Directions: In each of the following questions, two statements or three statements are given. You are expected to solve them and determine which statement or combination of statements is sufficient to answer the question.
1) The LCM of two positive integers P and Q is 165. What will be the 50% of HCF of P and Q?
Statement I: 50% of (P – Q) is a multiple 3 less than 12
Statement II: 75% of (P + Q) = 36 Statement III: P2 – 55P + 726 = 0
A. Statement I and II together are sufficient to answer the question
B. Statement II and III together are sufficient to answer the question
C. Statement III and I together are sufficient to answer the question
D. Combination of any two statements are sufficient to answer the question
E. None of these
Sol:
On combining (I + II)
50% of (P – Q) = 3 or 6 or 9
(P – Q) = 6 or 12 or 18…………….. (1)
Also, 75% of (P + Q) = 36
(P + Q) = 48…………… (2)
On solving both equations we get
P = 27, Q = 21
P = 30, Q = 18
P = 33, Q = 15
LCM of (33, 15) is 165
33 = 11 x 3
15 = 5 x 3
So, HCF of (33, 15) = 3
Required value = 50% x 3 = 1.5
This combination of statement is sufficient to
answer the question
On combining (II + III)
75% of (P + Q) = 36
(P + Q) = 48
Also,
P2 – 55P + 726 = 0
(P – 33)(P – 22) = 0
P = 33, 22
On putting these values in above equation
Q = 15, 26
LCM of (33, 15) = 165
33 = 11 x 3
15 = 5 x 3
So, HCF of (33, 15) = 3
Required value = 50% x 3 = 1.5
This combination is sufficient to answer the
question.
On combining (III + I)
50% of (P – Q) = 3 or 6 or 9
(P – Q) = 6 or 12 or 18
Also,
P2 – 55P + 726 = 0
(P – 33)(P – 22) = 0
P = 33, 22
On putting these values in above equation
Q = 27, 16, 21, 10, 15, 4
Only (33, 15) gives LCM 165
This combination of statements is sufficient to
answer the question.
So, a combination of any two statementsare
sufficient to answer the
question.
Hence answer is option D
2) In 9thstd there are four sections – P, Q, R, and S. Find the number of students in section R.
Statement I: The average number of students in P, Q, and R is 260 and the number of students in P is 240 less than S.
Statement II: Number of students in S is twice that of P. Number of students in P and Q together is 600.
Statement III: Number of students in Q is twice of R and 120 less than S.
A. Statement I and II together are sufficient to answer the question
B. Statement II and III together are sufficient to answer the question
C. Statement III and I together are sufficient to answer the question
D. Combination of any two statements are sufficient to answer the question
E. None of these
Statement I.
(P + Q + R) = 3 x 260 = 780
S = 240 + P
Statement II.
S = 2P
(P + Q) = 600
Statement III.
Q = 2R
S = Q + 120
On combining I and II
(P + Q + R) = 3 x 260 = 780………… (1)
(P + Q) = 600………… (2)
On solving both equations, we get
R = 780 – 600 = 180
This combination is sufficient to answer the
question
On combining II and III
S = Q + 120
Also, S = 2P
So, 2P – Q = 120……….. (3)
Also, (P + Q) = 600…………. (4)
On solving 3 and 4,
P = 240 and Q = 360
So, R = Q/2 = 360/2 = 180
This combination is sufficient to answer the
question
On combining I and III
S = 240 + P
Also, S = Q + 120
So, 240 + P = Q + 120
P = Q – 120
Also, Q = 2R
Also, (P + Q + R) = 780
So, 2R – 120 + 2R + R = 780
So, 5R = 900
R = 180
This combination of statements is sufficient to
answer the question.
Hence answer is option D
3) A bought an article at Rs. 25600 and sold it to B at Rs. P loss, then B sold it to C at Q% profit, if the marked price of the article is same for all then find the value of Q %.
Statement I: value of P = Rs. 1024 Statement II: Discount % offered to A was 37.5%
Statement III: Discount % offered by B was 31.25%
A. Statement I and II together are sufficient to answer the question
B. Statement II and III together are sufficient to answer the question
C. Statement III and I together are sufficient to answer the question
D. Combination of any two statements are sufficient to answer the question
E. None of these
Statement I.
Selling price for A or cost price for B = 25600 –
1024 = Rs. 24576
This statement alone is not sufficient
Statement II. Discount offered to A was 37.5%
So, Marked price of the article = 25600/62.5 x
100 = 40960
This statement alone is not sufficient to answer
the question
Statement III. Discount offered by B was 31.25%
This statement alone is not sufficient to answer
the question
On combining I and II
We need to calculate profit % for B, so we need
CP and SP for B.
Cost price for B = 25600 – 1024 = Rs. 24576
Marked price of the article = 25600/62.5 x 100 =
Rs.40960
We don’t know the selling price for B
This combination is not sufficient
On combining II and III
This combination gives MRP and SP for B not
CP. So this combination is not sufficient
On combining III and I
This combination gives only CP for B. this
combination is not sufficient to answer the
question.
On combining I, II and III
CP for B = 24576
MRP = 40960
SP for B = 40960 x 11/16 = 28160
So, Q % = (28160 – 24576)/24576 x 100 =
14.5833%
All three statements together necessary to
answer the question
Hence answer is option E
