diff --git a/numpy-1-21-xfails.txt b/numpy-1-21-xfails.txt
index 97a313b9..d9b76859 100644
--- a/numpy-1-21-xfails.txt
+++ b/numpy-1-21-xfails.txt
@@ -76,6 +76,10 @@ array_api_tests/test_set_functions.py::test_unique_counts
 array_api_tests/test_set_functions.py::test_unique_inverse
 array_api_tests/test_set_functions.py::test_unique_values
 
+# The test suite is incorrectly checking sums that have loss of significance
+# (https://github.com/data-apis/array-api-tests/issues/168)
+array_api_tests/test_statistical_functions.py::test_sum
+
 # NumPy 1.21 doesn't support NPY_PROMOTION_STATE=weak, so many tests fail with
 # type promotion issues
 array_api_tests/test_manipulation_functions.py::test_concat
@@ -113,6 +117,7 @@ array_api_tests/test_operators_and_elementwise_functions.py::test_floor_divide[_
 array_api_tests/test_operators_and_elementwise_functions.py::test_floor_divide[__ifloordiv__(x, s)]
 array_api_tests/test_operators_and_elementwise_functions.py::test_floor_divide[floor_divide(x1, x2)]
 array_api_tests/test_operators_and_elementwise_functions.py::test_greater[greater(x1, x2)]
+array_api_tests/test_operators_and_elementwise_functions.py::test_less[__lt__(x1, x2)]
 array_api_tests/test_operators_and_elementwise_functions.py::test_logaddexp
 array_api_tests/test_operators_and_elementwise_functions.py::test_multiply[__imul__(x, s)]
 array_api_tests/test_operators_and_elementwise_functions.py::test_multiply[__mul__(x, s)]
@@ -149,8 +154,10 @@ array_api_tests/test_special_cases.py::test_binary[__mod__(x1_i is +0 and x2_i <
 array_api_tests/test_special_cases.py::test_binary[__mod__(x1_i is +0 and x2_i > 0) -> +0]
 array_api_tests/test_special_cases.py::test_binary[__mod__(x1_i is -0 and x2_i < 0) -> -0]
 array_api_tests/test_special_cases.py::test_binary[__mod__(x1_i is -0 and x2_i > 0) -> +0]
+array_api_tests/test_special_cases.py::test_binary[__pow__(abs(x1_i) < 1 and x2_i is +infinity) -> +0]
 array_api_tests/test_special_cases.py::test_binary[__pow__(abs(x1_i) < 1 and x2_i is -infinity) -> +infinity]
 array_api_tests/test_special_cases.py::test_binary[__pow__(abs(x1_i) > 1 and x2_i is +infinity) -> +infinity]
+array_api_tests/test_special_cases.py::test_binary[__pow__(abs(x1_i) > 1 and x2_i is -infinity) -> +0]
 array_api_tests/test_special_cases.py::test_binary[__pow__(x1_i < 0 and isfinite(x1_i) and isfinite(x2_i) and not x2_i.is_integer()) -> NaN]
 array_api_tests/test_special_cases.py::test_binary[__pow__(x1_i is +0 and x2_i < 0) -> +infinity]
 array_api_tests/test_special_cases.py::test_binary[__pow__(x1_i is +0 and x2_i > 0) -> +0]
diff --git a/numpy-skips.txt b/numpy-skips.txt
index e69de29b..cbf7235b 100644
--- a/numpy-skips.txt
+++ b/numpy-skips.txt
@@ -0,0 +1,11 @@
+# These tests cause a core dump on CI, so we have to skip them entirely
+array_api_tests/test_operators_and_elementwise_functions.py::test_floor_divide[__floordiv__(x, s)]
+array_api_tests/test_operators_and_elementwise_functions.py::test_floor_divide[__floordiv__(x1, x2)]
+array_api_tests/test_operators_and_elementwise_functions.py::test_floor_divide[__ifloordiv__(x, s)]
+array_api_tests/test_operators_and_elementwise_functions.py::test_floor_divide[__ifloordiv__(x1, x2)]
+array_api_tests/test_operators_and_elementwise_functions.py::test_floor_divide[floor_divide(x1, x2)]
+array_api_tests/test_operators_and_elementwise_functions.py::test_remainder[__imod__(x, s)]
+array_api_tests/test_operators_and_elementwise_functions.py::test_remainder[__imod__(x1, x2)]
+array_api_tests/test_operators_and_elementwise_functions.py::test_remainder[__mod__(x, s)]
+array_api_tests/test_operators_and_elementwise_functions.py::test_remainder[__mod__(x1, x2)]
+array_api_tests/test_operators_and_elementwise_functions.py::test_remainder[remainder(x1, x2)]
diff --git a/numpy-xfails.txt b/numpy-xfails.txt
index 85aebf26..15f8016f 100644
--- a/numpy-xfails.txt
+++ b/numpy-xfails.txt
@@ -46,3 +46,7 @@ array_api_tests/test_special_cases.py::test_binary[__pow__(x1_i is -0 and x2_i >
 array_api_tests/test_special_cases.py::test_iop[__ipow__(x1_i is -infinity and x2_i > 0 and not (x2_i.is_integer() and x2_i % 2 == 1)) -> +infinity]
 array_api_tests/test_special_cases.py::test_iop[__ipow__(x1_i is -0 and x2_i > 0 and not (x2_i.is_integer() and x2_i % 2 == 1)) -> +0]
 array_api_tests/meta/test_hypothesis_helpers.py::test_symmetric_matrices
+
+# The test suite is incorrectly checking sums that have loss of significance
+# (https://github.com/data-apis/array-api-tests/issues/168)
+array_api_tests/test_statistical_functions.py::test_sum
diff --git a/torch-skips.txt b/torch-skips.txt
index f2d0f202..cbf7235b 100644
--- a/torch-skips.txt
+++ b/torch-skips.txt
@@ -1,10 +1,11 @@
 # These tests cause a core dump on CI, so we have to skip them entirely
-array_api_tests/test_operators_and_elementwise_functions.py::test_remainder[remainder(x1, x2)]
-array_api_tests/test_operators_and_elementwise_functions.py::test_remainder[__mod__(x, s)]
-array_api_tests/test_operators_and_elementwise_functions.py::test_remainder[__mod__(x1, x2)]
-array_api_tests/test_operators_and_elementwise_functions.py::test_remainder[__imod__(x1, x2)]
-array_api_tests/test_operators_and_elementwise_functions.py::test_remainder[__imod__(x, s)]
-array_api_tests/test_operators_and_elementwise_functions.py::test_floor_divide[floor_divide(x1, x2)]
+array_api_tests/test_operators_and_elementwise_functions.py::test_floor_divide[__floordiv__(x, s)]
 array_api_tests/test_operators_and_elementwise_functions.py::test_floor_divide[__floordiv__(x1, x2)]
-array_api_tests/test_operators_and_elementwise_functions.py::test_floor_divide[__ifloordiv__(x1, x2)]
 array_api_tests/test_operators_and_elementwise_functions.py::test_floor_divide[__ifloordiv__(x, s)]
+array_api_tests/test_operators_and_elementwise_functions.py::test_floor_divide[__ifloordiv__(x1, x2)]
+array_api_tests/test_operators_and_elementwise_functions.py::test_floor_divide[floor_divide(x1, x2)]
+array_api_tests/test_operators_and_elementwise_functions.py::test_remainder[__imod__(x, s)]
+array_api_tests/test_operators_and_elementwise_functions.py::test_remainder[__imod__(x1, x2)]
+array_api_tests/test_operators_and_elementwise_functions.py::test_remainder[__mod__(x, s)]
+array_api_tests/test_operators_and_elementwise_functions.py::test_remainder[__mod__(x1, x2)]
+array_api_tests/test_operators_and_elementwise_functions.py::test_remainder[remainder(x1, x2)]