2
Q:

What is the first term of an arithmetic progression of positive integers ?

(I) Sum of the squares of the first and the second term is 116.

(II)The fifth term is divisible by 7.

A) Only a is sufficient B) Only b is sufficient
C) Both a & b are necessary D) None

Answer:   A) Only a is sufficient



Explanation:

The sum of square of two no is 116 i.e no lie 1-11, because 11x11 =121 which is greater than 116
again after cheaking all possible pair of no only 4 and 10 satisfy this condsn , again the progression is of positive integer so 10 cant not be 1st term
so the 1st term is 4,
but from the 2nd we cant able to find the 1st term

so only 1st statement is sufficient to answer the question

Subject: Statement and Conclusions
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Q:

Some blankets are beds. Some pillows are blankets. All beds are pillows

Conclusions:

1. Some blankets are pillows

2. Some pillows are beds

3. Some beds are blankets

A) Only either 1 or 2 follows B) Only 1 and either 2 or 3 follows
C) Only 3 and either 1 or 2 follows D) All 1 ,2 and 3 follow
 
Answer & Explanation Answer: D) All 1 ,2 and 3 follow

Explanation:

1 is the converse of 2nd premise,2 is the converse of 3rd premiseand 3 is the converse of 1st premise and such, all the 3 follow

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17 53287
Q:

All flowers are toys. Some toys are trees. Some angels are trees

Conclusions:

1. Some angels are toys

2. Some trees are flowers

3. Some flowers are angels

A) None follows B) Only 1 follows
C) Only 2 follows D) Only 1 and 3 follow
 
Answer & Explanation Answer: A) None follows

Explanation:

All flowers are toys. Some toys are trees

Since the middle term 'toys' is not distributed even once in the premises,no definite conclusion follows.

 

 

Some toys are trees. Some angels are trees

Since both premises are particular,no definite conclusion an be drawn

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26 56188
Q:

Some blades are hammers. Some hammers are knives. Some knives are axes.

Conclusions:

1. Some axes are hammers

2. Some knives are blades

3. Some axes are blades

A) None follows B) Only 1 follows
C) Only 2 follows D) Only 3 follows
 
Answer & Explanation Answer: A) None follows

Explanation:

Since each combination has of premises has 2 particular premises, so no defenite conclusion follows

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24 49813
Q:

Some hills are rivers. Some rivers are desrets. All desrets are roads.

Conclusions:

1. Some roads are rivers

2. Some roads are hills

3. Some deserts are hills

A) None follows B) Only 1 follows
C) Only 1 and 2 follows D) All follow
 
Answer & Explanation Answer: B) Only 1 follows

Explanation:

Some hills are  rivers. Some rivers are deserts.

Since both the premises are particular, no defenite conclusion follows.

 

Some rivers are deserts. All deserts are roads

Since one premise is particular,the conclusion must be particular and should'nt contain the middle term. Since it follows that 'Some rivers are roads'. 1 is the converse of this conclusion and so it holds.

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18 48935
Q:

All snakes are trees. Some trees are roads. All roads are mountains.

Conclusions: 

1. Some mountains are snakes

2. Some roads are snakes

3. Some mountains are trees

A) Only 1 follows B) Only 2 follows
C) Only 3 follows D) Both 1 and 2 follow
 
Answer & Explanation Answer: C) Only 3 follows

Explanation:

All snakes are trees. Some trees are roads.

Since the middle term is not distributed even once in the premises,so no conclusion follows

 

Some trees are roads. All roads are mountains

Since one primise is particular,the conclusion must be particularand should'nt contain the middle term. So,it follows that 'Some trees are mountains'. 3 is the converse of this statement and so it holds.

 

All snakes are trees. Some trees are mountains.

Since the middle term is not distributed even once in the preises, so no definite conclusion follows

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25 40507