Directions for Questions 1 to 6: In a chemical lab, 6 chemicals added to make mixtures which are used to make perfumes. The chemicals are stored in exactly six types of boxes c1, c2, c3, c4, c5, c6. Remember there is no limitation in the number of chemicals stored in a box.
Chemicals must be added to make mixtures under following conditions:
1. Each mixture must contain at least three chemicals and chemicals of at least three different boxes.
2. At most two chemicals in a single mixture can be from c6 box
3. At most two chemicals in a single mixture can be from c5 box
4. There can be at most one chemical of c1,c2,c3 and c4 in a single mixture
5. If one chemical is from c1,then one chemical must be from c2 box
6. If one chemical is from c3,then no chemical can be from c4 box.
Question 1: Which of the following could be complete set of chemicals in an acceptable mixture?
(a) c4, c5, and c3
(b) c1, c6, and c2
(c) c1, c6, and c4
(d) c1, and exactly two chemicals from c6
Question 2: The maximum number of chemicals that can be used in an acceptable mixture
Question 3: If exactly one chemical from c6 box and exactly one chemical from c5 box are used in a mixture, which of the following is must be true?
(a) the mixture contains no more than five chemicals
(b) the mixture contains exactly six chemicals
(c) the mixture contains a chemical from c2 box
(d) the mixture does not contain any chemical from c1box
Question 4: If a c5 chemical and c3 chemical must be among the chemicals chosen for a particular mixture, any of the following sets of chemicals could complete the mixture except:
(a) a c6 chemical and a second c5 chemical
(b) a c2 chemical and a second c5 chemical
(c) a c2 chemical and a c6 chemical
(d) a c1 chemical and a c6 chemical
Question 5: If there is an additional requirement that a chemical from c3 must be used if chemical from c2 is used, which of the following is possible:
(a) a combination of one chemical from each of the six boxes.
(b) two chemicals each from c5,c6 and c1, and one from c2 and c3 each.
(c) one chemical each from c2 and c3, and two chemicals from c5 and c6.
(d) two chemicals from c5 and one from c4.
Question 6: If there is an additional requirement that a chemical from c2 must be used with one chemical each from c1, c2 and c4, the maximum possible number of chemicals in a mixture are:
Answers and Explanations: Click the down arrow to expand
Answer 1: (b)
If we read the conditions carefully, then we will come to know that only the second option satisfies the given conditions, while others do not and each option negates some condition or the other.
Answer 2 : (b)
We can have chemicals from maximum of five different boxes in a single mixture, and we also know that a chemical from c3 cannot be used with a c4 chemical. So we can use two c6 chemicals, two c5 chemicals and one chemical from each of other boxes. Thus a maximum of 7 chemicals can be used.
Answer 3 : (a)
If one chemical is from c6 box and one chemical is from c5 box, the we can use a maximum of 5 boxes as the other boxes can only contribute one chemical each, and c1 cannot be clubbed with c4.
Answer 4 : (d)
The forth option is not the correct set of chemicals, since the inclusion of a c1 chemical implies inclusion of a c2 chemical.
Answer 5 : (c)
Remember that if a chemical is from c1, then a chemical from c2 has to be used but the other way around is not necessarily true. keeping this in mind, option (c) becomes a possible option.
Answer 6 : (b)
The maximum possible number of chemicals that can be present in such a mixture are: 2 from c5 and c6 each, and one each from c1,c2 and c4. Thus, the answer is 7.
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