Ask your doubts in CAT and Banking

3 years, 5 months ago

Syllogisms are standard questions to be asked in banking exams. Once the concept is understood, they
are fairly easy to score and are hardly time consuming. It’s very important in Syllogisms to assume that
the statements are true and not go by common knowledge. Examples are given below to illustrate the
significance.
Venn diagrams can be drawn to simplify syllogisms. Though not a requirement, Venn diagrams can make
Syllogisms very easy to solve.
Solved Examples:
2 questions from IBPS 2011 clerical exam have been explained to give candidates clear understanding of
the concept.
Directions: In each question below are two statements followed by two conclusions numbered 1 and 2.
You have to take the two given statements to be true even if they seem to be at variance from commonly
known facts and then decide which of the given conclusions logically follows from the given statements
disregarding commonly known facts.
Give answer
(1) If conclusion 1 follows
(2) If only conclusion 2 follows
(3) If either conclusion 1 or 2 follows
(4) If neither conclusion 1 nor 2 follows
(5) If both conclusions 1 and 2 follow.
A) Statements – Some trees are bushes. All flowers are bushes.
Conclusions – 1) Atleast some bushes are trees. 2) Atleast some flowers are trees.
Solution: To solve this question, we draw a Venn diagram:
Trees and Bushes are overlapping sets as the statement
says some trees are bushes. (we have to assume that
statements are correct). Since all flowers are bushes,
flowers will be a subset of bushes. So, clearly conclusion 1
is true and conclusion 2 is false. So, we select option 1
B) Statements – All colours are paints. No paint is a brush.
Conclusions 1) Atleast some brushes are colours. 2) No brush is a colour.
Solution: Like we
mentioned earlier, we have
to assume the statement is
correct and not bother
about the real life
implication of them. All
colours are paints, so
colours is a subset of
paints. No paint is a brush,
so paint and brush are non
– overlapping sets. So
clearly, conclusion 1 is false
and conclusion 2 is true.
So, we choose option 2.

Syllogisms are standard questions to be asked in banking exams. Once the concept is understood, they are fairly easy to score and are hardly time consuming. It’s very important in Syllogisms to assume that the statements are true and not go by common knowledge. Examples are given below to illustrate the significance. Venn diagrams can be drawn to simplify syllogisms. Though not a requirement, Venn diagrams can make Syllogisms very easy to solve. Solved Examples: 2 questions from IBPS 2011 clerical exam have been explained to give candidates clear understanding of the concept. Directions: In each question below are two statements followed by two conclusions numbered 1 and 2. You have to take the two given statements to be true even if they seem to be at variance from commonly known facts and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts. Give answer (1) If conclusion 1 follows (2) If only conclusion 2 follows (3) If either conclusion 1 or 2 follows (4) If neither conclusion 1 nor 2 follows (5) If both conclusions 1 and 2 follow. A) Statements – Some trees are bushes. All flowers are bushes. Conclusions – 1) Atleast some bushes are trees. 2) Atleast some flowers are trees. Solution: To solve this question, we draw a Venn diagram: Trees and Bushes are overlapping sets as the statement says some trees are bushes. (we have to assume that statements are correct). Since all flowers are bushes, flowers will be a subset of bushes. So, clearly conclusion 1 is true and conclusion 2 is false. So, we select option 1 B) Statements – All colours are paints. No paint is a brush. Conclusions 1) Atleast some brushes are colours. 2) No brush is a colour. Solution: Like we mentioned earlier, we have to assume the statement is correct and not bother about the real life implication of them. All colours are paints, so colours is a subset of paints. No paint is a brush, so paint and brush are non – overlapping sets. So clearly, conclusion 1 is false and conclusion 2 is true. So, we choose option 2.

Srikanth Lingamneni

3 years, 5 months ago

There are four digits, i.e 1000s, 100s , 10s and units place.
Case 1: 1000s place: It can be taken by each of 1,2,3,4,5 . If one of these takes 1000s place, the other 5 digits can be arranged in the remaining 3 places in 5*4*3 = 60 ways. Hence sum of the 1000s place = (1+ 2+ 3+ 4+ 5) * 1000 * 60
case 2: 100s place: The case where 0 is chosen will not contribute to our sum. Hence it can be ignored. If one of 1,2,3,4,5 is chosen, the 1000s place can be chosen in 4 ways(excluding 0) , 10s in 4 ways, and units in 3 ways. Hence Number of ways =4 * 4* 3 = 48. Hence sum of 100s place = (1+ 2+ 3 + 4 + 5) * 100 * 48
Similarly for 10s place we get sum = (1+ 2+ 3 + 4 + 5) * 10 * 48 and sum in units place = (1+ 2+ 3 + 4 + 5) * 1 * 48
Hence total sum = 15 * 1000 * 60 + 15*111*48 = 979920.

In general if there are m digits, one of which is zero to form a n digit number, then the sum of the possibilities is
(sum of the digits)*[ $$10^{n-1} * ^{m-1}P_{n-1}$$ + $$(1111...(m-1)\ times)*(m-2)*^{m-2}P_{n-2}$$]

For the case where repetition is allowed,
Case 1 : Sum of the 1000s place =$$ (1+ 2+ 3+ 4+ 5) * 1000 * 6^3$$
Case 2: Sum of the 100s, 10s, units place = $$(1+ 2+ 3+ 4+ 5) * 111 * 5 * 6^2$$
Total sum = 15 * 1000 * 216 + 15 * 111* 180 = 3539700

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