If x is an odd integer, in which of the following equations must y be an even integer? I. xy = 5 II. x + 2y = 11 III. 2x + y = 12
A. Only I
B. Only II
C. Only III
D. both II and III
E. all of these
Explanation: i. xy = 5 শুধু Odd x Odd = Odd হয়, So y এখানে odd ii. x + 2y = 11 এখানে x odd, so 11-x even হবে। so 2y is even. কিন্তু y odd/even যেকোনটাই হতে পারে iii. 2x + y = 12 এখানে y = 12 - 2x x is odd, but 2x is even. So, 12-2x even. তার মানে y even.
Related Questions (Any University/Year)
- The average age of a man and his son is 20. after 10 years, their age will be in the ratio 2:1. What was the age of the man and his son 5 years ago respectively?
- A man purchased equal number of bananas at two different rates-one at the rate of 8 taka per dozen and the other at the rate of 10 taka per dozen. After that, he sold those bananas at an average rate of 11 taka per dozen and thus made a profit of 100 taka. How many dozens of banana did he purchase altogether?
- In a certain school, the ratio of Senior to Junior is 5:4, and the ratio of Senior to Sophomores is 6:5. What is the ratio of Junior to Sophomores?
- If a certain vase contains only roses and tulips, how many tulips are there in the vase?i. The number of roses in the vases is 4 times the number of tulips in the vase.ii. There is total of 20 flowers in the vase
- If (a+b+c)/4= (a+b)/3, then what is the value of c?
- A man purchased equal number of bananas at two different rates- one at the rate of 8 taka per dozen and the other at the rate of 10 taka per dozen. After that, he sold those bananas at an average rate of 11 taka per dozen and thus made a profit of 100 taka. How many dozens of banana did he purchase altogether?
- Think of a number and then double the number. Then add 8 and multiply the result by 6. Now divide, the result by 12, then subtract the number you first thought out. What is the final result?
- Three business people wish to invest in a new company. Each person is willing to pay one third of the total investment. After careful calculations, they realize that each of them would pay BDT 7,200 less if they could find two more equal investors. How much is the total investment in the new business?
- A woman says, "If you reverse digit of my own age, the figures represents my husband's age. He is, of course, senior to me and the difference between our ages is one-eleventh of our sum." What is the age of the women?
- \(x=y-(50/y)\), where x and y are both positive numbers. If the value of y is doubled, the value of x will.
- In a group of 100 adults, 75 percent of the women are left-handed. If there are 12 right- handed women in the group, how many men are in the group?
- Mother's age today is thrice as her daughter's . After 10 years it would be just double. How old is the daughter today?
- There are four toys and they are of the same price. They worth $4.80. If the price for one is decreased by the fourth of the sum of other three toys, and two items of original price are added, then how much will six of them worth?
- In the figure, AC = AD, and CD = BD = AB. What is the value of ∠CAD?
- দুইটি ক্রমিক সংখ্যার বর্গের পার্থক্য ১৯। তার মধ্যে একটি সংখ্যার বর্গমূল ৩ হলে অন্যটি কত?
- এক ব্যক্তি তাঁর স্ত্রীর চেয়ে ৫ বছরের বড় এবং তাঁর স্ত্রীর বয়স তাদের ছেলের বয়সের ৪ গুণ। ৩ বছর পর ছেলের বয়স ১৪ বছর হলে সেই ব্যক্তির বর্তমান বয়স কত?
- A vendor bought chocolate at 6 for a taka. How many for a taka must he sell to gain 20% ?
- If a man's weekly salary is Tk. P and he saves Tk. M, what faction of his weekly salary does he spend?
- Three persons A, B, C whose salaries together amount Tk. 7200, spend 80%, 85% and 75% of their salaries respectively. If their savings are 8:9:20. Find salary of B
- At a local appliance manufacturing facility, the workers received a 20% hourly pay raise due to extraordinary performance. If one worker decided to reduce the number of hours that he worked so that his overall pay would remain unchanged, by approximately what percent would he reduce the number of hours that he worked?
- If 6 workers can complete 9 identical job in 3 days, how long will it take 4 workers to complete 10 such jobs ?
- যদি y(x-1)=z হয়, তবে x=?
- ধর, x এবং y দুটি ধনাত্মক সংখ্যা। যদি xy = ১ এবং x/y = ১ হয়, তাহলে x + y এর মান কত?
- সঠিক বন্ধনীর ব্যবহার হয়েছে নিচের কোন সমীকরণে?
- If 12 men can build a wall 180 m long in 54 days ,how many days it will take to build a similar wall 160 m long ,if 16 men working on it
- By selling goods for Tk. 153, Shabit loses 10%. For how much should he sell them to gain 20%?
- A man traveled one-fourth of the total distance of his trip by car . He traveled the remaining distance on foot . The ratio of his walking time to driving time was 15:1 . Calculate the ratio of his driving speed to his walking speed .
- একটি ধাতব ঘন(cubical) বস্তুর ওজন ৮ কেজি।একই ধাতুর তৈরী আরেকটি ঘন বস্তু যার প্রতিটি বাহু দ্বিগুণ হলে বস্তুটির ওজন কত কেজ???
- Real Madrid has won 40 games out of 60 played. It has 32 more games to play. How many of these must the team win to make its record 75% win for the season?
- A trader normally makes a profit of 40% on items he sells. If he reduces the price by 10%, his sales increase by 40%. Let x be the total profit when he does not reduce the price, and y the total profit when he reduces the price. What is the ratio of y to x?
- If a and b are possible integers and (a1/2 b1/3)6= 432, what is the value of ab?
- A 112-meter rope is cut into three pieces with each piece twice as long as the previous one. How long is the longest piece?
- In a library system with 6 brances, 60 workers are employed. If no library has fewer than 7 workers and ne more then 11, what is the minimum number of workers in any two of the brances?
- A can work three times faster than B. A takes 60 days less than B to do a work. Find the number of days it would take to complete the work if both work together.
- Rahman is twice as old as Shermin. In y years Shermin will be 1.5 times older than she is now. What is Shermin's age?
- 50% of = 250
- মাহি, রাহি ও রাজনের বর্তমান বয়সের সমষ্টি ১০২ বছর। ৪ বছর পূর্বে তাদের বয়সের অনুপাত ছিল ৪ঃ৫ঃ৬। মাহির বর্তমান বয়স কত?
- In a certain village, m litres of water are required per household per month. At this rate, if there are n households in the village, how long (in months) will p litres of water last?
- একটি সংখ্যার ৭৫% এর সাথে ৭৫ যোগ করলে ফলাফল হিসেবে পূর্বের সংখ্যাটি পাওয়া যায়। সংখ্যাটি কত?
- The greatest possible value of C is how much greater than the smallest possible value of D?
