In the x-y plane, is angle BAC = 60o? (1) The length of AB = BC. (2) T

Question

Screenshot 2020-04-30 at 11.31.59 PM.png In the x-y plane, is angle BAC = 60 degrees? (1) The length of AB = BC. (2) The perpendicular from A on BC bisects BC.

nick1816 · Answer

Statement 1-

AB=BC; hence, ∠A = ∠C

Case 1 - If ∠B= 60, then ∠A = ∠C = 60

Case 2 - If ∠B= 40, then ∠A = ∠C = 70

Insufficient

Statement 2 -

It tells us that AB = AC; hence, ∠B = ∠C.

Case 1 - If ∠B = ∠C = 60, then ∠A = 60

Case 2 - If ∠B = ∠C = 70, then ∠A = 40

Insufficient

Combining both statements

∠A = ∠B = ∠C = 60

Sufficient

MathRevolution · Answer

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. Visit https://www.mathrevolution.com/gmat/lesson for details. Since we have 3 variables (∠A, ∠B and ∠C) and 1 equation(∠A+∠B+∠C=180°), C is most likely the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first. Conditions 1) & 2) Condition 1) tells ∠A = ∠C since the triangle is an isosceles with legs AB = BC. Condition 2) tells ∠B = ∠C since the triangle is an isosceles with legs AB = AC. Thus we have ∠A = ∠B = ∠C and ∠A + ∠B + ∠C = 180°, we have ∠A = ∠B = ∠C = 60°. Since both conditions together yield a unique solution, they are sufficient. Therefore, C is the answer. Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B, or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D, or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.

SaquibHGMATWhiz · Answer

Solution:      
  Pre Analysis:  
  In the triangle ABC, we are asked if  \angle BAC=60^o  or not

Statement 1:   The length of AB = BC
  According to this statement AB = BC which means  \angle ABC=\angle ACB  
 However, this doesn't tell us if  \angle BAC=60^o  or not  
 2 cases:    \angle ABC=\angle ACB=60 , then  \angle BAC=60     \angle ABC=\angle ACB=45 , then  \angle BAC=90    
 Thus,  statement 1 alone is not sufficient and we can eliminate options A and D

Statement 2:   The perpendicular from A on BC bisects BC
  Accoring to this statement triangle ABC is either isosceles with AB = AC or equilateral with AB = AC = BC 
 Similar to statement 1, this is not sufficient to say if  \angle BAC=60^o  or not  
 Thus,  statement 2 alone is also not sufficient

Combining:   
  From statement 1, we get AB = BC 
 From statement 2, we get either AB = AC or AB = AC = BC  
 Upon combining, we can be sure that ABC is an equilateral triangle and  \angle BAC=60^o

Hence the right answer is    Option C

chetan2u · Answer

The x-y plane doesn’t really affect the figure, so just concentrate on the triangle.

(1) The length of AB = BC.
This tells us that  \angle C= \angle A , but they could be anything between 0 and 90, both excluded. 
Insufficient

(2) The perpendicular from A on BC bisects BC
Let it bisect BC at E. so, we have two triangles ABE and ACE. 
AE is common, BE=CE and included angle is 90. Thus, the triangles are similar and  \angle C= \angle B 
But A could be again anything between 0 to 180, both excluded. 
Insufficient

Combined 
 \angle C= \angle A   = \angle B=60. 
Sufficient

C

In the x-y plane, is angle BAC = 60o? (1) The length of AB = BC. (2) T

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GMAT Data Sufficiency (DS) Questions

In the x-y plane, is angle BAC = 60o? (1) The length of AB = BC. (2) T

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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My Rewards