
Options:
A)2640, 1000
B)3660, 4400
C)3000, 4160
D)2490, 4150
E)4660, 3000
Rationale: Let the numbers be x and y. Then, 7.5 % of x =12.5% of y
X = 125*y/75 = 5*y/3.
Now, x-y =1760
5*y/3 –y =1760
2*y/3= 1760
y =[ (1760*3)/2] =2640.
One number = 2640, Second number =5*y/3 =4400.
Answer B.
Answer: B
Question: A student multiplied a number by 3/5 instead of 5/3.
What is the percentage error in the calculation?
Options:
A)34%
B)44%
C)54%
D)64%
E)None
Rationale: Let the number be x
Then error = 5/3x - 3/5x = 16/15x
Error%= (16x/15 x 3/5x x 100)% = 64%
Answer: Option D
Answer: D
Question: If it is assumed that 60 percent of those who receive a questionnaire by mail will respond and 222 responses are needed, what is the minimum number of questionnaires that should be mailed?
Options:
A)280
B)370
C)460
D)550
E)640
Rationale: Let x be the minimum number of questionnaires to be mailed.
0.6x = 222
x = 370
The answer is B.
Answer: B
Question: A fruit salad mixture consists of apples, peaches, and grapes. There are 2 times as many pounds of apples as grapes and 3 times as many pounds of peaches as grapes. If a mixture that has an average (arithmetic mean) of 12 pounds per fruit, how many more pounds of apples than grapes does the mixture have?
Options:
A)15
B)12
C)9
D)6
E)4
Rationale: A+P+G= 12*2
A=2G
P=3G
3G+2G+G= 12*2
G= 12*2/6= 4
A= 4*2=8
Difference = 8-4=4
'E' is the answer
Answer: E
Question: 34 is related to 12 in the same way as 59 is related to
Options:
A)45
B)66
C)77
D)88
E)61
Rationale: Explanation:
The second number is the product of the digits of the first.
Answer: A) 45
Answer: A
Question: Evaluate 28% of 450 + 45% of 260
Options:
A)232
B)243
C)252
D)262
E)282
Rationale: Explanation:
= (28/100) * 450 + (45/100) * 260
= 126 + 117 = 243
Answer: Option B
Answer: B
Question: Find the principal which yields a simple interest of Rs. 20 and compound interest of Rs. 25 in two years, at the same percent rate per annum?
Options:
A)s. 40
B)s. 48
C)s. 49
D)s. 20
E)s. 60
Rationale: Explanation:
SI in 2 years = Rs. 20, SI in 1 year = Rs. 10
CI in 2 years = Rs. 25
% rate per annum = [(CI – SI) / (SI in 1 year)] *100
= [(25 – 20) / 20] * 100
= 25 % p.a.
Let the principal be Rs. X
Time = T = 2 years
% rate = 25% p.a.
SI = (PRT/100)
20 = (X*25*2) / 100
X = Rs. 40
ANSWER: A
Answer: A
Question: What is the largest 4 digit number exactly divisible by 88?
Options:
A)9999
B)9944
C)9988
D)9900
E)9991
Rationale: Largest 4 digit number = 9999
9999 ÷ 88 = 113, remainder = 55
Hence largest 4 digit number exactly divisible by 88 = 9999 - 55 = 9944
Answer is B
Answer: B
Question: Two cyclists are running on a circular track of 500m.They start from the same point A at the same time.If they meet for the first time at a point 300 m from A, which of the following could be the possible ratio of their speeds?
Options:
A)1:3
B)2:3
C)3:2
D)5:7
E)7:11
Rationale: well, the key aspect of this question is the distance mentioned, when they met for the first time, which is 300m away from the starting point. This distance between their first meeting can be less than 500 in only two circumstance.
1) if both are travelling in the same direction and one of them has been given a head start say by few meters.
2) or if both are travelling in the opposite direction.
now since they start their journey at the same time. hence option 1 is ruled out. hence they must be running in the opposite direction. hence answer should be 3:2
Why?? here is a solution
As here time is constant, therefore, distance traveled will be directly proportional to the the respective velocities/speed of the two runners.(d1/d2=v1/v2)
now one of them has covered 300m, therefore other must have covered 200m, therefore ratio of their speeds/velocities will be 3:2
C
Answer: C
Question: There are 4 more women than there are men on a local co-ed softball team. If there are a total of 18 players on the team, what is the ratio of men to women?
Options:
A)10/16
B)6/16
C)7/11
D)6/10
E)4/10
Rationale: w = m+4
w+m = 18
m+4+m = 18
2m = 14
m = 7
w = 11
ratio:7:11
Ans: C
Answer: C
Question: What value should come in place of question mark (?) in the following equations ?
64% of 1775 + 36% of 550 = ? % of 6670
Options:
A)20
B)24
C)30
D)40
E)45
Rationale: Explanation :
64x1775/100 + 36x550/100 = ?x6670/100
∴ ? = 1136 + 198/6670 x 100 = 20%
Answer : Option A
Answer: A
Question: Solution X is 10 percent alcohol by volume, and solution Y is 30 percent alcohol by volume. How many milliliters of solution Y must be added to 200 milliliters of solution X to create a solution that is 20 percent alcohol by volume?
Options:
A)200
B)300
C)400
D)500
E)600
Rationale: 20% is an equal distance between 10% and 30%.
Thus there should be equal parts of both solutions.
We should add 200 ml of solution Y.
The answer is A.
Answer: A
Question: If each term in the sum a1+a2+a3+.....+an is either 7 or 77 and the sum equals 329, which of the following could be equal to n?
Options:
A)37
B)38
C)39
D)41
E)42
Rationale: Since, there is no 47 in the answer choices (329/7 = 47), we know there is at least one 77.
329 - 77 = 252
252/7 = 36
36+1 = 37.
If 37 wasn't there, I would have subtracted 77 from 252 and continued in a similar way.
Ans. A
Answer: A
Question: If N is the product of all positive integers less than 31, than what is the greatest integer k for which N/18^k is an integer?
Options:
A)3
B)6
C)7
D)14
E)26
Rationale: Basically the question is asking us what is the highest power of 18 that can give us a number that is a factor of 31!
So remember 18 after prime factorization is (3^2)(2). Now there are going to be less factors of 3 in 31!, than factors of 2.
Therefore, let's find how many factors of 3 in 31! We can use this quick method
31/3^1 = 10
31/3^2= 3
31/3^3=1
Sum = 14
Just ignore the remainders.
So we have that 3^14 must be the least. Now don't forget that 18 is 3^2k so k must be ONLY 7, because 2k will give us the 14.
Hence answer is (C)
Answer: C