1. 2 Marks
When Arthur is as old as his father Hailey is now, he shall be 5 times as old as his son Clarke is now. By then, Clarke will be 8 times older than Arthur is now. The combined ages of Hailey and Arthur are 100 years. How old is Clarke ?
2. 2 Marks
I have one orange glass containing orange juice and another white glass containing apple juice. I take 50 ml of orange juice and mix it with apple juice in the white glass. Then I take 50 ml of this mixture and transfer it back to the orange glass. If you compare amount of apple juice in the orange glass and
amount of orange juice in the white glass which is more than the other
and by how much ?
3. 3 Marks
The seven digits in this subtraction problem are 0,1,2,3,4,5 and 6.
Each letter represents the same digit whenever it occurs.
D A D C B
E B E G
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B F E G
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What digit is represented by each letter ?
4. 4 Marks
The Jones have named their four boys after favourite relatives; their friends, the Smiths, have done the same thing with their three boys. One of the families has twin boys. From the following clues, can you determine the families of all seven children and their ages ?
i) Valantine is 4 years older than his twin brothers.
ii) Winston, who is 8, and Benedict are not brothers. They are each named after a grandfather.
iii) Briscoe is two years younger than his brother Hamilton, But three years older than Dewey.
iv) Decatur is 10 years old.
v) Benedict is 3 years younger than Valentine; they are not related.
vi) The twins are named for uncles.
5. 4 Marks
Motorboat A leaves shore P as B leaves Q; they move across the lake at a constant speed. They meet first time 600 yards from P. Each returns from the opposite shore without halting, and they meet 200 yards from Q. How long is the lake ?
6. 4 Marks
Fanta, Pepsi and Citra often eat dinner out.
a) Each orders either coffee or tea after dinner.
b) If Fanta orders coffee, then Pepsi orders the drink that Citra orders.
c) If Pepsi orders coffee, then Fanta orders the drink that Citra does not order.
d) If Citra orders tea, then Fanta orders the drink that Pepsi orders.
Which person/persons always orders the same drink after dinner ?
7. 6 Marks
On the Island of imperfection there is a special road, Logic Lane, on which the houses are usually reserved for the more mathematical inhabitants.
Add, Divide and Even live in three different houses on this road (which has houses numbered from 1-50). One of them is a member of the Pukka Tribe,
who always tell the truth; another is a member of the Wotta Tribe, who never
tell the truth; and the third is a member of the Shalla Tribe, who make statements which are alternately true and false, or false and true.
They make statements as follows :
ADD :
1 The number of my house is greater than that of Divide's.
2 My number is divisible by 4.
3 Even's number differs by 13 from that of one of the others.
DIVIDE :
1 Add's number is divisible by 12.
2 My number is 37.
3 Even's number is even.
EVEN :
1 No one's number is divisible by 10.
2 My number is 30.
3 Add's number is divisible by 3.
Find to which tribe each of them belongs, and the number of each of their houses.
8. 8 Marks
The names of the inhabitants of Walkie Talkie Land sound strange to the visitors, and they find it difficult to pronounce them, due to their length and a few vowel sounds they contain. The Walkie Talkie guide is discussing the names of four inhabitants - A,B,C and D. Their names each contain upto eight syllables, although none of the four names contain the same number. Two of the names contain no vowel sounds; one contains one vowel sound; and one contains two vowel sounds. From the Guide's statements below, determine the number of
syllables and vowel sounds in each of the four Walkie Talkie names :
i) The one whose name contains two vowel sounds is not A.
ii) C's name does not contain more than one vowel sound or fewer than seven syllables.
iii)The name with seven syllables does not contain exactly one vowel sound.
iv) B and C do not have names with the same number of vowel sounds.
v) Neither the name with five syllables nor the name with seven syllables
contains more than one vowel sound.
vi) Neither the name with six syllables, nor the B's name, contains two vowel sounds.
10. 8 Marks
Two identical twins have a very unusual characteristic. One tells nothing but lies on Mondays, Wednesdays and Fridays, and tells nothing but the truth all other days. The other tells nothing but lies on Tuesdays, Thursdays and Saturdays, and tells nothing but the truth all other days. On Sundays both children speak the truth.
1) Which of the following statements can be deduced from the information presented ?
i) If it is Sunday, the twins will both say so.
ii) If it is not Sunday,one twin will give the correct day and the other will lie about everything.
iii)On any given day, only one twin will give his correct name.
a) i only
b) i and ii only
c) i and iii only
d) ii and iii only
e) i,ii and iii
2) According to the information presented, which of the following
conversations will be impossible.
a) Twin A : "Today you are a lier"
Twin B : "You are telling the truth"
b) Twin A : "Today you are a lier"
Twin B : "Today I am a truthteller"
c) Twin A : "Tommorow I shall be a lier"
Twin B : "That's correct"
d) Twin A : "Tommorow you will be a lier"
Twin B : "Today you are a truthteller"
e) Twin A : "Yesterday we were both truthtellers"
Twin B : "You are lying"
3) Assume that the twins followed a different set of rules, so that on a given day both told only the truth while next day both only lied, alternating days of truth telling and lying. Under these rules,which
of the following conversations would be possible ?
a) Twin A : "Today you are a lier"
Twin B : "That is correct"
b) Twin A : "Today you are a lier"
Twin B : "That is not so"
c) Twin A : "Tommorow we will be liers"
Twin B : "Yesterday we were truthtellers"
d) Twin A : "Tommorow we will be liers"
Twin B : "You are 1 year older than I am"
e) Twin A : "We always tell the truth"
Twin B : "We some times tell the truth"
4) If the twins are heard saying the following on the same day, which choice presents a correct statement ?
Twin A : "It is Sunday Today"
Twin B : "Yesterday was Sunday"
Twin A : "it is summer season now"
a) it is a summer sunday
b) it is a summer monday
c) it is Monday but not summer
d) it is Sunday but not summer
e) it is impossible to determine whether it is Sunday or Monday.
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