# Logical Reasoning :: Flow Chart

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## 5. Study the flow chart give below and the questions that follow.

The purpose of the following chart is to double the number in each of the boxes 2, 4, 6, 8 and 10.

In order to accomplish exactly this - no more and no less - What is the smallest number Which may be in box 1 ?

**Answer:**

**Option A**

**Explanation :**

Correct answer is Option D - 11

FYI "box number" is not same as number in the "number in the box"

In above case during last iteration, the second box number is 12 which should be greater than number in the box 1. ie it should be 11.

[Box 12] > 11[Box 1]

**Asked In :: **
ThoughtWorks

answer is 9.

we have to consider box numbers,not numbers(values) in boxess.

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Correct answer is Option D - 11

FYI "box number" is not same as number in the "number in the box"

In above case during last iteration, the second box number is 12 which should be greater than number in the box 1. ie it should be 11.

[Box 12] > 11[Box 1]

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Answer is C.9

Explanation : Assume Box 1 = 9(taling the lowest option available)

Instruction 1 : 2[Box 2] 2[Box 2] = 4[Box 2]

Instruction 2 : [Box 2] 2 = [Box 4]

Instruction 3 : IS 9[Box 1] < [Box 2] ? NO

Instruction 1 : 4[Box 4] 4[Box 4] = 8[Box 4]

Instruction 2 : [Box 4] 2 = [Box 6]

Instruction 3 : IS 9[Box 1] < [Box 4] ? NO

Instruction 1 : 6[Box 6] 6[Box 6] = 12[Box 6]

Instruction 2 : [Box 6] 2 = [Box 8]

Instruction 3 : IS 9[Box 1] < [Box 6] ? NO

Instruction 1 : 8[Box 8] 8[Box 8] = 16[Box 8]

Instruction 2 : [Box 8] 2 = [Box 10]

Instruction 3 : IS 9[Box 1] < [Box 8] ? NO

Instruction 1 : 4[Box 10] 4[Box 4] = 8[Box 4]

Instruction 2 : [Box 10] 2 = [Box 12]

Instruction 3 : IS 9[Box 1] < [Box 10] ? YES

Therefore Box 1's content is 9.

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Correct answer is **Option D**.

Instruction 3 tests for: is number in box 1 less than the second box number mentioned in instruction 1.

Final test for 9 would be: is 9 less than 10 (box number 10): true, therefore break the loop, thus box 10 won't be updated but it should be.

Final test for 11 would be: is 11 less than 12 (box number 12, was box 10 before and increased by 2 in instruction 2): true, break the loop so box 12 doesn't receive an update (but boxes 2, 4, 6, 8 **and 10**).

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Assume [Box 1]= 19

Instruction 1: 2[Box 2] 2[Box 2] = **4[Box 2]**

Instruction 2: [Box 2] 2 = **[Box 4]** // increase box num from 2 to 4.

Instruction 3: IS [Box 1] 19 < [Box 2] 4 **NO**

Instruction 1: 4[Box 4] 4[Box 4] = **8[Box 4]**

Instruction 2: [Box 4] 2 = **[Box 6]**

Instruction 3: IS [Box 1] 19 < [Box 4] 8 **NO**

Instruction 1: 6[Box 6] 6[Box 6] = 12**[Box 6]**

Instruction 2: [Box 6] 2 = **[Box 8]**

Instruction 3: IS [Box 1] 19 < [Box 6]12 **NO**

Instruction 1: 8[Box 8] 8[Box 8] = 16**[Box 8]**

Instruction 2: [Box 8] 2 = **[Box 10]**

Instruction 3: IS [Box 1] 19 < [Box 8]16 **NO**

Instruction 1: 10[Box 10] 10[Box 10] = 20**[Box 10]**

Instruction 2: [Box 10] 2 = **[Box 12]**

Instruction 3: IS [Box 1] 19 < [Box 10] 20 **YES**

**END**

**SO the ans should be 19//option A**

**// If you put [Box 1] = 9 then instruction end @ **Instruction 3: IS [Box 1] 9 < [Box 6]12 **Yes**

**// **** If you put [Box 1] = 11 then instruction end @ **Instruction 3: IS [Box 1] 11 < [Box 6]12 **Yes**

**// If you put [Box 1] = 15 then instruction end @ **Instruction 3: IS [Box 1] 15 < [Box 8]16 **Yes**

**As per mention above we have to double 2,4,6,8,10 value...so loop never ends before updating upto**

**[Box 10] thats why our ans become 19**

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The answer given is wrong. It should be **11**.

Step 1: 2 [Box 2] + 2 [Box 2] = 4 [Box 2]

Step 2: Increase all box numbers in 1st instruuction by 2. So, change [Box 2] to [Box 4].

Step 3: Number in [Box 1] < 4 (2nd Box number in 1(now 4))? Should be false to double the value in [Box 4].

Step 4: 4 [Box 4] + 4 [Box 4] = 8 [Box 4]

Step 5: Increase all box numbers in 1st instruuction by 2. So, change [Box 4] to [Box 6].

Step 6: Number in [Box 1] < 6 (2nd Box number in 1(now 6))? Should be false to double the value in [Box 6].

Step 7: 6 [Box 6] + 6 [Box 6] = 12 [Box 6]

Step 8: Increase all box numbers in 1st instruuction by 2. So, change [Box 6] to [Box 8].

Step 9: Number in [Box 1] < 8 (2nd Box number in 1(now 8))? Should be false to double the value in [Box 8].

Step 10: 8[Box 8] + 8 [Box 8] = 16 [Box 8]

Step 11: Increase all box numbers in 1st instruuction by 2. So, change [Box 8] to [Box 10].

Step 12: Number in [Box 1] < 10 (2nd Box number in 1(now 10))? Should be false to double the value in [Box 10].

Step 13: 10 [Box 10] + 10 [Box 10] = 20 [Box 10]

Step 2: Increase all box numbers in 1st instruuction by 2. So, change [Box 10] to [Box 12].

Step 3: Number in [Box 1] < 12 (2nd Box number in 1(now 12))? Should be true to exit.

So **Answer is 11 (D)**

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Number in box and box-number is two different number. The right answer is: Option D,the number in box 1 should be 11.

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